SYSTEM DESIGN NOTE
SDN0007.01 - Thermal Stability Control of GNIRS
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Prepared by
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Date
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Approved by
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Date
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Rev.
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Rev Date
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J Elias
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5/27/99
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N. Gaughan
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6/1/99
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A
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5/12/00
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1. Introduction
The purpose of this design note is to address in more detail the issues of thermal stabilityof the instrument discussed in SDN007 (mainly section 4), and to address design solutions to the issues. Revision A contains some added material on CTE non-uniformity. The discussion on motor heating has been revised to reflect the operation of the motors as defined in SDN015.
The design note considers only the issues arising from operation of the instrument, and does not address thermal control during cool-down or warm-up (to be discussed in SDN007.02).
2. Requirements
Four aspects of the internal temperature distribution of the instrument affect its performance during operation:
2.1 Average Temperature
The average temperature of the instrument must be low enough for emission from the cold instrument to be negligible compared with dark current and sky background. This limiting temperature is calculated taking into account the fact that InSb has measurable sensitivity at wavelengths out to 5.7mm. The table below shows calculated backgrounds per pixel for two cases. In one, DQE is assumed to be 100% out to the extreme of wavelength response at 5.7 mm. The other is for a shorter wavelength which represents a compromise between the falling response of the InSb and the rising background.
For comparison, the expected dark currents will be ~0.1 electron/sec/pixel; internal background should be well under this.
Table 1 – Background per Pixel from Hemisphere
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100% QE to 5.7 mm
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0.013
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0.047
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<0.001
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0.003
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<0.001
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<0.001
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The desired operating temperature is 65K or colder.
2.2 Variations in Average Temperature
There are two constraints on the variation in average temperature.
If the nominal average temperature is close to the
upper limit set by internal background (2.1, above), any increase above
that will produce unacceptable background, or variations in accumulated
background over long exposures.For
example, a background of 0.01 electrons/sec/pixel will produce a negligible
additional contribution to photon noise, even over a 1000 second exposure
– but if this background is present in one exposure and not in another,
it will produce a difference between the two of 10 electrons/pixel, which
is
significant. The <65K operating temperature specified above is low
enough that if the temperature only decreases from that value, variations
in background will not be a problem. A value of 60K is preferable because
it permits fluctuations above and below nominal.
The second constraint is set by the fact that the instrument optics are not fully athermal. In the spectrograph itself, the refractive camera foci are somewhat more temperature sensitive than the aluminum structure supporting them, with the result that focus changes at the detector by roughly 20 microns/degree for the long cameras and roughly 8 microns/degree for the short cameras – in both cases resulting in a blur at the detector of roughly 1.5 microns/degree shift.) Details are provided in the relevant document by Ming Liang.
For the on-instrument wave-front sensor the situation
is more uncertain. A preliminary review of the optics (SDN004) suggests
that the sensitivity may be significantly greater. The temperature sensitivity
of the OIWFS has not been determined by the IfA design team, due to their
decision to maintain a stable bench (“cold plate”) temperature.
2.3 Spatial Gradients in Temperature
There are two concerns regarding spatial gradients in the instrument temperature.
The first is that “hot” spots will produce excess internal background. Because emission is an exponential function of temperature, it does not require a large amount of material significantly above the mean operating temperature to produce measurable background. Thus, in addition to maintaining an appropriate average temperature, it is important to maintain all points of the instrument below 70K (see Table 1). This requirement can be relaxed somewhat for the optics ahead of the filter wheels, since the filters will block the long-wavelength emission.
The second point is that the athermal optics will remain in alignment only to the extent that the instrument temperature is uniform. The main concern is loss of image quality, which mainly affects the powered elements – the Offner relay, the collimator, and the cameras. The tolerance analysis (document by Ming Liang) suggests that the collimator is probably the most sensitive in this regard, since the allowable focus shift is 50 microns and separation between the slit and the collimator is most of the length of the bench – roughly 1.5 m. (Some correction for defocus of the collimator can be done with the detector focus, not considered in the error budget, but there will be residual astigmatism.)
Such a focus shift is produced by a differential contraction between the bench and collimator mirror of roughly 33 ppm, which would be produced by a temperature difference of about 6K between bench and mirror (equivalent to about a 12K gradient from the slit to the collimator). This calculation assumes that the collimator focus is perfect warm, so that the entire error associated with defocus can be absorbed by the temperature-gradient defocus. More realistically, therefore, temperature gradients must be less in order to avoid focus adjustment.
It should be noted, though, that some difference in
the thermal contraction of the collimator mirror and of the bench is likely,
even though both are made of the same alloy. A 2% difference in the contraction
of the two results in a focal shift of roughly 80 ppm, or 120 mm,
on cooling. This difference will be stable, and therefore be measured and
adjusted for. Any effects due to a stable temperature gradient will
be buried in the differential contraction due to CTE differences. However,
any large temperature gradient is not likely to be stable to the precision
needed (see below).
2.4 Variations in Temperature Gradients
Variations in temperature gradients over relatively short periods (hour) will almost certainly not have significant effects on image quality. They can, however, introduce small tilts in the system that will have an effect equivalent to flexure. Allowable cumulative changes in tilt in reflective elements over 1 hour are <1 mrad (total motions <0.1 pixel/hour). If the tilt at any one element due to temperature gradient changes is set to be 0.1 mrad or less, and the typical dimensions of the support structure are taken as ~100 mm, the maximum allowed tilt is produced by a change across the 100 mm width of the element of0.01 microns (100Å!). For a depth to the support structure of similar size, this corresponds to a differential contraction of only 0.1 ppm, which for aluminum at ~60K is produced by a change in temperature gradient of ~0.02K. Thus the maximum allowable change in temperature gradients is roughly 0.2K/m/hour. Note that this figure is approximate.
This requirement is as tight as it is for two reasons – the large f/ratios produce large amplifications of small mechanism tilts, and the demanding flexure requirements mean even small motions are not acceptable. To illustrate, if only the short cameras were considered and the allowable flexure was increased to 0.2 pixel/hr, the allowable change in gradient would be ~1.2K/m/hour.
Since the heat inputs which produce gradients tend be highly variable, and the time constant of the bench structure is at most a few hours, the need to limit variations indicates that the gradients themselves should be modest – less than 1K along the bench is a good target figure.
3. Evaluation of Effects
This section evaluates the effects in order to determine which require more work or more attention to design.
3.1 Heat Inputs
For an ambient temperature of 280K, Earl Pearson’s original model showed a total heat input of roughly 120W, divided roughly equally between radiation and other sources. The radiation comprised radiation through the window (about 10 W) and radiation from the innermost floating shield (about 60 W) for 70 W total.
These figures were unlikely to differ much in a new design unless the floating shields are redesigned (see section 4). The other sources were conduction through structural supports and wiring; heat input from internal motors was not included as these were not then present in the instrument. For purposes of the present discussion, conduction input is taken as 30 W and average motor heat input (from all internal motors, including OIWFS) is taken as 20 W (see 4.1 for more detailed discussion).
As ambient temperature increases, the radiation input will go as T4, the conductive inputs will go (approximately) as T, and the motor inputs will not change; total inputs are therefore as indicated in the following table (remembering always the approximate nature of the initial values). Values are provided for 300K and 260K, which represent laboratory operating temperature and near-extreme summit temperature respectively. From the table, one can see that there is almost a factor of 1.5 range in total heat input into the instrument. It is also clear that the variation is dominated by radiation. It should be noted, though, that a variation of a factor of 2 in motor duty cycle – e.g., the frequency of short observations – would produce a variation in heat input of similar magnitude.
Table 2 – Heat Inputs vs Ambient Temperature
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3.2 Cooling Power
The baseline instrument design calls for the use of 2 single stage “150” coolers and 2 dual stage “130” coolers. The former have somewhat greater cooling power at their first stages, so simply allocating the heat load equally is not optimal. Examination of the cooling curves indicates that the steady state temperature of the cooler first stages will be somewhere in the range 30-35K for heat loads like those in Table 2.
Use of the newer RGD5/100 heads provides similar performance.
An important point is that the first stage temperature is a function of cooling power; a 50% increase in heat removed produces (for the temperatures in question) roughly a 5K increase in the first stage temperature. For both coolers the power vs. temperature curve is very roughly linear, with a slope of about 4W/K (for each cooler). Over the range of heat input between the extremes in Table 2, the first stage temperature should therefore vary by about 3K.
Note that elimination of the two “150” heads would give marginal performance. The cooling curves show that first stage temperatures would be somewhat above 45K for 280K ambient, which suggests that it would be difficult to maintain the cold structure at a 65K average temperature. Also, with only two heads the excursion in first stage temperature over the range in heat input would be roughly double that with four heads.
For the RGD5/100 heads the performance is somewhat worse, because the heads have slightly less capacity and are not as “stiff”.
3.3 Temperature Stability
The structural temperature in this configuration cannot be precisely assessed without modeling more extensive than that in this memo. However, both experience with other instruments and models of the preceding version indicate that the temperature will be 10-20K warmer than the average of the cryocooler first stages. The temperature gradient between the structure and the cryocoolers must increase or decrease as the heat load decreases, so that the variation in structural temperature would be amplified by several degrees over the cryocooler first stage variation. For a difference between mean bench temperature and cryocooler temperature of 15K, a change of ±20% in heat input would change the differential by ±3K, for a total bench excursion of about 9K when added to the cryocooler variation.
3.4 Temperature Gradients
Again, details of temperature gradients cannot be provided without models, but crude estimates can be made based on simple assumptions. Assume that the dominant heat flow is along a plate 50 cm x 5 cm and about 2 m long, with cooling provided at the center and 50W of heat at each end. 6061 aluminum has a conductivity (from Earl’s report) of about 80 W?m?1?K?1. The plate has a gradient of 0.5 K/W, implying a temperature gradient of roughly 25K from ends to center.
This gradient is roughly double that allowed for the collimator (see section 2.3) which suggests that either a substantial increase in cross-section or a substantial reduction in heat load is needed – and more realistic modeling in any case. (In fact, the support for the collimator from the bench is likely to be less massive, aggravating the situation.)
3.5 Variations in Temperature Gradients
Variations in temperature gradients are difficult to assess crudely. However, it is clear from the preceding section that gradients along meter distances will be several degrees, and plausibly as large as 10K/m. Furthermore, heat input variations of ±20% are entirely possible, leading to variations in gradients of similar size. Thus changes in gradient of ~2K/m (under the assumptions used up until now) are entirely possible. At the instrument’s operating temperature, 6061 Al has a specific heat of ~180 J?Kg?1?K?1, so the plate above, which has a total mass of 135 Kg (assumed density 2.7) has a heat capacity of roughly 24,000 J/K.
A rough time constant is given by
,
which for C=180 J?Kg?1?K?1, r=2,700 kg/m3, L=1 m, and k=80 W?m?1?K?1 gives t=615 sec (assumes cooling at mid-point of plate). This time constant is shorter than or comparable to that for changes in ambient conditions, so one can model the effects of variations in ambient conditions as different steady-state situations.
Some caution is needed in using this result, since much of the cold mass is in the form of mechanisms, which will lag the bench in responding to thermal variations. Hence the effective time constant of the instrument will be somewhat longer; lenses and prisms may show significantly longer time constants.
The effects of varying motor power are of similar magnitude. However, because motors are localized (or can be), one needs to look at effects on smaller scales; for L=10 cm the time constant is <1 minute. Also, it is clear that motor operating conditions will change more abruptly than external temperatures. One could imagine running motors frequently during the afternoon to perform calibrations and tests (see SDN005), and then going to a much lower duty cycle during the night while observations are being done, or a series of standard star observations with frequent motor motions followed by long observations of a faint object. The instrument would take many minutes to adjust to this if the motor power is absorbed by the optical bench. The localized effects of running a single motor will damp out more quickly, but the time scale is still significant. If the motor heat is dissipated in the optical bench close to the mechanism being driven, it will not damp out for seconds or minutes. This is slightly less critical than it might appear, since movement of larger mechanisms will generally be followed by a period of object acquisition during which the damping can occur.
4. Solutions
From the discussions above, it is clear that the most demanding requirements are those involving changes in temperature gradients – both the limits on overall temperature variation and on temperature gradients are nearly met by the “cartoon” design. The discussion below therefore focuses on reducing gradient variations, though it should be noted that these measures will also reduce the other effects as well.
4.1 Reduction of Heat Input Variations
There are two dominant sources of heat input variations: variations in ambient temperature and variations in motor duty cycle. If it were possible to decouple the bench structure from the radiation shields, and cold-station the supporting structure and wiring so that the bulk of the heat load from outside was coupled to the cryocoolers directly rather than through the bench, the external heat load on the bench would be roughly 10W radiation from the window. The gradient on the front of the bench defined in 3.4 would then be 5K, and would be zero on the rear half. The cryocooler temperature would still vary by 3K, and since the heat load on the bench would now be almost purely radiative, it would vary by ±30%, for a total range in gradient of another 3K. Hence the bulk of the bench would vary by 3K but the extreme front would vary by as much as 6K. The variation in the gradient at the front of the instrument would be ±1.5 K/m.
The radiation input through the window cannot be eliminated, but further reductions are possible if the fore-baffle is not coupled to the instrument bench; this can reduce heat input further (possibly below 2 W). The coupling of the cryocoolers to the bench should occur (in part) forward of the center, thus shortening the conduction path. Measures such as these would reduce the forward gradient further, down to perhaps a degree. Variations in the gradient would then be ±0.3K/m. This is close to the maximum acceptable value discussed in 2.4. However, the only part of the bench affected is the portion ahead of the slit, including the OIWFS field lens. The dominant effect here will be a modest change in length of the bench, which will have no effect on the instrument focus.
The heat input from motors will also be variable. In the spectrometer itself, there are a total of 9 cold motors. We can assume (see Baseline Scenarios, SDN005 and GNIRS Motor and Mechanism Data, SDN002.13) that the filters, decker, slit and acquisition mirror are run four times an hour, and that half of the remainder are run once an hour (or, equivalently, each of the remainder is run every two hours). The acquisition mirror motion is always the maximum; the remainder is assumed to be ½ the maximum, though it is assumed both filter wheels are moved. If the IFUs are not involved, the total motor time for an acquisition exchange is then:
Slit9 sec
Filters0.5 sec each
Decker0.8 sec
Acquisition Mirror 0.9 sec
The additional motor time for a general reconfiguration is:
Prism17 sec
Grating15 sec
Camera17 sec
Focus 0.1 sec
Total motor usage (motor-seconds) according to the above scenario is thus 63 seconds/hour.
Motion to an IFU adds on average another 88 sec of motor usage. If it is necessary to go from the IFU to a wide slit position for acquisition, total motor usage increases by roughly a factor of six. If acquisition can be done with the IFU in place, motor usage increases by less than a factor of two.
The average power dissipation assumed above was 20 W. Total power use by the spectrograph motors can be estimated a little better. The series 52 Phytron motors dissipate about 10 W each in the mode we will operate them (see SDN015). The considerations above indicate an average power dissipation of 10*(63/3600) W = 175 mW – but peak power during a reconfiguration could be as much as 90 W, though only briefly. The heat input from the OIWFS is not presently known, but it is undoubtedly dominated by the gimbal mirror, which is frequently moved. Peak power dissipation from the OIWFS would be about half that from the spectrograph.
The duration of motor motions is less than the overall bench time constant, so heat spikes are smoothed out. Nonetheless, it is clear that one needs to exercise caution in mounting motors on mechanisms. The effects can be minimized if the motors are thermally isolated from the spectrograph structure and they are connected to the cryo-coolers more or less directly. This is particularly true for the four mechanisms for which motions will normally take longer than one or two seconds: the slit slide and the three turrets.
Even if the motors are totally isolated, some heat is deposited through frictional heating. A typical mechanism drive torque is likely to be in the range 1-2 oz-in, and motors will be operated as fast as 600 rpm. The frictional heating would then be as much as 0.9 W. This indicates that there is little point in trying for motor isolation much better than about 90%, since at that level the heat from the motor itself will roughly equal the frictional heating. It is therefore reasonable to assume a heat flow into the structure of about 2 W per motor (peak) and an average heat flow of 35 mW.
4.2 Active Thermal Control
Active thermal control will help with some of the above problems. In particular, unless extremely effective MLI is installed, the cryocooler first stages will move up and down in temperature with external conditions, dragging the optical bench up and down with them.
The available evidence suggests that the expected 3K change will require refocus of both the science and OIWFS detectors. Control of the optical bench temperature would eliminate this need. It should be noted that the decoupling of the radiation shield from the structure suggested above (4.1) would tend to reduce the temperature differential between the bench and the cryocooler first stages, because the heat to be removed by from the bench is now 10W or less. The bench temperature would then drop well below its nominal operating temperature of 60K, which may stress mechanisms.
The most robust scheme would be to operate the bench at ~60K, with the amount of heat injected sufficient to keep it at this value. The bench needs to be well-coupled to the cryocoolers in order to have an efficient initial cool-down; this suggests that heater power of the order of 50 W is needed, presumably with some head-room.
This assumes that the cryocoolers are all inter-connected; if the radiation shield is connected to one pair of heads and the bench is connected to the other, then the bench temperature will be affected primarily by motor operation. The pair of heads on the bench will have a combined sensitivity of about 8W/K, so under normal circumstances bench temperature will vary less than 0.5K. However, a prolonged period of near-continuous operation of the motors could elevate the bench temperature by >5K. This could occur as a result of daytime testing or calibration, and could leave the instrument in a state from which it would take an hour or more to fully recover.
This suggests that thermal control of the bench is preferable to attempts to completely isolate it. The bench heater should generate enough power to permit all but the most pathological scenarios for motor operation. (Note that excessive operation of the motors might elevate temperatures or cause some flexure, but will not damage the instruement.)
4.2.1 Thermal Control Details
The simplest means of thermal control is one in which there is a single control circuit, which uses feedback from a diode or average of more than one diode. In this case, the control loop should be tied to a point near the mid-section of the optical bench (center of mass).
In this configuration, the separation between the individual heat sources (mechanisms) and the control point is tens of cm, and hence time constants are several minutes or longer. Varying heat inputs of a few W over these distances will set up (steady state)
gradients of roughly a degree; for short periods of operation the effects will be smaller. Thermal isolation and realistic duty cycles will kee gradients acceptably small.
Control is very difficult if large amounts of heat
from the motors are conducted into the optical support structure. The
motor mountings should be designed so as to minimize the demands on the
thermal control system. This also minimizes the amount of heat needed for
bench control. In order to keep gradients on the scale of mechanisms below
0.1K, the critical spectrograph motors must have >90% of their heat redirected.
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