3.1

160-mm test mirrors

Fig.3 shows the setup of the cryogenic optical measurements for the 160-mm-diameter mirrors of the sandwich-type SiC or the C/SiC composite material. The mirror is hung by a stainless steel belt in a liquid-helium chamber to avoid extra stress for the support. The changes in the surface figure are directly measured through the vacuum-sealing entrance window from outside the chamber by a ZYGO GPIxp interferometer. The alignment between the mirror and the measurement system is adjusted by the X/Y and Z stages upon which the interferometer is placed. The measurement system and the chamber are set up on a vibration-free table. Three thermal straps are attached to the backside ribs of the mirror. A thermometer is also attached to the backside rib to monitor the temperature of the mirror itself. The lowest temperature of the mirror reached in every measurement ranges from 6 K to 15 K. The measurements of the surface figure were performed while the mirror was being warmed up, where the stable measurements were possible.

Fig.3.

Setup of cryogenic optical measurements of the small-size SiC or C/SiC composite mirrors.

3.2

ASTRO-F primary mirror

Fig. 1a shows the test chamber facility for optical measurements of large-aperture (<800 mm) mirrors and telescopes at a liquid-helium temperature. The whole facility is placed inside the clean booth; the chamber has a height of 3.4 m, and the scaffolding with a similar height surrounds the chamber that enables us to reach the upper side of the chamber. The measurement system which consists of a ZYGO GPIxp interferometer and a combination of three-axis shift and two sets of two-axis tilt adjustment stages is placed upon the top plate of the chamber. During the optical measurements, the whole system is being sustained by four vibration-free supports, which have a capability of auto-leveling adjustment within accuracy of 0.25 mm. There are four windows to observe the inside of the chamber, one on the top, one on the bottom, and two on the side wall in the X/Y directions. Each window is closed by a cold shutter during the cooling down which is thermally connected to the 80 K shroud. There are X/Y shift and two-axis tilt adjustment stages inside the chamber, which can be driven at a liquid-helium temperature.

Fig.4a displays a schematic view of the cryogenic optical measurements of the primary surface. The primary mirror is mounted onto the top plate of the tilt adjustment stage via the triangular base-plate in the chamber (Fig. 1b). The surface figure of the mirror is measured from outside the chamber by the interferometer through the null lens and the entrance window. The alignment between the optical axes of the mirror and the measurement system is monitored by the alignment telescope; first the alignment telescope is set up on the bottom plate of the chamber and the alignment between the primary mirror and the entrance window is adjusted by the inner adjustment stages, and then, the alignment telescope is put on the top plate of the chamber and the alignment between the entrance window and the null lens is adjusted by the upper adjustment stages. In installing the null lens, the distance between the primary mirror and the null lens is measured by the absolute distance meter and adjusted by the upper Z-axis adjustment stage.

Fig.4.

Schematic views of optical measurements of (a) primary mirror, and (b) telescope assembly.

Six thermal straps and two thermometers attached to the backside ribs of the primary mirror (Fig. 1c). The mechanical connection between the base-plate and the cold adjustment stage was set to be loose in order to avoid extra stress on the mirror. The cryogenic measurements of the primary mirror were performed twice. The lowest temperatures of the mirror reached in the two measurements were about 10 K, which was slightly above the expected operating temperature (5.8 K) of the ASTRO-F telescope. The difference in the temperature between the two thermometers attached to the primary mirror was very small (<200 mK) at low temperatures, indicating good thermal conductivity of the SiC material even at cryogenic temperatures.

3.2

ASTRO-F telescope system

After the testing of the primary mirror, the secondary mirror and the telescope truss were integrated into the flight-model telescope system. The manufacturing process of the secondary mirror is the same as that of the primary mirror except for the size and the curvature. The secondary mirror is supported by titanium alloy flexures in a similar way to the primary mirror. The telescope truss is made of beryllium. Before cooling, 0 dB random vibration tests were conducted for the telescope assembly (Fig5a). By interferometric measurements before and after the vibration test, we confirmed that the wave-front error did not change significantly and thus the telescope retained the alignment even after launch vibration. The telescope was then installed into the chamber (Fig.5b) and tested under the configuration shown in Fig.4b. The telescope assembly is suspended from the top ring of the 4 K innermost thermal shroud, while the reflecting flat mirror is placed on the inner adjustment stages through the Hindle mounting technique (Fig.10a). The reflecting flat mirror is made of fused silica with a diameter of 750 mm, manufactured by SAGEM. Since fused silica has low thermal conductivity, we had to cool the flat mirror using 64 thermal straps, which were attached to the rear surface of the mirror. The flat mirror has two reflecting flat surfaces in the X/Y directions on the lateral side, which are used to monitor the tilt angle of the flat mirror by auto-collimators from outside the chamber.

Fig.5.

ASTRO-F flight-model telescope during (a) vibration test and (b) installation into the chamber.

The mechanical connection between the telescope and the 4 K top ring was set to be loose to avoid extra stress on the telescope due to the thermal contraction of the top ring. The lowest temperatures thus achieved were 13 K for the primary mirror, 14 K for the secondary mirror, and 17 K for the flat mirror. The difference in the temperature between the primary and the secondary mirror was at most 2 K at low temperatures.

The ASTRO-F telescope has a one-axis movement mechanism of the secondary mirror for focus adjustment, so that the distance between the primary and the secondary mirrors is adjustable within a stroke of 0.80 mm and a resolution of 0.47 μm. The focus adjustment was conducted at a cryogenic temperature during the optical measurements of the mirror surfaces, which confirmed that the focus of the telescope was well adjustable with the designed stroke and resolution.

4.1

160-mm SiC mirrors

The surface figures measured for the 160-mm SiC mirrors at a room and a cryogenic temperature are shown in Fig.6. Here and hereafter, the surface figure is shown after subtraction of the ideal surface figure, and is given as half a wave-front error measured by the interferometer. A conspicuous local minimum is observed in the central region for every mirror figure, which is attributed to additional spherical aberrations due to the presence of the vacuum-sealing window along the optical path.

Fig.6.

Changes of surface figures for the second (upper) and the third SiC mirror (lower) with temperature.

As clearly seen in Fig.6, the cryogenic performance has been improved considerably from the second to the third mirror owing to the optimizations of the manufacturing process. Details on the differences in the manufacturing process among the three SiC mirrors and their effects on the measured cryogenic performances are described in [9]. Major differences between the second and the third SiC mirror are as follows: the CVD coating was made only once for the second mirror and the bottoms of the three interface holes on the rear surface (Fig.2b) have been left uncoated with CVD to keep the reference surface of the core blank. For the third SiC mirror, the CVD coating was conducted twice so that coating over all the front and rear surfaces was achieved and the top SiC layer on the mirror surface was removed completely during the grinding process. Since the phase of the peaks seen in the second mirror exactly corresponds to that of the above non-CVD-coated holes, the deformation may originate from bi-metal effects due to a slight difference in the CTE between the porous and CVD SiC. On the other hand, the surface figure of the third SiC mirror changed very little under temperature variations. Hence, the importance of the SiC-CVD coating over the whole surface of the porous core has been confirmed.

As for the second and the third SiC mirrors, the surface figure error for every measurement is plotted against the temperature in units of λ in Fig.11. Here and hereafter, λ is 632.8 nm of He-Ne laser. The figure error relative to the initial surface figure measured before the cooling is also plotted, which is lying on the lower side for each mirror. The third SiC mirror shows the smallest figure error among the three mirrors at 6 K, although the figure error at 300 K is larger than that of the second mirror. The differences from the initial surface figures of the second and the third SiC mirror around 300 K are as small as 0.01 λrms, which supports no significant hysteresis produced by the cooling cycle considering the systematic error due to the subtraction of the two data files. From Figs.6 and 11, it can be concluded that the surface figure of the third mirror at 6 K is the same as that at 300 K within the measurement uncertainties; there may be a possible transient deformation around 180 K for the third mirror. This distortion could reflect a material property peculiar to the combination of the porous SiC and CVD SiC. However, it is still as small as 0.03 λrms and disappears at lower temperatures.

By using the third SiC mirror that showed the best cryogenic performance, the effects of the support structures have been investigated. For their attachment to the rear holes (Fig.2b). three kinds of cryogenic adhesive agents, Stycast 2850FT, EC2216, and EP007, were used separately at three attaching points of the mirror, all of which had been confirmed to have a sufficient adhesive strength at a liquid nitrogen temperature. The super-invar support structures were pre-cooled twice down to a liquid nitrogen temperature before the attachment. As a result of optical testing, Stycast 2850FT yielded the smallest deformation at cryogenic temperatures among the three glues, although it showed non-negligible hysteresis upon return to a room temperature. Hence, Stycast 2850FT was concluded to be the best choice for the ASTRO-F telescope.

4.2

ASTRO-F primary mirror

The surface figures measured for the primary mirror at a room and a cryogenic temperature are shown in Fig.7. Three-phase rotationally-symmetrical local maxima are clearly observed at a room temperature (Fig.7a). The phase of the peaks corresponds to that of the flexures and the support structures (Fig. 1c). Before the installation into the chamber, such maxima had not been observed under the configuration that the primary mirror was placed on the whole rear surface without any support structures. Therefore, we concluded that the resultant three-phase deformation originated from gravitational effects. The surface figure error of the primary mirror without the support structures is 48 nm rms, which is much smaller than that of the mirror with the support structures, 130 nm rms, and thus degradation in the mirror figure due to the gravity is quite serious. A model prediction shows a fair agreement with the observed deformation.

Fig.7.

Changes of surface figure for the primary mirror with temperature. Both are shown in the same scale.

As seen in Fig.7b, the surface figure changed appreciably from 287 K to 10 K. Trefoil deformation was clearly observed at cryogenic temperatures in the same phase as the gravitational deformation. Judging from the result that the surface figure of the 160 mm SiC mirror showed very little cryogenic deformation, the main fraction of the cryogenic deformation is reasonably considered to be due to the thermal contraction of the base-plate; the flexures cannot absorb entire difference in CTE between the SiC primary mirror and the aluminum base-plate. Such deformation has been predicted to some extent by a model calculation, however the model cannot reproduce exact figure such as sudden depressions and sharp ridges. The former may be associated with the attachment of the thermal straps, which further degrade the surface figure of the primary mirror at cryogenic temperatures.

The primary mirror showed serious permanent deformation upon return to a room temperature. Fig.8a displays the surface figure that was measured at a room temperature after the first cooling and shown after subtraction of the mirror figure measured at a similar temperature before the cooling. From Fig. 8a, the permanent change of the mirror surface that occurred by the first cooling cycle consists of two components: dimples at the positions of the support structures and turn-ups around the circumference. The phase of the latter component is the same with that of the depression observed at cryogenic temperatures, which corresponds to that of the thermal straps at the backside ribs. From the positional coincidences, it is reasonable to consider that the three-phase dimples are due to residual deformation of the super-invar support structures, while the turn-up deformation is related to plastic deformation of the structures of the heat anchors made of copper; the copper structures have not been pre-cooled before attachment to the backside ribs, although the super-invar support structures were pre-cooled twice. As described later, the permanent deformation of the support structures is well explained by the anomalous behavior of super-invar metal at low temperatures.

Fig.8.

Difference in surface figure of the primary mirror between before and after (a) the first cooling cycle and (b) the second cooling cycle.

Since the hysteresis was detected unexpectedly, the primary mirror was re-cooled and the mirror figure was measured again before and after the cooling. As seen in Fig. 8b, the mirror surface did not show any further hysteresis significantly after the second cooling cycle. Hence, the hysteresis that was observed just after the first cooling degraded the surface figure of the primary mirror seriously. Since it was confirmed that the telescope system still barely met the requirements (see next section), we decided not to make further work on it.

4.3

ASTRO-F telescope system

The wave-front errors measured for the telescope system at a room and a cryogenic temperature are shown in Fig.9. In this case, the rms values indicated together are evaluated by a quarter of the wave-front errors measured by the interferometer. We have to be aware that, if the flat mirror has an ideal flat surface, the total wave-front error of the telescope itself is equal to half the measured wave-front error, and thus the rms value evaluated by a quarter of the error corresponds to the surface figure error of a combination of the primary and the secondary mirror. The phase of the figure in Fig.9 should be rotated by 30 degrees to match with that of the figures in Figs.7 and 8. The shade area seen in Fig.9 is attributed to the baffle of the secondary mirror and the telescope truss.

Fig.9.

Changes of surface figure (half the total wavefront error) for the telescope assembly with temperature

In comparison between Fig.7a and Fig.9a, the three-phase local enhancements at the support structures observed in the measurement of the primary mirror alone are replaced by the local depressions at the same positions in the measurement of the telescope assembly. This is because the gravity force relative to the primary mirror surface works in reverse. In consequence of the cryogenic measurements, the surface figure exhibited trefoil deformation similarly to the case of the primary mirror alone except for the local minima at the support structures that are again gravitational distortions. The ridges are more clearly seen in the figure due to the presence of the local minima. In addition to the similarity in the surface figure, the surface figure error itself at cryogenic temperatures shows a similar value to that of the primary mirror alone. Hence, we can conclude that a substantial fraction of the cryogenic deformation of the telescope system is due to the deformation of the primary mirror and almost no misalignment between the primary and the secondary mirror was generated by the cooling. It implies that the cryogenic deformation of the secondary mirror is negligible and uniformity in the thermal contraction of the telescope truss is quite well.

The flat mirror can exhibit significant deformation at cryogenic temperatures and thus may affect the above evaluation. Therefore, we attempted the extraction of the surface figure of the flat mirror itself by independently moving the flat mirror in the X/Y directions with the inner adjustment stage. Every time the flat mirror is shifted, the tilt angle of the flat mirror is monitored by the auto-collimator from outside the chamber and the observed tilt was taken into account in the following calculation. We differentiated the surface figure using the two sets of wave-front data measured before and after a 40-mm shift of the flat mirror in the X or Y direction. Two differential figures obtained from the shifts of the flat mirror in the X/Y directions are then averaged. The differential figure thus derived is shown in Fig. 10b by Zernike polynominal approximation. Details of the methodology are described in [10].

Fig.10.

(a) Reflecting flat mirror mounted on the stage inside the chamber. (b) Cryogenic deformation of the flat mirror.

One particular problem to be concerned here is whether or not the shift of the flat mirror can generate misalignment between the telescope and the flat mirror as well as that between the primary and the secondary mirror because the small change in the center of gravity can cause the significant bending of the 4 K thermal shroud and thus that of the telescope truss. Owing to the capability of the auto-leveling adjustment of the vibration-free supports, however, the chamber cannot be tilted at an angle of more than 2 arcmin and therefore we concluded that there was no significant misalignment introduced by the shift of the flat mirror. The surface figure error of the flat mirror at a cryogenic temperature is estimated to be as small as 41 nm. As a result, we can safely neglect the contribution of the distortion of the flat mirror to the total wave-front errors of the telescope. Since the surface figure error of the flat mirror at a room temperature is only 7.6 nm, the change in the surface figure at cryogenic temperatures is yet significant.

3.4

160-mm C/SiC composite mirror

The surface figure was measured for the 160 mm C/SiC composite mirror at a room and a cryogenic temperature. The obtained figure error for every measurement is plotted against temperatures in Fig. 11. The figure error relative to the initial surface figure measured before cooling is also plotted. As seen in Fig. 11, there are no dramatic changes of the surface figure error toward cryogenic temperatures. However, significant permanent deformation was produced by the cooling cycle; the difference from the initial surface figure around 300 K is as large as 0.15 λrms. An origin of the observed large-scale permanent deformation is still under investigation; it does not seem to correlate with the pattern of the three segments. Apart from the large-scale structure, local depressions of λ/20 in depth appeared along the joint lines of the three segments, where the separate C/C composite materials had been bonded together at the stage of the Si infiltration (Fig.2). The C/SiC composite mirror was then re-cooled and the surface figure was measured again; the mirror surface did not show any further hysteresis significantly before and after the cooling. Obviously, the initial surface figure error of the tested sample mirror is rather large, and thus measurement sensitivity for the surface figure is limited by its poor accuracy. Hence, further polish of the mirror to a higher precision would be inevitable as a next step, and therefore polishing technology of bare C/SiC surfaces should be established. Alternatively, polishability of C/SiC surfaces might be enhanced by application of some coating technique.

Fig.11.

Plots of surface figure error for the C/SiC composite mirror against temperature (pluses). Figure error relative to the initial surface figure measured before the cooling is also plotted (crosses). In addition, figure errors for the second and the third 160-mm SiC mirror are shown in a dotted and a solid line, respectively.

Degradation of the surface roughness by the carbon fibers at low temperatures is another major concern for this type of composite mirrors. So far, by using the flat mirror of the C/SiC composite material, microscopic measurements of the surface by using a ZYGO Newview interferometer, as well as speckle measurements by scattering rays of light incident on the mirror, have been performed at a room and a liquid-nitrogen temperature. Preliminary results of the measurements showed no significant degradation of the surface roughness toward a liquid-nitrogen temperature as compared with the initial surface roughness of about 20 nm rms for the tested flat mirror. Details of these cryogenic tests of the C/SiC composite mirror will be reported in a separate paper.