3.1.

Mechanical Samples

A number of bar samples $7\times 2\times 1{\mathrm{cm}}^3$ were made. Dynamic elastic properties were measured at room temperature by BuzzMac International LLC of Glendale, Wisconsin, using a proprietary nondestructive impulse excitation test system. Results as provided by the company are given in Tables 1Table 2–3.

Table 1

Bar sample bulk properties.

Table 2

Bar sample resonant frequency measurements.

Table 3

Bar sample elastic moduli measurements.

The sample length was measured with a micrometer of 9.01-mm precision and the width and height to 0.001-mm precision. The mass was measured to 0.01-g precision. The frequencies were measured to 6 Hz or better precision. A total measurement error of $\sim 0.3\%$ is estimated for the Young’s modulus derived from the flexural frequency. The tolerances conform to ASTM E1876-09 specifications.

3.2.

Optical Samples

We made CNT/E optical mirrors in many sizes, shapes, compositions, constructions, and optical functions. Most samples are optical flats, but a number of curved mirrors have also been made in the shape of spheres, parabolas, and hyperbolas. In Fig. 2, there are three samples showing the reflections from a lighted rectangular hole pattern. Here, we present data and discussions on the 5-cm diameter mirror shown in Fig. 1(a) that has the best optical figure obtained to date.

Fig. 2

CNT epoxy nanocomposite mirrors. (a) 5-cm diameter, 1-cm-thick optical flat of homogeneous composition. (b) 20-cm diameter heterogeneous composition mirror with a 3-mm thick facesheet bonded to a 5-cm thick rigid carbon foam backing. (c) Thin (2-mm) facesheet adaptive mirror 25 cm in diameter.

3.2.1.

Optical characterization

The 5-cm homogeneous CNT/E mirror was measured with a Zygo interferometer. The result is shown in Fig. 3.

Fig. 3

Zygo interferometer measurement of the 5-cm diameter CNT/E mirror.

3.2.3.

Simple active optics experiment

A simple experiment was performed to study active figure control. Figure 4(a) is the interferogram obtained by overlaying a 5-cm reference glass flat on top of a 5-cm replica (contact interferometry).⁹ A densely packed pattern of curved fringes is seen. The amount of curvature, measured by laying a straight edge across the pattern, is seen to be about three waves at the wavelength of sodium light (589.3 nm). By applying light pressure (estimated force $\sim 3$ to 4 N) with a fingertip [shadow at the lower left corner of Fig. 4(b)] the fringes become wider, less numerous, and less curved. By pressing down with the thumb [Fig. 4(c)] with an estimated force of 40 N, the fringes become wide, straight, and parallel. In effect, the application of a light to moderate force in this case sufficed to deform the replica in such a way as to reduce tip/tilt and the spherical aberration (SA) terms. The dark spots seen in the interferograms are caused by micron-sized impurities in the CNT samples.

Fig. 4

The 5-cm diameter replica flat mirror viewed under light from a sodium lamp (589.3 nm) against a reference flat. Dark shadows at lower left corner in frames (b) and (c) are from a thumb pressing down on the reference flat.

3.2.4.

Numerical modeling and comparison with experiment

The active optics experiment reported in Sec. 3.2.3 was simple to perform but, according to at the NASA Goddard Space Flight Center, difficult to model without accurate measurements of the optical surfaces and mechanical parts including imperfections. We, therefore, performed a proof-of-principle experiment as follows:

Another 5-cm CNT/E mirror, in contact with a 4.57-cm diameter optical flat, was observed using Newton interferometry under a low pressure sodium vapor lamp. A metal fixture was machined to have a central opening for the reference flat and a step that contacted the CNT/E sample at its rim in a 2-mm-wide band. Figure 5 is a schematic of the test setup. Figure 6 shows the interference fringe patterns observed with and without the applied ring weight.

Fig. 5

Schematic of the test apparatus. (a, b) A fixture (red) holds a ring weight (blue) so that the force is applied to the outer rim of the CNT/E mirror (black).

Fig. 6

Interferograms of a 5-cm CNT/E mirror. (a) No weight applied. (b) With a 1.468-kg ring weight.

The OpenFringe interference fringe reduction program (version 10.4.1) written by Dale Eason¹⁰ was used to compute optical surface maps of the CNT/E mirror with and without the applied loading. The program employed a fast Fourier transform algorithm to generate a map for each surface represented by Zernike polynominals. Subtraction of the two Zernike polynomials (1.468-kg weight—no load) yielded a surface whose cross-sectional profile is shown in Fig. 7. The difference in height of the two surfaces is seen to be $\sim 200\mathrm{nm}$.

Fig. 7

Cross section of surface formed by subtraction the Zernike polynomials representing the surface of Fig. 6(a) from the corresponding Zernike terms representing the surface of Fig. 6(b).

Next a NASTRAN model was computed using the following parameters: a right cylinder of diameter 5.0 cm, thickness 2.5 cm, Young’s modulus 4.2 GPa, and Poisson’s ratio 0.353. The top surface is flat. The bottom faces of the cylinder are fixed. A force of 1.5 kg (14.7 N) is applied at the top surface over an annulus 2-mm wide at the rim. The resulting surface is shown in Fig. 8(a). Figure 8(b) is a cross section taken through the center of the cylinder.

Fig. 8

NASTRAN model computed to show the change in shape of a 5-cm diameter, 2.5-cm-thick CNT/E right cylinder with load applied around its top rim. (a) Solid model and (b) cross section of cylinder through the center. Computations by Babak Farrokh, NASA Goddard Space Flight Center Structural Mechanics Branch.

It can be seen from Fig. 8 that the top face of the cylinder, when loaded with a 1.5-kg force at the rim, is changed from a flat surface to a protrusion of height $\sim {10}^{-4}\mathrm{mm}=100\mathrm{nm}$. This is within the same order of magnitude as the measured displacement (Fig. 7). The difference between the observed and the predicted values can most likely be attributed to noise in the numerical fringe reduction process as well as the fact that the CNT/E optic is not a geometrically perfect cylinder.

4.1.

Mechanical Properties

The measurements show that CNT/epoxy is a low density material at $1.2\mathrm{g}{\mathrm{cm}}^{-3}$. The uniformity in the values of the Poisson ratio and Young’s modulus in the three orthogonal directions confirms that the material is homogeneous and isotropic. As a further check, the fundamental resonance frequency $F$ of a uniform solid rectangular rod in the longitudinal direction is¹¹

This is in reasonable agreement with the measured value of 13355 Hz (Table 2). The assumption of a uniform solid is, therefore, justified.

The mechanical properties of CNT/E bear comment. They are quite different from traditional optical materials. Compared to aluminum, for example, the Poisson ratio is about the same, but the Young’s modulus is lower by an order of magnitude (4.2 GPa versus 70 GPa).¹² This suggests two possible paths for the development of large telescope mirrors:

These topics will be discussed in Sec. 4.4.

4.2.

Optical Figure Accuracy

The interferometric measurement (Fig. 3) shows that the replica deviates from a perfect flat by a peak to valley value of $4.4\lambda$ and by rms value of $0.9\lambda$ (at 632.8 nm). The corresponding values for the glass mandrel are $0.15\lambda$ and $0.01\lambda$, respectively. We note that the largest contribution to the wavefront error is an SA of amplitude $\sim 3\lambda$. Subtracting this term, the residual rms error is reduced to $0.1\lambda$. The presence of the SA term indicates that, despite the care taken in fabrication, there is still much room for improvement. Epoxies shrink as the process of polymerization takes place.¹³ Heating, which is required to bring to completion the many chemical reactions inherent in a thermosetting polymer, causes additional cure shrinkage as does the subsequent cool down. The presence of fillers, in this case CNT and other additives, serves to counteract this shrinkage. Therefore, the SA term suggests that there is some amount of residual shrinkage in the replica with respect to the mandrel. The predominance of the SA term is an indication that the shrinkage is largely isotropic; hence confirming again that the material has good uniformity. Overall, the results thus far are encouraging. Work is currently under way to refine the replication procedure toward the goal of fabricating higher quality optics.

4.3.

Surface Smoothness

The surface rms microroughness is a measure of the surface texture at high spatial frequencies (nanometers to millimeters). This parameter quantifies the ability of an optical system to resolve point sources that are closely spaced.¹⁴ From Table 4, the average value measured at six points on the CNT/E mirror is about 36 Å. The averaged value of six points measured at random on the glass mandrel is 6.0 Å. The difference suggests either that, again, the fabrication process needs improvement, or else the presence of CNTs contributes to the increase in surface roughness. Work is currently under way to produce highly smooth ($<10\text{-}Å\mathrm{rms}$) surfaces. We note, however, that the 36-Å value is in the mid-range for polished glass surfaces.¹⁴ Thus CNT/E in its present state appears to be sufficiently smooth for most telescopic applications.

4.4.

CNT/E as an Optical Material

It remains to be demonstrated that meter-class telescope mirrors can be achieved using this new material. However, on the basis of what is known so far, two statements can reasonably be made:

4.5.

Implementing Active Optics

The simple experiment described in Fig. 3 above illustrates the ease with which the optical surface can be adjusted. It suggests that active figure control in CNT/E mirrors would not require high force, high power, and relatively massive actuators typical of other mirror technologies. In fact, with the appropriate construction, external components may not be required at all.

An active optics system requires the ability to sense and to actuate. For CNT/E, the sensing function can be built-in. Temperature and strain can be monitored by measuring the resistance at various points in the substrate without the use of external sensors.⁴ Actuation can be effected by heat, taking advantage of the ability of CNT/E to function as a heating element.²¹ Alternatively, specifically designed actuation layers can be added into the substrate. Such a layer can contain, for example, embedded shape memory alloy wires,^22,23 CNTs aligned by mechanical, electrical, or magnetic means,²⁴ CNT yarns,²⁵ or piezoelectric powders.^26,27

In summary, CNT/E as it exists is a low density material capable of giving a $1\lambda$ rms optical figure and 40-Å rms surface microroughness. The uniformity of the measured resonance frequencies in the three orthogonal directions, and the good agreement between observed and computed values, show that the material is homogeneous and isotropic. The relatively low modulus of elasticity (compared to traditional optical materials) suggests that active figure control in CNT/E can be accomplished with low force requirements. This is confirmed by a simple experiment using manual actuation. There appear to be numerous ways to implement self-sensing functions and embedded actuators into the mirror substrate. These remain to be explored.