As discussed in the section on asteroids, the scientific aims of an asteroid mission can be accomplished using a range of sensors. Such sensors fall into a number of categories.

• Imaging Sensors allow the shape and surface structure of a target to be examined. If they operate at a range of wavelengths then the can provide some measure of spectral response and hence an indication of the composition of regions of the target's surface. Imaging sensors need not be confined to visible wavelengths; UV and near-IR wavelengths can offer valuable spectral information whilst thermal-IR measurements can provide clues as to the surface structure of a body. A recent development of this technology is hyperspectral imaging which makes use of sensors combining imaging with spectroscopy to provide a parallel set of images of the same scene in hundreds of narrow wavelengths. Modern imaging sensors based on charge-coupled devices (CCDs) are compact, low-power and extremely sensitive over a range of wavelengths [McLean97]. However they require telescopic optics to achieve high resolution at long ranges. Such optics can be heavy and need to maintain accurate internal alignment. The sheer quantity of data provided by imaging sensors is also a problem as is can easily dwarf the output from all other sensors on a spacecraft put together. This is particularly true for ultra-high bandwidth data sources such as hyperspectral imagers.
• X-Ray Fluorescence Spectroscopy involves looking at the X-rays produced by the impact on the target surface of high-energy X-rays from solar flares. It can provide direct data on surface composition but has very limited range and resolution and is only really suitable for in-situ measurements from a lander or orbiting probe
• Radar can be used for remote sensing in a number of ways. A simple measure of radar reflectivity can give information on the surface composition of a target whilst the use of synthetic aperture radar allows a target to be imaged at high resolution without the need for good lighting conditions. Radar can be monostatic (transmitter and receiver collocated) or bistatic (transmitter and receiver separate). Bistatic radar has the advantage of freeing the transmitter EIRP or the receiver sensitivity from the limits of size and power aboard a probe. It also allows for very shallow grazing angles for polarization measurements, as used in the Clementine experiment to look for ice at the Lunar poles. However, for distant targets the large path loss on the target-Earth leg can offset any advantages.
• Lidar, i.e. laser radar, can provide very accurate range information and can be used to built a surface profile across a target. The lidar experiment on Clementine provided a high-resolution topographic map of the Moon [Wertz96]. Such experiments are, though, more useful for an orbiting probe than can repeated scan its target.
• Fields and Particles experiments can look at the magnetic field around a body, e.g. its own field or the distortions it introduces in the solar magnetic field. Dust detectors can examine the dust environment around a body which can give indications of remnant cometary activity or recent impacts. However, fields experiments require careful probe design (EMC compliance, avoidance of magnetic materials) whilst even a close flyby mission of a NEO is likely to be far enough away that the dust environment will be minimal.

Based on these criteria two types of sensor were selected for further consideration: imaging and radar.

Imaging Sensors. The prime considerations in the design of an imaging sensor are resolution and sensitivity. Taking resolution first, the resolution of an optical system is determined by is aperture d_o and its operating wavelength lambda according to the Airy formula

(9-1)

this being the minimum angular distance between 2 features that can be optically resolved by a system of this aperture.

What resolution is required? To achieve a reasonable-quality surface image equivalent to, say, a VGA computer display requires that the image of the target body be 500 pixels across. This also means that for a typical 1000-pixel wide CCD the IFOV will be twice the target diameter, allowing for some tracking error. From this we can derive the minimum acceptable optical resolution.

It should be noted here that pixel resolution and optical resolution are not necessarily the same [McLean97]. The former is determined by the ratio of sensor image element size to the focal length of the optical assembly, whereas the latter is determined by the optical aperture as described above. If the optical resolution is better than the pixel resolution then several optical resolution elements are covered by each pixel and the overall image resolution is sensor-limited. Conversely if the pixel resolution is better than the optical resolution then several pixels cover each optical resolution element and the system is optics-limited. As we are specifying the resolution in terms of pixels we want a sensor-limited system, implying that there is a minimum aperture below which it would become optics-limited. This critical point is assumed to be where the pixel resolution is twice the optical resolution, as this is where the optical resolution elements are critically Nyquist sampled. We thus require an optical resolution of at least 500/2 or 250 elements across the target. For a typical NEO target of 1 km diameter this equates to an linear optical resolution of 4 m. The equivalent angular optical resolution and aperture required to achieve this are shown at Fig 9.1a and b. For these calculations lambda is taken as 500 nm, i.e. the middle of the optical range.

For the nearest point of a close flyby an aperture of only a few cm would suffice for resolution purposes. As discussed in the Section 8 though, it is better to try to achieve high-resolution imaging shortly before the time of closest flypast to avoid trying to image during the period of maximum slew rate. This drives the aperture towards a larger value.

Another design driver to consider here though is the mass of the optical assembly. Even assuming that elements such as mirror and optical tube walls are of constant thickness then the mass of such an assembly will scale with the square of linear dimensions. There is little easily-obtainable data on the mass scaling factor for such systems, so as a first-order guide the mass of commercially-available Schmidt-Cassegrain* telescopes was obtained from manufacturers' data. Fig 9.2 shows that in fact the quoted mass was surprisingly linear with diameter.

[*An optical design consisting of a paraboloidal or spherical primary mirror combined with a hyperboloidal secondary to increase focal length, often with a shaped correcting plate covering the aperture. Such a design is generally similar to the telescope that would be used for the probe imaging payload.]

Taking this as a rough guide to optics mass, the available aperture is strongly driven by the mass budget. For a small probe that can be launched to V_hyp = 5 km/s via a lightweight launcher, a maximum probe mass of 140 kg was derived (see Section 10). The spacecraft sizing section of Space Mission Analysis and Design [Larson92] quotes payload mass as an average of 30% of spacecraft dry mass. Bearing in mind that even though the optics will be the heaviest part of the imaging payload, some of the payload mass needs to be reserved for the imaging system itself, not to mention any other payloads. To give some mass margin a dry mass of 100 kg is assumed; if we allow the optical assembly to be 2/3 of the total payload mass this gives 20 kg as a maximum optical assembly mass. From Fig 9.2 this indicates that a maximum aperture of 0.2 m is probably achievable. Such an aperture would give an optical resolution of 3 x 10^-6 radians, which equates to 4 m at a range of 1330 km.

How well would such a system work in practice? A typical CCD pixel is 20 m across [McLean97] so for it to cover a region 2 metres across at a range of 1330 km requires an optical assembly with a focal length of

(9-2)

For an aperture of 0.2 metres this gives an f/ratio of f/67. This is rather slow by day-to-day standards but not unreasonable for astrophotography. To check how feasible imaging a NEO with such a system is its sensitivity needs to be calculated.

For a CCD with pixel size d_pix imaging a target at range r via optics of focal length f the pixel resolution R_pix at the target (i.e. the size of a pixel at its distance) will be

(9-3)

If the target has brightness B_o at range r_o then its brightness B at range r will be

(9-4)

For a target of diameter D its area in pixels will thus be

(9-5)

and its brightness per pixel B_pix will thus be

(9-6)

Note that this is independent of range, as expected, but is inversely proportional to the square of f.

To evaluate the performance of a CCD imager we need to know B_pix in terms of photons/second. A typical CCD pixel will saturate with a charge of 2 x 10⁵ electrons; assuming 100% quantum efficiency (real CCDs are fairly close to this) this number of photons is needed to saturate a pixel. To determine B_pix we note from McLean that Mag -14 is equivalent to 3 x 10⁹ photons/second/mm² at the receiving aperture. From the brightness/distance graph calculated in Section 8 a typical NEO would be this bright at a range of 30 km so for an aperture of 0.2 m some 9.4 x 10¹³ photons/second would be collected from the target. This is B_o for our target so from Eqn 9-6 with the parameters quoted B_pix is found to be 7.75 x 10⁴ photons/second. Thus this system will take 2.6 s to saturate a pixel. In practice it is not desirable to saturate pixels at the average target brightness, as thus means that brighter albedo features will not be seen. If we thus allow a factor of 10 brightness variation above this then the exposure time become 0.26 s.

This seems like a long exposure, but it is for a very dark object being imaged through long focal-length optics. Exposure time can be reduced by shortening the focal length at the expense of lower angular pixel resolution. For example, halving f to 6.65 metres reduces exposure time by a factor of 4 to 65 ms. This implies reducing the target range it which it is imaged to our specification to 665 km but has the advantage of increasing the IFOV by a linear factor of 2 and thus reducing the required pointing accuracy.

In summary, the combination of a faint target and the need for long focal length optics to allow it to be imaged far enough away to avoid excessive slew rate drives the optical design towards the largest practical aperture, as light collecting becomes much more important than optical resolution. The above calculations give an extremely approximate estimate design model, but serve to provide a reasonable guide to allowable payload size and mass. They also allow some design decisions to be made regarding the probe as a whole. There is no way that a 100 kg probe can support a scan platform mounting a 20 kg or more optical assembly, so the flyby scan will have to be achieved by a periscope or slewing the entire probe. In addition, 20 kg is a substantial fraction of the spacecraft mass concentrated into one unit, so it will have to be carefully located within the spacecraft to ensure that the probe's centre of mass is not unduly disturbed.

So far we have considered single wavelength images. By inclusion of a filter wheel the CCD could image the target at a number of wavelengths to allow multispectral images to be built up. The system as described is limited to wavelengths around the visual region (near UV to near IR) but in principle beam-splitting optics could be used to focus the image onto other sensors as well, e.g. a thermal IR (5-20 m) CCD. Such devices are available but tend to have larger pixels, smaller array sizes and lower quantum efficiencies than optical-wavelength CCDs [McLean97]. More importantly, they required cooling to near-cryogenic temperatures; for longer wavelength work, the entire optical system must be so cooled (and specially constructed). An IR imaging sensor would thus be an interesting potential addition to the payload but has not been considered further for this study.

Radar. The first design decision regarding radar is whether monostatic or bistatic radar should be considered. Monostatic radar involves the probe in carrying a receiver and transmitter operating on the same frequency. As the probe would normally carry a receiver operating on the telecommand uplink frequency and a transmitter operating on the telemetry downlink frequency a radar system requires an additional transmitter or receiver. However, bistatic radar involves the introduction of path loss from the target to the Earth-based element of the system. For a closest approach of 100 km to an asteroid at 0.05 AU (7.5 x 10⁶ km) from Earth this involves an additional loss of

(9-7)

relative to a monostatic system, which is more than would be offset by the increased power or sensitivity of an Earth-based transmitter or receiver.

To determine the feasibility of a probe-based radar system its signal-to-noise ratio (SNR) can be determined by the method of Space Mission Analysis and Design. This quotes the received power for a radar system of wavelength lambda, transmitted power P_t and antenna gain G as

(9-8)

where r is the target range and its radar cross-section. The latter is very dependent on target shape, composition and surface texture but for 1 km diameter asteroid a value of 10,000 m² is probably reasonable. The antenna gain depends on its size; for the final probe study configuration this was 0.7 m diameter. For an 8.4 GHz radar (lambda = 3.6 cm) then, assuming the probe's main antenna is used for this experiment, this gives a gain of approx 32 dB. Again, assuming the transmitted power is the same as for the downlink transmitted power in the final configuration (5W) then at a range of 100 km P_r is found to be about 8 x 10^-16 W. The noise in the receiver will depend on its bandwidth, which is determined by the desired radar resolution. A bandwidth of 10 MHz gives a resolution of 15 m; for a system temperature of 300 K this gives a noise power of 4 x 10^-14 W, or a SNR of 0.02. This is far too low for any useful results to be obtained and so a radar payload is not practical for this mission.

Probe Design Aspects. As already discussed the imaging payload optical assembly has a mass of 20 kg. The CCD itself, including its associated electronics will be quite light by comparison. Similar cameras used on other low-cost space applications [Foquet96, Wertz96] have a mass of under 1 kg. To allow for mounting and interface equipment such as filter wheels a sensor mass of 2 kg has been allowed, giving a total payload mass of 22 kg.

Payload Summary. Given the science requirements of this mission and the constraints applied by the probe trajectory and size the most promising science payload is a CCD imaging system viewing the target via an 0.2 m aperture f/33 optical system. Repeated exposures via a filter wheel would allow multispectral images to be obtained. Tracking would be via either a periscope system or by slewing the entire spacecraft body. Payload mass has been estimated as 22 kg.