A Thousand Earths: A Very Large Aperture, Ultralight Space Telescope Array for Atmospheric Biosignature Surveys

Diffractive optical elements perform lens-like functions, which can be analyzed with the principle of interference. For example, light transmitted through an aperture with radius a that is illuminated by point source P_src is conceptually illustrated in Figure 2(a). The aperture can be divided into equal-area Fresnel zones that identify which parts of the transmitted light interfere constructively at the observation point P₀ and which parts interfere destructively, as shown in Figure 2(b), based on the optical path difference (OPD) through point Q of (r_src + r₀) − (z_src + z₀). Boundaries of the Fresnel zones are defined by an increase of λ/2 in OPD between successive zones. In this example, the first and second Fresnel zones produce a net zero light amplitude at the observation point, because light from an even-numbered zone combines destructively with light from an odd-numbered zone owing to the λ/2 OPD between them. Likewise, light from the third and fourth zones combines destructively, leaving only light from the fifth zone to produce nonzero light amplitude at the observation point.

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The well-known Fresnel zone plate (FZP) operates by blocking only the even or odd zones in the aperture, thus producing only constructive wave combination at the observation point. By extending this argument to off-axis illumination, it is understood that the FZP acts as a lens with a focus spot size that is equivalent to a classical lens of the same diameter and focal length. However, due to the fact that other focal positions can be identified along the axis, the classical FZP results in high-intensity background levels at the primary focus. In addition, since the constructive or destructive nature of the wave combination depends on wavelength, the focal point changes chromatically with a focal length proportional to 1/λ. That is, as wavelength increases, FZP focal length decreases, which is opposite the sense of a classical refractive lens (Milster 2018). The combination of a properly designed FZP on a refractive singlet leads to compensating focal dispersions, which results in an achromatic singlet (Stone & George 1988).

In order to increase the diffraction efficiency of light into the desired primary focal order, the FZP is replaced by a diffractive Fresnel lens (DFL), in which the opaque-zone FZP is replaced by a transmissive phase pattern that changes OPD as a function of radius. Neighboring zones are combined into a single quadratic phase surface, as shown in Figure 3. The profile in each zone pair has a maximum of one wavelength of OPD across it. Although the DFL has the same chromatic dispersion properties of a FZP, diffraction efficiency into the desired focal order is much greater. In fact, under ideal conditions, all of the light is focused into the primary order. Since the step height to achieve one wavelength of OPD at the transitions is very small (about 1 μm for visible light), the DFL is an extremely thin, planar optical element.

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In order to decrease chromatic focal dispersion, a multiple-order diffractive (MOD) lens was developed (Faklis & Morris 1995). Instead of setting phase transitions based on a single wave of OPD, phase transitions are defined based on integer multiples of M waves of OPD, where M is the MOD number. As shown in Figure 3 for M = 4, the MOD lens profile is thicker than the DFL by a factor of M and zone spacings are increased. However, even if M = 1000, the transition step is only about 1 mm high for a visible light design. The MOD lens operates over a set of higher diffracted orders where each order contains a wavelength of peak diffraction efficiency and each of these wavelengths comes to a common focus. The lens exhibits strong chromatic dispersion at intermediate wavelengths, but, interestingly, the maximum focal dispersion of the MOD lens is decreased to a range of approximately f/M compared to the large range of a DFL. For example, an f = 5 m focal length M = 1000 MOD would have a focal range of only ±0.005 m over a wavelength range from 500 to 1000 nm, where a DFL would have a focal range of approximately ±3.0 m over the same range of wavelengths.

Design of a MODE lens for a particular application begins with the same desired first-order properties as a traditional refractive lens, such as the operating wavelengths and focal length. When designing for broadband performance, the design wavelength is the central wavelength of the wavelength range. Transition depths are defined based on the formula $M\tfrac{\lambda }{{n}_{2}-{n}_{1}}$, where n₂ and n₁ are the index of refraction of the lens material and the incident index, respectively. Transition locations are based on integer multiples of M waves of OPD for on-axis rays. The individual zones are modeled and optimized in standard lens design software.

The change of refractive index with wavelength in each radial zone of the MOD surface also produces a chromatic focal shift, although it is much smaller in magnitude than for a DFL. This problem is compensated for by fabricating a weak DFL on the rear surface of the MOD lens to create an achromatic singlet for each MOD radial zone. This combination is what we call a MODE lens (Milster et al. 2018a, 2018b). The DFL is incorporated into the design by using a Sweatt model surface (Sweatt 1977) in lens design software, in which a fictitious glass with index approximately equal to the wavelength in nm is used to allow for significant optical power to exist in a very thin region. The Sweatt surface must later be converted to a physical surface by wrapping the OPD it produces. The MOD surface cannot be modeled as a Sweatt surface, as it no longer has a negligible physical thickness.

Following optimization in lens design software, the MODE design is verified using a physical optics simulation to confirm the diffractive performance. Optical path length is determined at the exit pupil reference sphere using ray tracing. A Hankel transform calculation is used to determine field values at a sampled image plane. The magnitude squared of these field values provides the irradiance, which represents the point-spread function of the lens. This simulation is performed over a finely sampled spectrum of the full bandwidth, as well as for a range of image planes to account for both refractive and diffractive chromatic dispersion.

In this section we briefly explore the mass reduction achieved by MODE lenses compared to conventional lenses. The discussion presented here aims to provide a first, general approximation, from which individually designed MODE lenses may differ slightly.

We describe the mass of a conventional (refractive) lens as a planoconvex lens (sphere cap) as

$$\begin{eqnarray}&&{M}_{\mathrm{lens}}=\rho \displaystyle \frac{1}{6}\pi h(3{R}^{2}+{h}^{2}),\end{eqnarray} \tag{ 1 }$$

where ρ is the density of the glass, h is the height of the lens, and R is the radius of the lens. In contrast, the mass of a MODE lens (of order M) designed for a center wavelength λ_c is simply

$$\begin{eqnarray}&&{M}_{\mathrm{mode}}=\phi \rho ({R}^{2}\pi )(M{\lambda }_{c}),\end{eqnarray} \tag{ 2 }$$

where ϕ is the volume-filling factor of the MODE lens, close to 0.5.

The mass ratio of a refractive lens to a MODE lens is then

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\mathrm{lens}}}{{M}_{\mathrm{mode}}}=\displaystyle \frac{h(3{R}^{2}+{h}^{2})}{6\phi {R}^{2}M{\lambda }_{c}}.\end{eqnarray} \tag{ 3 }$$

For cases of relatively thin lenses (h < R) this ratio can be approximated to the first order by

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\mathrm{lens}}}{{M}_{\mathrm{mode}}}\approx \displaystyle \frac{h}{M{\lambda }_{c}}.\end{eqnarray} \tag{ 4 }$$

For example, for a lens with a radius of 5 m and a relative thickness of h/R = 0.1, an M = 1000 MODE lens optimized for λ_c = 600 nm would provide about two orders of magnitude of mass reduction. The mass reduction by replacing a thick lens with a MODE lens would be even greater. In short, MODE lenses represent at least two orders of magnitude lower mass for a given lens diameter, a transformative advantage for space telescopes.

Diffractive optical elements (DOEs) are used for both space and commercial applications as small-scale internal optics. For example, the Lunar Orbiter Laser Altimeter mission uses a glass DOE as a beam splitter to divide a laser beam (Ramos-Izquierdo et al. 2009). The high-quality Canon EF telephoto zoom lenses incorporate two diffractive optical surfaces that are first diamond-turned in a mold and then replicated onto a curved glass substrate with epoxy resins (Nakai 2003). Similarly, Nikon's new Phase Fresnel (PF) high-end telephoto lens series utilizes a Fresnel lens in combination with a refractive group to allow large-aperture, high-quality, but very light photolenses.

The pioneering Eyeglass project is a very large aperture (D = 25–100 m) diffractive space telescope concept developed by Lawrence Livermore National Laboratories (Hyde 1999; Hyde et al. 2002). Eyeglass uses a transmissive, DFL as its primary DOE light-collecting element. Corrective optics in a Schupmann configuration are used to provide broadband (470–700 nm) diffraction-limited imaging at visible wavelengths (Bernet & Ritsch-Marte 2017). A 5 m diameter segmented (72 panels) prototype was built and successfully tested (see Figure 4), and extrapolations suggest 2–3 orders of magnitude lower weight per aperture area than that for HST's primary mirror (180 kg m⁻²—in itself relatively low weight due to its "egg crate" structure). For Eyeglass options for the primary DOE material are thin sheets of glass or silica and films of polymers such as CPI or other fluorinated polyimides.

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In a newer concept, the DARPA-funded Ball Aerospace project MOIRE (Membrane Optical Imager Real-Time Exploitation) aims to develop a 20 m aperture telescope using circular diffractive optics. MOIRE plans to deploy with a dedicated launch and capture live video and images of terrestrial targets in narrow spectral bandwidths (∼30 nm; see Hansen 2013). The MOIRE project has been under development since 2010, and results from a 5 m scale brassboard instrument have recently been reported (Atcheson et al. 2014). The published plan is to make a glass master and then replicate membranes directly from it. The process used to make the MOIRE master is a multilevel lithographic approach.

Although Eyeglass and MOIRE demonstrate the interest and potential for very large aperture and relatively low cost space telescopes based on diffractive optics, neither of the designs is optimal for astrophysical applications, where broad wavelength coverage, faster optics (short relative focal lengths), and long operational lifetime are important.

Our baseline science goals are to simultaneously assess the diversity of possibly Earth-like planets and to carry out a statistically meaningful search for life on these worlds. The detection of biosignatures in the atmospheres of a sample of transiting Earth-sized planets (sample size N_pl) is a necessary prerequisite to achieving these goals. In the following we will discuss the desired sample size, the wavelength range of interest, and the distance to which transits must be detected (as a function of sample size and composition) and explore the effective telescope diameter required to carry out the survey.

The sample size (number of planets studied, N_pl) is a fundamental parameter for an exoplanet characterization and biosignature survey. The ideal sample size will depend on both the specific hypotheses to be tested and the degree of background knowledge completeness. Our current knowledge on the properties and composition of small (1–3 R_Earth) exoplanets is very limited (typically based only on measurements of stellar irradiation, mass, and bulk density; e.g., Rogers 2015; Fulton et al. 2017; Grimm et al. 2018). Such limited data and large uncertainties may only allow probabilistic assessment of the possible nature of the detected planets (e.g., Bixel & Apai 2017; Catling et al. 2018), although this assessment can be supplemented by statistical predictions from planet formation models (Apai et al. 2018). Models predict that rocky planets with compositions different from Earth may be common and some classes may be habitable (e.g., waterworlds; Kite & Ford 2018). Our current understanding of the diversity of exoplanet formation and evolution scenarios does not provide a robust basis for predicting the diversity of present-day exoplanet population.

Checlair et al. (2019) argue that, fundamentally, there are two approaches to exploring the diversity of exo-earths and to the search for life: one in which a direct extrapolation of solar-system-type exoplanets are tested (i.e., search for Earth analogs), and one in which general hypotheses are tested. Checlair et al. (2019) show that the expected yield of LUVOIR could enable a statistical test of the predicted relationship between the carbon cycle efficiency and insolation, but our larger sample would allow us to observe this relationship over more dimensions such as planet size and stellar mass. A somewhat similar argument is laid down by Ramirez et al. (2019), who argue that understanding rocky planets as systems and identifying those that harbor life will likely require the study of hundreds if not thousands of planets: "We also suggest that next-generation missions are only the beginning of a much more data-filled era in the not-too-distant future, when possibly hundreds—thousands of HZ [habitable zone] planets will yield the statistical data we need to go beyond just finding habitable zone planets to actually determining which ones are most likely to exhibit life." Also consistent with this argument is the exoplanet community report by Apai et al. (2017), which highlights the need for large samples of exoplanets to be studied in order to build up the contextual knowledge necessary for understanding abiotic diversity and outliers of potentially biological nature.

The variety of processes and the range of key parameters involved in planet formation and subsequent evolution suggest that there is a strong likelihood for a great diversity in rocky planets—even without considering the possible impacts of extraterrestrial life on the evolution of the planetary atmosphere and climate. With this motivation we set the target sample size of potentially habitable planets to N_pl = 1000 for our science case. This sample size should be thought of as a sample size representative of the anticipated complexity of the parameter space exo-earths may occupy, rather than a well-determined value.

For transmission spectroscopy, the target selection fundamentally impacts the effective telescope collecting area (aperture) required, and it is thus a key property of any survey. In this section we explore several potential target samples and determine the distances at which the farthest target stars in each are located. The target selection consideration described below aims to demonstrate that viable options exist for multiple target samples, rather than to provide a final, optimized sample; additional considerations will lead to different target samples but should not affect the general feasibility.

In the following we will consider four different samples defined by host star spectral type distribution. For each of the samples we estimate the distance of the farthest host star, its brightness, and the relative and absolute amplitudes of the transit spectroscopy signal. In order to explore the range of target star distances, we first calculate the expected number of transiting Earth-sized planets as a function of stellar mass (M_*, a proxy for stellar spectral type), distance (d) based on the volume density of stars (ρ(M_*)), the occurrence rate of Earth-sized habitable zone planets (η_⊕(M_*)), and the probability of these planets transiting (P_tr):

$$\begin{eqnarray}&&N(d,{M}_{* })=\displaystyle \frac{4}{3}\pi {d}^{3}\times \rho ({M}_{* })\times {\eta }_{\oplus }({M}_{* })\times {P}_{\mathrm{tr}}.\end{eqnarray} \tag{ 5 }$$

The transit probability is P_tr = R_*/a_HZ, where a_HZ is the semimajor axis of the habitable zone. The volume density of stars of different spectral types is calculated based on the RECONS sample of the local 10 pc volume (Henry et al. 2018). We follow the model of Kopparapu et al. (2013) for the habitable zone boundaries, adopt their optimistic boundaries, and assume that the planets have transit probabilities that are the mean of the transit probabilities of planets at the inner and outer boundaries of the habitable zone. With a self-developed program—utilizing the astropy (Astropy Collaboration et al. 2013, 2018) and numpy (van der Walt et al. 2011) libraries—we calculated the properties of stars and planets in potential target samples, including distance, transit probability, transit depths, apparent brightness, and relative and absolute transit signals. Table 7 captures the key assumptions of our calculations.

In Figure 5 we show the cumulative number of transiting, Earth-sized, habitable zone planets as a function of distance and host spectral type (dotted curves). We also show four possible target samples selected from these planets. Sample 1 (red dotted curve) consists of the closest 1000 transiting Earth-sized habitable zone planets. This sample is dominated by planets orbiting M-type host stars (blue dotted curve), but the stars in this sample are confined to within ∼55 pc within the solar system. Our Sample 2 consists of up to 500 M-dwarf planets, supplemented by planets around FGK hosts. Stars in this sample are within ∼130 pc of the solar system. Our Sample 3 consists of only planets of FGK-type stars (no M-dwarf planets). In this sample, to reach 1000 planets, we need to include stars up to 160 pc. In our Sample 4 we included only planets orbiting broadly Sun-like stars (G spectral type). With this criteria our targets are located up to 330 pc away (see top panel of Figure 5). Table 1 summarizes the spectral type distribution in each sample, as well as the distance of the farthest star and the brightness of the faintest star in each sample. The table also provides the period range of the habitable zone planets for the target sample.

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Exoplanet transit observations are relative measurements: the signal strength measured is relative to the apparent brightness of the host star and the ratio of the planet's and the star's projected surface areas. As the four samples defined in our study contain stars of very different sizes, brightness, and typical distances, the comparison of the samples in terms of the ease of detectability is nontrivial. The bottom panel of Figure 5 shows the absolute flux density difference during the transit of an Earth-sized planet around the target stars, as a function of spectral type and distance. We note that the flux density difference shown on the y-axis is continuum transit depth and not specific spectral features (which are typically several orders of magnitude fainter). For each of the curves (for stars of different spectral types) we also mark the faintest (most distant) stars in the target samples (as determined and marked in the top panel of the same figure). The dashed lines parallel with the x-axis denote the flux density levels corresponding to the transits around the faintest stars in the sample.

Interestingly, the out-of-transit to in-transit difference signal (in flux density) predicted for the faintest stars in all four samples falls within a relatively narrow range: (2–5) × 10⁻⁹ erg cm⁻² s⁻¹. This finding suggests that the absolute differential photometric precision required to detect a single transit of an Earth-sized planet around the faintest host stars in each sample is very similar between the samples, and that the precision floor is primarily set by the target sample size. However, because the number of transits of habitable zone planets that occur within a given time window and the brightness of the host stars (and therefore the required precision) are strongly spectral type dependent, the four samples discussed above are not equally well suited for a survey. We will consider these factors further in Section 2.4.

Considering the connections between stellar luminosity, habitable planet occurrence rate, transit probability, transit depth, and the volume (number) density of stars of different spectral types, we evaluated target definition choices and the resulting absolute signal strength. Our three key conclusions from the target selection study are as follows: (1) In the case of a single transit the resulting absolute signal strength—corresponding to the transit of an Earth-sized planet—is insensitive to the spectral type distribution of the target stars. (2) For a survey limited by single-transit absolute signal strength, the key parameter of the survey definition is the sample size. (3) Considering the order-of-magnitude shorter orbital periods of habitable zone planets around M-type host stars and the deeper (relative) transit depths, for a survey limited by total telescope time and by relative photometric precision, a sample rich in M-type host stars may be advantageous. Such a sample is also optimal if the transiting planets must be located by the survey before the spectroscopic characterization can begin (due to the shorter transit periods around M dwarfs, much shorter temporal coverage is required to detect or exclude transits). We note, however, that more detailed future studies are warranted to assess the impact of other factors not considered here, including stellar activity and the photometric variability it causes, and low-level stellar contamination of the transit spectra due to stellar heterogeneities (Rackham et al. 2018), which affect Sun-like stars much less than M dwarfs (Rackham et al. 2019).

We utilize the Planetary Spectrum Generator⁶ (PSG; Villanueva et al. 2018) to provide an approximate assessment of the expected quality of the spectra obtained by the telescope concept and explore what equivalent telescope diameter is required for the Nautilus observatory to ensure the detectability of O₂, O₃, H₂O, and CO₂ absorption features in our target sample. The PSG is capable of simulating observations of model atmospheres from a variety of viewing geometries, either for planets within the solar system or around distant host stars of varying spectral types.

We run the PSG for the four models presented in Table 2. These include a mid-M dwarf and solar analog, each at a nearby and far distance based on the relative abundance of transiting planets in Figure 5 (10 and 50 pc for the M dwarf, 100 and 300 pc for the G dwarf; see Table 2). In all models, the planet is an Earth-sized, Earth-mass planet with the PSG's default profile for the Earth's atmosphere. The orbit is placed in the middle of the habitable zone as estimated from the host star's properties by Kopparapu et al. (2014). The viewing geometry is set to "Observatory" mode, with a planetary inclination of 90° and orbital phase of 180°, and the viewing distance set to one of the four values in Table 2.

The PSG can incorporate both Poisson and instrumental (e.g., readout) sources of noise, but we ignore the instrumental noise to focus on the effect of aperture size. The Poisson noise is calculated for a telescope array, each taking 1 s exposures. We set the number of exposures such that the total exposure time equals the transit duration, and generate a spectrum from 200 to 1800 nm with 1 nm resolution for each of the four models in Table 2.

The output of the PSG for the viewing geometry described above is the fraction of light blocked by the planet as a function of wavelength, with uncertainty estimates in each bin. The uncertainty estimates correspond to the amount of light collected over the entire transit duration. We take this to be the uncertainty on the transit depth, but we inflate the uncertainties by 20% to account for limb-darkening degeneracy. We assume that each planet will be observed in transit multiple times—10 times over the course of a year for the M-dwarf planets, and 5 times over the course of ∼7 yr for the G dwarf planets—and we reduce the uncertainties by $\sqrt{{N}_{\mathrm{obs}}}$ for N_obs observations. The justification for the number of revisits for each type of host star is explored in Section 2.5. We varied the telescope array configuration to explore the equivalent collecting area that satisfies our science goal.

Finally, in each spectral bin we draw a value from the normal distribution defined by the uncertainty to simulate the transmission spectrum achieved for each of the four models. The simulated spectra are presented in Figure 6 and binned for visibility according to Table 2. We find that with a 35-element array of 8.5 m diameter telescopes three partial biosignatures—O₃, H₂O, and potentially O₂—could be identified in the atmosphere of an Earth twin orbiting a nearby solar-type star. For nearby M-type hosts, all of these plus CO₂ could be identified with high confidence. Furthermore, detection of O₃ and H₂O could be achieved for the most distant planets in the sample, allowing for a statistical analysis of the presence of biosignatures for hundreds of planets. Although our simulations show a broader wavelength range, we conclude that a narrower range (such as 500–1000 nm) is sufficient for simultaneously detecting three key atmospheric components (O₃, H₂O, O₂) of an Earth analog.

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Transit spectroscopy benefits from repeated transit observations. Combining the transmission spectra from several transits decreases uncertainties by $\sim \sqrt{{N}_{\mathrm{obs}}}$. This strategy has been employed several times from the ground (e.g., Rackham et al. 2018; Bixel et al. 2019) and space (e.g., Kreidberg et al. 2014; de Wit et al. 2018; Zhang et al. 2018). A similar approach could be followed to achieve low- to moderate-S/N spectra of the atmospheres of Earth-sized planets in systems such as TRAPPIST-1 with JWST (Batalha et al. 2018).

When possible, it is therefore optimal to observe a planet's spectrum during every transit. A candidate exo-earth in the middle of the habitable zone of a Sun-like star will transit once every ∼1.5 yr, and the duration of each transit observation (including baseline measurements) would be up to ∼15 hr. Observing all of the planets with G-type hosts in Sample 3 during every transit would cost ∼1600 hr (∼2 months) per year; this commitment of time would be justified by the value of characterizing >100 "true" Earth twins.

However, planets orbiting low-mass stars are far more common with orbital periods of <30 days. The required amount of time for a transit observation is still significant (up to ∼5 hr), and to observe every transit of, for example, 500 such planets (Sample 2) would require 5–10× more observing time per year than is available. Fortunately, the short orbital periods and larger transit depths of such planets will allow an observer to achieve a high-S/N transmission spectrum with ∼10 observations in less than a year, and the full sample of planets with M-type hosts could be studied sequentially over a decade.

Finally, since the S/N scales with $\sqrt{{N}_{\mathrm{obs}}}$, there are diminishing returns when combining a large number (tens) of transit observations for a given target. Nevertheless, closer to ∼100 visits could be scheduled for a handful of nearby interesting low-mass systems (e.g., TRAPPIST-1; Gillon et al. 2017) to enable very high S/N spectroscopy, but we assume that the amount of time spent on such systems will be negligible in the overall scope of the mission. We use these arguments to set the number of combined transit observations for the results shown in Figure 6, and we see that in about 8 yr we can achieve statistically significant positive results for the samples suggested in Table 1.

In this section we introduce the Nautilus observatory, a novel telescope array concept developed to meet the science requirements (see Section 3 and Table 3) of the large-scale atmospheric biosignature survey we described in Section 2. The Nautilus concept described here is not a complete, final, and fully optimized mission design. Rather, it is a notional design that highlights the potential of novel large-scale diffractive optics to answer key astrophysical questions. In this manuscript we focus on technical opportunities and challenges unique to MODE-lens-based space observatories or the Nautilus concept. We do not address technical aspects that are shared with other space observatories. We will first review the baseline concept for the observatory and its operations and then review individual unit telescope architecture, their launch and deployment, and various fundamental considerations.

Our study described in Section 2.4 established that a telescope system with a light-collecting power equivalent to a single 50 m diameter aperture will be required for the biosignature survey. As no such large-diameter single telescope is realistic to launch in the foreseeable future, our mission design envisions multiple unit telescopes that combine light noncoherently to match the light-collecting power of a 50 m telescope. Our notional Nautilus concept utilizes an array of ultralightweight, very large aperture, and low-cost unit space telescopes with powerful light-gathering capabilities. In considering the diameter of the individual unit telescopes, we adopted a size that is consistent with the largest rigid (nonfolding) diameter that can be launched in the next decades: specifically, we adopted a diameter of D = 8.5 m, about 5% smaller than the maximum inner dynamic envelope diameter of the fairings of the next-generation vehicles (SpaceX/BFR, NASA SLS B2). In order to match the light-collecting power of a 50 m telescope, 35 such unit telescopes will be required. We note that the design presented here is not sensitive to the specific diameter of the unit telescope's diameter: if unit telescopes with smaller apertures are used, the number of unit telescopes can be increased to keep the total area constant. Future trade studies will be required to verify that the 35 × 8.5 m configuration is an optimal choice.

This novel telescope architecture is potentially enabled by the rapid progress in replicated multiorder diffractive engineered material (MODE) lenses, which have the potential to replace primary mirrors. Their incoherently combined light (digitally co-added signal) collecting capability will equal that of a single 50 m mirror diameter space telescope.

We envision Nautilus to operate primarily in follow-up transit spectroscopy mode, but also to have the capability for exoplanet transit searches. The combined operations will allow discovering and characterizing a very large number of habitable zone Earth-sized transiting exoplanets.

Transit search mode: The Nautilus observatory will benefit from multiple powerful transiting exoplanet search missions that precede it (e.g., Kepler; Borucki et al. 2010; TESS; Ricker et al. 2015; PLATO; Rauer et al. 2014), which are expected to identify tens of thousands of transiting exoplanets. Nevertheless, the Nautilus observatory will be capable of searching for transits on its own, enlarging the potential target sample. Operating independently of each other, unit telescopes will monitor potential exoplanet host stars in the target sample, and through their parallel operation they will have the potential to carry out the most sensitive and most comprehensive transiting exoplanet search yet. The unit telescopes will use their smaller (2.5 m diameter) MODE lens—optimized for wide-field-of-view imaging—for the transit search. The transit search component will greatly expand the number of known transiting habitable zone Earth-sized planets.

Follow-up transit spectroscopy mode: During known transit events, all unit telescopes will record the transmission spectrum of the same planet using their larger, 8.5 m diameter MODE lenses. The signal measured by the individual unit telescopes will be combined noncoherently (by digitally co-adding), enabling the confident detection of major atmospheric absorbers (O₂, O₃, H₂O) in Earth twins up to about 300 pc.

The noncoherent combination of signal, as planned in the Nautilus observatory concept, does not require formation flying for the unit telescopes. As light is combined noncoherently, the relative locations of the individual telescopes during the observations (as long as the target star is visible) are not important.

Figures 7–9 illustrate our baseline concept for the Nautilus unit telescopes in compact launch and deployed configurations. Figure 10 illustrates the observatory (telescope array) in operation. Each unit telescope will use an 8.5 m diameter f/1.0 focal ratio MODE lens as the light-collecting element for the exoplanet transit spectroscopy observations, and a smaller, 2.5 m diameter, wide-field-of-view MODE lens for the photometric exoplanet transit search operations. The two lenses will focus the light on two simple instruments. Each Nautilus unit will be a stand-alone telescope equipped with two visual/near-infrared detectors and a low-resolution spectrograph optimized for the 0.45–1.0 μm wavelength range.

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In this study we will not address the details of posited instruments and detectors, as our focus is on the novel use of MODE lens technology and the measurements strategy it enables. We note, however, that the measurements proposed herein are generally compatible with low-noise detectors and low spectral resolution spectrographs that are currently available. If a sufficient amount of light is collected, currently available measurement technology offers viable solutions for the observations. For example, Kepler's CCD cameras were able to detect ppm-level modulations (after detrending, in white light) the same level of precision required by the observations proposed here. We also note that lower light throughput and detector noise can be compensated by increasing the number of unit telescopes, i.e., will not have a major impact on the overall concept.

In this section we demonstrate that several satisfactory options exist for the orbit of the Nautilus observatory. The determination of the ideal orbit will be based on a detailed assessment of the mission concept; here we provide only a preliminary discussion. The primary considerations for the Nautilus array's orbit are low-energy (Δv) access, orbital stability, a very stable thermal and radiation pressure environment, and quasi-constant illumination (from Sun, Earth, and Moon).

With these considerations in mind we identified the Earth-Sun L2 point as one of the possible locations for the Nautilus array. Stationed at the L2 point, the Sun, Earth, and Moon will be seen by the Nautilus units from nearly identical directions, allowing for a very stable radiation environment and constant communication windows. A possible alternative, easier-to-access orbit would be a Sun-synchronous, high-inclination, terminator-following low Earth orbit. This orbit would provide somewhat less stable illumination and thermal environment and more limited sky coverage but would be easier to access and to communicate with. In addition, a low Earth orbit would enable passive angular momentum management (magnetic torquing rods). The ultimate choice of orbit will impact the spacecraft design.

The Nautilus unit telescopes utilize inflatable spacecraft components for deployment, allowing the instrument package and MODE lenses to form very compact packages (see Figures 7–9). The unit telescopes are launched in a compact configuration, in cylindrical containers (approximately 9 m diameter and 1 m tall), with multiple containers positioned in a single fairing (Figure 9). Over the next two decades multiple launch options will exist that are suitable for the Nautilus observatory. Next-generation rockets and their largest fairing will allow over a dozen units to be launched in a single payload (Figure 7): NASA's Space Launch System's Block 2B fairing is expected to offer a ∼9.1 m diameter payload envelope with a height approaching 30 m; such a fairing may be capable of launching ≃24–28 Nautilus units in a single launch. SpaceX's upcoming Big Falcon Rocket (BFR) will offer a fairing with a diameter very similar to that of the SLS Block 2B long fairing, but with a probably shorter height (17 m). Correspondingly, SpaceX/BFR may be capable of launching 15 Nautilus units. In our reference design we adopt a BFR-style fairing (see Figure 7).

We note that currently existing fairings are well suited for launching smaller—but still very capable—pathfinder units. For example, the currently operational SpaceX Falcon 9 accommodates a dynamic payload envelope (cylindrical) with a 4.6 m diameter and 6.7 m height. This could accommodate up to six Nautilus launch modules with up to ∼4.2 m MODE lens diameter. The 5 m diameter "Long" fairing offered for the Atlas V has a fairing accommodating 4.6 m diameter with a 12.2 m height, which could be sufficient for 10 Nautilus units based on MODE lenses with diameters up to ∼4.4 m.

After orbital insertion the individual Nautilus unit telescopes separate from the fairing and from each other and begin inflation. Mechanically, the telescope deployment is driven by the inflation of a spherical Mylar balloon (diameter ∼14 m), which will shift the two MODE lenses (in front and behind of the instrument package) forward and backward by about 6.5 m. In addition to the simple deployment mechanism, the Mylar balloon will also provide stray-light control, sunshield functionality, and solar energy to the telescope. The inflation itself is a nonreversible operation, initiated by the release of a low amount of chemically inert but relatively high atomic weight noble gas (Kr). Once the target shape is reached, mechanical struts lock in, fixing the telescope structure, providing long-term mechanical stability. The instrument packages will be aligned precisely to the focal plane of the deployed MODE lenses through observations of a reference star field.

The estimated power requirements of the Nautilus array unit telescopes are smaller than the power requirements of large space telescopes and therefore are not expected to pose a significant challenge. We anticipate that the major systems requiring energy will be communications, spacecraft attitude control, and the instrument package; similar components exists on HST, JWST, and Herschel Space Observatory, all powered via solar cell arrays.

As a baseline we estimate the operational power requirements of a Nautilus unit telescope by scaling the power use of HST (2.8 kW) and JWST (2.2 kW). We anticipate that the power consumption of a single Nautilus unit telescope will be lower than HST and JWST owing to the Nautilus units' simpler design, the lack of cool instruments required for long-wavelength observations (>1.5 μm), its smaller number of instruments/subsystems, and considering more efficient electronics. As a reference value for power requirements we assume 1.5 kW for each telescope.

Unlike HST and JWST, Nautilus units will utilize flexible solar cell film, which has space heritage (Venus Express) and—due to the flexibility and low areal density—will provide ideal structural match for the inflatable spacecraft. Nautilus units will integrate solar cell film into the inflatable balloon in a rotationally symmetrical configuration. Assuming that the average fraction of the solar panels' surface illuminated is η_ill = 0.3, a solar cell efficiency of η_eff = 0.1, an average distance of d = 1 au from the Sun, and a solar constant (at 1 au) of c_Sun = 1.37 kW m⁻², the total surface area of Nautilus units covered in solar cell film will be ${A}_{\mathrm{sc}}=\tfrac{1.5\,\mathrm{kW}}{{c}_{\mathrm{Sun}}{\eta }_{\mathrm{eff}}{\eta }_{\mathrm{ill}}}=36.5\,{{\rm{m}}}^{2}$ to provide 1.5 kw average power. The power will be stored in batteries, providing a stable power source also when the solar array is not illuminated. The 36.5 m² solar cell film corresponds to only about 6% of the spacecraft's (balloon's) surface (for a balloon radius of 7 m). An orbit with greater average distance from the Sun will require a somewhat larger fraction of the balloon to be covered with solar cell film. In short, an available, low-weight and low-cost power source with space heritage exists that can, by a large margin, cover the energy needs of a unit telescope.

Given the thin MODE lenses, we estimate the available instrument package volume as a cylinder z = 0.6 m high and with a radius of up to r = 4.0 m, which translates into a volume of up to ∼30 m³. In comparison, HST's aft shroud is approximately 60 m³ (radius of 2.2 m and height of 3.55 m). Therefore, a Nautilus unit telescope's instrument package volume would be overall comparable to instrument packages of existing major observatories. Given the goal to provide simple, compact, and identical instrumentation for each unit telescope, the volume available in the units is not expected to pose particular challenges.

Nautilus units will use four reaction wheels (all offset for the inertial axes) to manage the rotation (pointing, tracking) of the spacecraft along three axes (a fourth wheel provides redundancy). The reaction wheels will spin in the direction opposite to the intended rotation of the spacecraft. Nautilus units—like any spacecraft—will be subjected to net torques (primarily due to asymmetric exposure to solar irradiation and solar wind pressure). Although the reaction wheels will ensure stable pointing during operations, Nautilus units will periodically need to dump angular momentum. We envision two possible pathways for this: a passive and an active mechanism. In the passive angular momentum management mode—as the distribution of transiting planets is closely isotropic on the sky—each unit telescope's observing schedule can be planned in such a way to average out torques. In the active angular momentum management mode ambient-temperature, pressurized nitrogen is released through thrusters affixed to the exterior of the Mylar balloon (possibly at the connecting points of the lock-in struts; see Figure 7). Nitrogen does not affect the planned observations and will not react with or freeze onto the spacecraft. Given the unusually symmetric architecture of the unit telescopes, net torques will be lower than they are for most other spacecraft architectures, resulting in a much lower than typical rate of angular momentum accumulation.

The driver for the guiding stability is the high photometric precision: pointing drifts, combined with detector sensitivity variations and possible position-dependent systematics, will introduce apparent position-dependent intensity variations. While significant reduction in the power of such systematics is possible via post-processing (such as in the Kepler mission), it is desirable to keep image drifts at or below the level of the diffraction-limited spatial resolution of the telescope. Therefore, a guiding precision of approximately 15 mas/10 hr would be targeted. The Nautilus unit telescopes will use the Sun as a coarse attitude reference point and the antisolar star field for precise pointing position measurements. The unit telescopes will use the target stars and reference stars within the field of view for fine guiding during long exposure series (typically ∼20 hr) before, during, and after planetary transits.

At an orbit with an average distance of 1 au from the Sun, the spherical Nautilus units may operate close to room temperature (25°C) with only modest active thermal management (heating). The inflatable balloons of the Nautilus units will protect the instrument package (in the interior) from large temperature excursions, as the nitrogen gas and emission/absorption within the balloon redistribute heat. Nevertheless, the high-precision measurements require a thermally stable system (instrument package, lens alignment, and lens itself). Therefore, Nautilus units will actively control the temperature of the elements within the spacecraft and of the MODE lenses. Heating will be provided by battery-powered thermoelectric cells, and excess heat will be dumped at the dark (nonilluminated) side of the Nautilus units, possibly through a metal ring surrounding the MODE lens (as MODE lenses are not exposed to the Sun during normal operations).

Due to their noncontinuous surface microstructures, MODE lenses cannot be fabricated through traditional grinding and polishing methods. Potential fabrication for noncontinuous surfaces includes diamond turning and molding, gray-scale lithography, deep-reactive ion etching, UV imprinting, and glass slumping. Among these, diamond turning and molding are the most powerful approaches for MODE lens fabrication owing to their accuracy and scalability. The combination of diamond turning and pressure molding offers very powerful and flexible fabrication paths for MODE lenses: diamond turning enables precise fabrication, and pressure molding enables reliable and low-cost replication.

Ultraprecision diamond-turning machines have been successfully used to fabricate conventional lenses and diffractive optical elements (e.g., Lee & Cheung 2003; Huang & Liang 2015). For example, state-of-the-art Moore Nanotech 350FG free-form generators are capable of diamond turning or milling MODE lenses or MODE lens segments with diameters up to 0.6 m. Precision glass compression molding is a replicative process that allows the production of high-precision optical components from glass and polymer (Zhang & Liu 2017), including those of diffraction surfaces (Huang et al. 2013; Nelson et al. 2015). By using chalcogenide glasses, precision molding also allows replicating optical elements for infrared applications (Staasmeyer et al. 2016). Compression molding has been successfully used to mold glass free-form optics from diamond-machined molds (He et al. 2014).

By combining diamond turning/milling to fabricate molds and glass press molding, it is thought to be possible to replicate large-aperture MODE lenses. Our team is actively developing this technology and fabricated, replicated, and tested lens prototypes. To illustrate the fabrication approach, we diamond-turned molds and molded the MODE lens from poly(methyl methacrylate). One such prototype is shown in Figure 11. The measured lens profile and image quality verified the molded surface shape and quality. Our University of Arizona–based team is developing this technology toward very large aperture MODE lenses that can be replicated reliably and at low cost.

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As part of the MODE lens development effort at the University of Arizona, our team has designed and fabricated several generations of diffraction-based lenses, from single-order to more complex (M = 1000) MODE lenses. The latest prototype MODE lens combined a high-order diffractive lens (M = 1000) at the front surface with a single-order Fresnel lens on its back surface. The optical design has been optimized to provide diffraction-limited performance in the astronomical R band (589–727 nm). Laboratory optical tests with super-continuum laser and imaging tests demonstrated that the measured performance is consistent with that predicted by the physical optical models (T. Milster et al. 2019, in preparation). Prototypes equipped with additional, conventional color-corrector optics (much smaller in diameter than the MODE lens) are predicted to provide diffraction-limited performance over a broad wavelength range (>200 nm).

In order to manufacture, align, and assemble a large MODE-lens-based space telescope system, specialized metrology concepts and solutions testing and verifying its optical performance need to be developed and applied. The challenging science goals of next-generation space telescopes are often achieved through a new optical design and components, such as a MODE lens. Measuring and aligning those complex optical surfaces and components require a large dynamic range in metrology, high accuracy, comprehensive spatial frequency coverage, and real-time data acquisition and analysis to test the multiscale optical features. Unlike the traditional small-size diffractive optical component, the diffractive optical surface of the MODE lens has a precision microscopic surface profile over its large-aperture area, enabling its light-collecting power. As stray light and surface scattering must be controlled for high-quality imaging performance, the nanoscale surface roughness must be measured and controlled. In order to realize the next-generation optical systems producing a near-optimal point-spread function with superb imaging quality, an entire spectrum of the optical system's wavefront must be measured and confirmed during the telescope manufacturing, assembly, and testing process.

As the entire spatial frequency spectrum of the optical surface/wavefront errors has to be controlled, the MODE-based space telescope optics need to be modeled and specified using a power spectral density (PSD) or structure function (Hvisc & Burge 2007; Parks 2010). Parks (2008) experimentally demonstrates the severe image quality degradation due to the presence of intermediate to high spatial frequency surface errors.

Phase-shifting deflectometry is applied to measure, align, assemble, and evaluate the performance of a large optical system with nanometer-level accuracy through its direct slope-measuring capability (Su et al. 2010; Oh et al. 2016). During fabrication, the quality of the MODE lens local surface finish (i.e., microroughness rms value) is monitored and sampled across the large aperture using a portable white-light interferometer (Parks 2011). Various metrology systems covering different ranges of spatial frequencies measure and test the MODE-based space telescope by providing a comprehensive PSD evaluation similar to the 4.2 m Zerodur primary mirror of the Daniel K. Inouye Solar Telescope (DKIST) tested with a suite of metrology systems as shown in Kim et al. (2016).

Other key components of the space telescope system utilize aspheric optics to achieve better achromatic imaging performance for a larger field of view within a compact and light-weighted design. For most cases, temporal phase-shifting interferometry uses a null component such as computer-generated holograms that provides high-accuracy wavefront/surface measurement data with sufficient spatial frequency sampling. During the manufacturing and aligning process, in order to guide the processes, high dynamic range metrology methods are utilized. The wide range ensures the measurement of the optical component's or system's quality when it is still far away from its final specification performance. For instance, the 4–8 m diameter class high-precision optics manufacturing process and final testing of the Giant Magellan Telescope and DKIST primary mirrors were guided with a successful rapid convergence by utilizing nonnull deflectometry measurement feedback (Su et al. 2012; Huang et al. 2015).

For the alignment of MODE lens systems (as also applicable for active/adaptive wavefront correction or bending mode measurements) instantaneous metrology is applied using a multiplexed deflectometry solution. The real-time metrology system uses a multiplexed color fringe pattern in x and y spatial frequency domain in order to contain and process six fringe patterns from a single-shot data acquisition offering about 25 nm rms accuracy (Trumper et al. 2018). Such a dynamic measurement and active characterization of the MODE lens telescope system will monitor and verify the opto-mechanical performance as a function of time, orientation with respect to gravity, and thermal gradient changes. An overview of the baseline MODE lens optical specification as a function of spatial frequency (i.e., cycles per aperture) is given in Table 4.

As an indication of system optical performance, spot diagrams are calculated that show geometrical ray intercepts at the image plane. These diagrams trace bundles of rays through the optical system from a point source (like a star) at a large distance. Figure 12 shows spot diagrams of a 0.24 m prototype MODE lens telescope at an intermediate image plane after color correction. The location of the idealized 1st Airy ring minimum is shown as a black circle. The Airy pattern is the image-plane light distribution due to diffraction of the optical system illuminated by a distance point source. The diameter of the Airy ring is dependent on the wavelength and f number. In this case, the Airy ring is calculated from the prototype system parameters with a central wavelength of λ_c = 658 nm and an f-number of 1.83. The image is considered diffraction limited if all of the geometrical ray intercepts fall within or near the Airy ring. In Figure 12, the geometrical ray intercepts are calculated from three wavelengths of the point source, 589, 658, and 727 nm, which are shown as blue, green, and red colors, respectively. Calculations are also made from three field angles of the point object, from on-axis (at H = 0) to a maximum field angle of 7.5 arcmin (H = 1). The prototype design is diffraction limited on-axis at H = 0 and out to 70% of the maximum field of view (H = 0.7). It is nearly diffraction limited at the maximum field of view (H = 1). Degradation of the system performance with increasing field angle is due to residual wavelength-dependent aberrations. While this design shows a 0.24 m diameter MODE-lens-based telescope system's performance, similarly diffraction-limited performance can be achieved by larger systems.

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No existing telescope is capable of searching for atmospheric biosignatures in exoplanets. JWST may be able to search for water and methane in the most favorable transiting exoplanets around very nearby red dwarf host stars, but probably in not more than two to four habitable zone Earth-sized planets. The mission concepts HabEx and LUVOIR would utilize high-contrast direct imaging to study Earth-like planets; they may image 50–300 planetary systems and search for biosignatures in up to about 10 to ∼60 habitable planet candidates, respectively.

In contrast, Nautilus is a system concept developed to survey ∼1000 Earth-like planets, providing more than an order-of-magnitude increase over the capabilities of even the most ambitious missions yet studied. The proposed survey can be accomplished with an array of telescopes that combine light incoherently. Achieving this level of light collection in a single, phased aperture is not a realistic possibility for the foreseeable future.

In terms of light-gathering power Nautilus offers an orders-of-magnitude increase over current facilities. Currently the largest-diameter space telescopes are HST (D = 2.4 m) and Herschel (D = 3.5 m), with the D = 6.5 m JWST soon to follow. A single element of the Nautilus concept will exceed HST's light-gathering power by a factor of 12.5, and the Nautilus array will exceed JWST's collecting area by a factor of 60 (The LUVOIR Team 2018).

Unlike reflecting telescopes, our MODE lens design is inherently more tolerant of optical element misalignments, a fact that will significantly reduce fielding costs (e.g., Lo & Arenberg 2006). If a mirror orientation is tilted by angle α, the reflecting beam will be deflected by 2α, which requires a very tight alignment tolerance and complex control solutions. However, with a basic first-order geometrical optics analysis, a chief ray going through the center of a refractive lens does not change its direction, although the lens is tilted. In a similar manner, transmissive refractive/diffractive optics are insensitive to surface figure errors, including intermediate to high spatial frequency errors. For example, an anomaly with height h on a mirror surface in space will induce 2h optical path length (OPL) change owing to its double-path nature. However, for a lens with a refractive index of n, the same surface anomaly will cause only an (n − 1) × h OPL difference, i.e., only a ∼0.5 hr change in OPL (assuming a typical n = 1.5). Also, if the thin MODE lens is bending or locally rippling while it is maintaining the thickness of the MODE lens, there is almost no OPL change since the front and back surfaces are moving together. This robustness of the alignment and shape error tolerance is one of the most fundamental strengths of the MODE-lens-based telescope system.

As an illustration of the anticipated mass advantage of MODE-based space telescopes over reflecting space telescopes, we contrast scaled-up versions of the HST and JWST mirror systems with MODE telescopes. HST uses a 2.4 m diameter, 33 cm thick, monolithic mirror, whose weight is reduced with respect to a conventional monolithic mirror by about a factor of five through the implementation of a honeycomb structure in the body of the mirror. The mass of HST's mirror is approximately 826 kg, which corresponds to about 7.4% of the total observatory mass. The HST mirror provides an excellent reference point for relatively lightweight monolithic space telescope mirrors.

JWST is a primarily infrared telescope with diffraction-limited optical performance at and beyond 2 μm. It utilizes 18 gold-coated beryllium mirror segments, each of which is 20.1 kg. The segments are periodically co-phased between observations. Considering the mirror control structure (wire harness), the complete primary segment assembly for each mirror segment is 39.48 kg. This leads to a combined mass of 710 kg for the 6.5 m mirror, corresponding to 9.6% of the total observatory mass. JWST is the natural reference for state-of-the-art segmented space telescope mirrors.

In Table 5 we compare the masses of hypothetical 8.5 m diameter mirrors that use HST- and JWST-like mirror systems. We provide two bracketing cases for the mass scaling with diameter: an optimistic case when the mass M is directly proportional to the D collecting area of the mirror (M ∝ D^2.0), and a more conservative one (M ∝ D^2.8) in which the larger area also translates into a thicker mirror (or additional co-phasing system). We compare these extrapolated mirror masses to two MODE lenses: a thin (h = 0.5 cm thick, optimistic case) and a thick (h = 5 cm thick, pessimistic case) lens. We note here that the thickness of the MODE lens will be likely set by mechanical structural considerations and not the optical design, as even few-millimeter-thick MODE lenses can provide excellent image quality. To calculate the mass of the MODE lens (see Section 1.3), we consider its volume (R²π × h) and the volume-filling factor ϕ = 0.5 and assume a glass density of ρ = 2500 kg m⁻³ .

Table 5 demonstrates that the MODE lens technology is expected to be a factor of 2 (worst case) to 70 (best case) lighter than an HST-like honeycomb mirror. Compared to JWST-like segmented mirrors, MODE lenses have similar mass (between 3 times lighter and about 3 times heavier). Compared to a conventional mirror (about 5 times more massive than honeycomb mirrors), MODE lenses would provide about two orders of magnitude lower mass.

Not only will MODE technology enable ultralight light-collecting capability (on par with or better than the lightest mirrors), further significant reduction in the total mass for a MODE-based telescope system is expected given the overall lighter support structure required and owing to the fact that the MODE lenses are much more tolerant to misalignments.

The Nautilus concept benefits from a potential for greatly reduced launch costs through four factors: First, MODE-lens-based telescopes will be much lighter than telescopes based on monolithic mirrors and about as light as the lightest segmented mirror systems (Section 5.3). Second, with the typically two-orders-of-magnitude more relaxed alignment tolerances (Section 5.2), the structural support requirements are milder and allow for the use of lightweight structural elements, such an inflatable deployment mechanisms (Section 3.1). The lightweight and inflatable structural elements represent significant further reductions in the telescope's mass. Third, MODE lens systems can provide simultaneously fast systems (small focal ratios) and wide fields of view. This allows the MODE telescopes to be very compact (f/1.0 systems), thus alleviating the need for light path folding and secondary mirrors. Fourth, the very compact launch configuration and low weight enable the simultaneous launch of many unit telescopes in a single launch fairing (e.g., up to 15 with SpaceX/BFR or 25 with NASA SLS B2 Long). This dramatically reduces the per-telescope launch costs. The Nautilus concept is too preliminary to allow for reliable costing. It seems, however, that due to the four factors discussed above, MODE-lens-based systems—and, in particular, the Nautilus observatory—have the potential to provide a significantly lower launch cost solution than those following a more conventional design.

It is argued that current mission costs and complexity are driven by the so-called "space spiral," in which higher reliability requires a longer development phase, which results in fewer missions and higher mission costs, which—in turn—requires even higher reliability (Wertz et al. 2011). This self-reinforcing cycle arguably drove mission costs, and it is estimated that at present day the average cost of space systems launched by the US is about 3 billion USD per launch (Wertz et al. 2011).

The Nautilus observatory represents a new approach to space telescope fabrication, one in line with the development of small satellites and diversified launch capabilities. The Nautilus concept has the potential to reduce mission costs in three major ways: First, it utilizes a low-cost (replicated) optical element instead of massive and complex mirror systems. This reduces the fabrication cost of one of the primary components of telescopes that conventionally drives mass, risk, and cost budgets. This represents a fundamental paradigm shift, making the production of space telescopes far more economical. Second, the MODE lenses provide ultralightweight alternatives to mirrors and enable lightweight telescope structures also utilizing inflatable elements, translating into a major reduction in launch costs (Section 5.4). Third, unlike many past space telescopes and space observatories, Nautilus is envisioned not as a unique, high-reliability, and very expensive telescope but as an array of replicated, identical, relatively low cost telescopes. This major difference is enabled by the ability to efficiently replicate the key optical element by using the MODE technology.

The model in which many unit telescopes are built and launched also alleviates the very high reliability requirement: compromised operation (or even failure) of one unit telescope would not compromise the array's overall capabilities. Similarly, the instruments envisioned for Nautilus units are simple and replicated, less capable than typical HST and JWST instruments, but also with individually relaxed fault tolerance, and they can be built for a fraction of the cost. In addition, the risks could be better distributed than possible in the current single, unique mission model: we can envision the launch of one or two smaller-size demonstrator units to mitigate risks.

The specific cost of the MODE lens and its associated system cannot be rigorously derived at this early TRL and mission concept maturity level (CML). However, the technology offers a likely cost advantage over traditional systems, and a qualitative argument can be provided to establish that MODE lenses are less expensive than traditional approaches. Let the cost of each stage i in the development of the MODE and traditional optics be denoted as M_i and T_i, respectively. Correspondingly, the total cost of a MODE-based system is Σ_iM_i, while the total cost of a traditional mirror-based system is Σ_iT_i.

Since at this early system TRL and CML we cannot reliably predict total cost, we use another method of analysis. This method is a heuristic one and shows that M_i ≤ T_i for all i. Consider Table 6, which lists the assessment at each stage of why the traditional approach is likely to be equal to or more costly than the MODE technology.

As shown in Table 6, our assessment is that for each step the cost for the MODE lens is less than or equal to the cost of traditional methods, meeting the condition that Σ_iM_i < Σ_iT_i, and therefore indicating the cost efficiency of the MODE technology. As the technology and concept develop, we will be able to improve on the originally heuristic cost argument more quantitatively and precisely, but the qualitative result given is likely not to change.

Due to its relatively low production and launch costs and the identical multispacecraft model that is relatively new to astrophysical space telescopes, the general Nautilus system proposed here provides an easily scalable approach. Such multispacecraft models (multiple identical units) are used commercially (Iridium system) and for geo- and planetary sciences (Voyagers, Mariners, Mars exploration rovers, etc.) to reduce per-unit costs and risks and to extend capabilities. Furthermore, telescopes utilizing similar architecture but increasing in size could demonstrate feasibility and mitigate risks, while producing scientific data.

As discussed in Section 4.1, the combination of optical high-precision diamond turning and compression molding has a clear potential for enabling the efficient replication of very large scale diffractive optical elements. In Section 4.3 we reviewed considerations for optical quality monitoring for such large-scale optical elements and showed that the required technology already exists today and that only minor changes will be required to adopt it for MODE lenses.

Here we will briefly review three challenges that must be overcome to enable the replication of large-scale MODE lenses. First, diamond-turning and molding machines must be scaled up significantly. Both of these technologies are fundamentally not very sensitive to spatial scales, i.e., the construction of large diamond-turning and molding machines is thought to be entirely possible by just building larger versions of the current machines. No change in technology is required.

Second, the structural integrity of the large-diameter MODE lenses must be preserved during launch (unless molded in space). Large-scale, relatively strong, yet thin transmissive glass elements exist in a variety of fields. For example, car windshields (layered glass panels) are large diameter and strong, yet typically only 4–6 mm thick. Nevertheless, the fabrication, handling, and launch of very large, lightweight optical glass elements will clearly represent a challenge. Third, the deployment of the large MODE lenses through a lightweight structural element (such as a balloon; Section 3.1) must be demonstrated. Inflatables and optical deployables have a long heritage in satellites (e.g., ECHO-1, or solar panels), and heritage solutions may already exist for smaller scales. The fact that MODE lenses are very tolerant of misalignments (deployment errors) is encouraging. Although there are reasons to believe that all three of these challenges are surmountable in the very near future, MODE lens technology development and mission concept design must mitigate these risks.

MODE-lens-based, very large aperture telescopes in general, and the Nautilus concept specifically, offer a possible revolution in the light-gathering power of astronomical space telescopes. The greatly enhanced light-gathering power equals greatly enhanced sensitivity to faint astrophysical objects (such as the earliest, very high redshift galaxies; supernovae at high redshifts; individual stars in nearby resolved galaxies; or small minor bodies in the solar system). The enhanced sensitivity also enables more precise and higher-cadence time-resolved observations. One important application of such observations is the characterization of transiting extrasolar planets, the science case that motivated the Nautilus concept described in this manuscript. As demonstrated, our baseline Nautilus concept may enable spectroscopic studies of approximately 1000 potentially habitable Earth-sized exoplanets. Such a survey would undoubtedly revolutionize astrophysics, planetary sciences, and astrobiology. The spectroscopic observations would enable the identification of several key atmospheric absorbers and would provide a pathway to determine or constrain the atmospheric composition. The survey envisioned here is distinct from other surveys proposed or planned owing to its very large sample size: the ability to study 1000 Earth-sized habitable zone planets may likely be essential for understanding the complexity and diversity of extrasolar planets (e.g., Seager 2014; Apai et al. 2017; Bean et al. 2017).

A sample size of 1000 planets would allow, for example, identification of potential trends between atmospheric absorbers and bulk properties of the planets. Comparison of the planets' atmospheric composition to the stellar irradiation received may allow empirical mapping of the inner and outer boundaries of the habitable zone (Kopparapu et al. 2013, 2018) and identification of possible atmospheric loss mechanisms (e.g., Owen & Wu 2016). Seager (2014) argues that a sample size of 1000 or greater potentially Earth-like planets is likely required for a confident, statistical identification of life-bearing planets.

The fundamental theme of this paper is to explore the conjecture that large astronomical telescopes could be built based on multiorder diffractive engineered lenses and that such telescopes could be uniquely well suited to address astrophysical problems that require a large light-collecting area. The Nautilus observatory concept described herein is not a complete design reference mission, and it is not informed by detailed trade studies; instead, our study shows that possible solutions exist to most challenges MODE-lens-based telescope architectures may pose.

The technology readiness level of several components of the Nautilus concept is low; chief among these are the MODE lenses themselves with TRL2–3. In order to verify and realize the potential for very large MODE lenses for astronomical observations, a significant technology development and demonstration program is required. We briefly describe here a possible technology maturation pathway toward large MODE-lens-based telescopes.

First, technology development is required to demonstrate that high-quality MODE lenses can be fabricated and replicated with submeter diameters. Second, these lenses must be demonstrated in astronomical observations, firmly establishing such lenses at TRL3. Operational demonstration in thermal-vacuum chambers will help move MODE lens technology to TRL5. A parallel technology development effort is required to scale up the fabrication/replication technology by building larger free-form optical fabrication and molding machines, preferably to 1–3 m diameters, and possibly beyond. With MODE lenses at TRL4–6, small-scale pathfinder, science-driven space missions will become viable, including small satellites and stratospheric balloons.

As MODE technology addresses a fundamental attribute of space telescopes (light collection), interesting science cases exist for even relatively small MODE-lens-based space telescopes. After a successful demonstration of the MODE lens technology in space or near-space environments on a SmallSat or stratospheric flight, a pair of 1–1.5 m diameter units may be flown as a NASA Small Explorer or Mid-Explorer mission, or a single 8 m diameter telescope could be flown as a Probe-class mission. If successful, a scaled-up and replicated version of these unit telescopes could serve as the first step in realizing the Nautilus observatory or an observatory with a similar scope.

We note here that the initial steps of this process are underway: small (0.05 m diameter) MODE lenses have been fabricated, replicated, and demonstrated already; our team is currently working toward developing 0.24 m diameter MODE-lens-based telescopes, and their on-sky demonstration is scheduled for winter 2020. In addition, we are planning small satellite and balloon-borne MODE telescopes.