Novel spectrophotometer concept for the characterization of transiting exoplanets

Thanks to the high-precision photometry of the Kepler spacecraft, numerous small worlds orbiting late-type stars have now been discovered.¹ Within these discoveries, there are a number of small-radius planets in the so-called habitable zone of their parent stars (i.e., candidate habitable planets). However, the spectral characterization of nearby transiting planets—for the study of their atmospheric properties and compositions—is becoming more and more difficult. Although transmission spectroscopy can be used to characterize ‘super-Earths’ and terrestrial planets with high stability (i.e., down to 10⁻⁵) in just a few hours,² there are remaining problems associated with observational data from space (e.g., from the current Spitzer Space Telescope and Hubble Space Telescope observatories). These datasets tend to be dominated by a large amount of instrumental systematic noise, which is caused by image center movement and point spread function enlargement in the variability of intra-pixel and inter-pixel sensitivity.³

The Transiting Exoplanet Survey Satellite (TESS)⁴ and the Planetary Transits and Oscillations of Stars (PLATO)⁵ missions will be the successors to Kepler. These missions will provide the opportunity to detect many smaller and cooler transiting exoplanets around nearby late-type stars. To make improved spectral characterizations of the transiting exoplanets, however, it is necessary for the telescope image movements and the deformation of the primary mirror to be much smaller than the point spread function of a conventional spectrophotometer (i.e., in which spectra are acquired on the focal plane).

In our work we have thus proposed a new concept for the spectral characterization of transiting exoplanets.⁶ With our concept—known as densified pupil spectroscopy—we open up the possibility of using any telescope with modest pointing accuracy (i.e., comparable to the size of the point spread function) to study small-radius planets. In our densified pupil spectroscopy technique, we realize pupil spectrophotometry with a number of small telescopes that are aligned on an aperture plane (such as for the PLATO mission) by using a single large telescope. This approach allows us to perform highly stable spectrophotometry and to mitigate the telescope pointing jitter and primary mirror deformation problems (i.e., conditions that normally prevent an imaging capability).

An overview of our densified pupil spectroscopy concept is shown in Figure 1. First, the densified pupil spectrometer divides the telescope aperture into a number of sub-pupils (each of which is densified with two lens arrays). Each of these divided and densified sub-pupils can be treated as a point source, which means that we can use a simplified spectrometer to acquire the spectra of the densified sub-pupils on the detector plane (an optical conjugate of the primary mirror) by placing the divided and densified sub-pupils on the entrance slit of the spectrometer. The spectral resolution of our method is determined by the diameter of the beam that is formed on the dispersive element. For higher spectral resolutions, therefore, larger beam diameters are required. With our concept we can thus realize spectroscopy of the sub-pupils on the telescope aperture with simplified optics.

Figure 1. Conceptual design of the densified pupil spectroscopy concept. The downward-pointing arrows represent the pupil planes that are optical conjugates of the primary mirror. Cross-sectional views of the exit, entrance, and detector pupil planes are shown in the bottom row. P: Pupil. f: Focal length.

Our densified pupil spectroscopy approach has several advantages compared with conventional spectrometers, in terms of spectrophotometry. First, by producing an optical conjugation between the telescope aperture and the detector plane, we can significantly reduce the amount of systematic noise that arises from telescope pointing jitter and distortion of the primary mirror. By optically dividing the telescope aperture into a number of sub-apertures, and therefore producing multiple equivalent spectra simultaneously, we can also provide highly reliable scientific data with our concept. In this way, we can obtain scientific data without concern for defective detector pixels and pixels being hit by cosmic rays. In addition—for cases where the systematic noise is randomly added to the data—we can further reduce the amount of noise by averaging the many equivalent spectra. It is also possible to apply various non-parametric data analysis techniques, such as independent component analysis,⁷ to our method instead of the averaging operation. Finally, the division of the telescope aperture into multiple small sub-apertures allows us to mitigate the optical requirement of the primary mirror. Our method can thus be used to reduce systematic noise (i.e., a major issue in current space transit spectroscopy) and potentially to achieve observations that are limited by shot noise rather than by instrumental systematic noise.

An optimized design of our pupil densified spectrometer, which is suitable for planned or proposed cryogenic telescopes such as the Space Infrared Telescope for Cosmology and Astrophysics (SPICA)⁸ and the Cryogenic Aperture Large Infrared. Space Telescope Observatory (CALISTO),⁹ is illustrated in Figure 2. In this design, the diameter of the telescope's primary mirror is 2.5m, the observation wavelength range is in the 10–20μm range (for detection of ozone and carbon dioxide molecules in planetary atmospheres), and the spectral resolution at 10μm is set to 100. We also restrict the field of view (up to 10arcseconds) by placing an aperture mask on the telescope's focal plane to remove background stars. We use an additional mask (with the same design as shown in Figure 1) positioned on the output pupil to divide the collimated beam into 20 sub-pupils. The two microlens arrays are used to densify each sub-pupil with a densification factor of 10, and the densified sub-pupils—with diameters of 200μm—are then formed on the output pupil (corresponding to the entrance slit of the spectrometer). Twenty spectra are independently acquired on the detector plane, but the light beam of only one sub-pupil, positioned at the center of the entrance slit, is shown in Figure 2.

Figure 2. Design of an optimized (e.g., for cryogenic telescopes) densified pupil spectrometer optical system. The optical system is shown in the upper left combined with a 2.5m-diameter telescope. The purple, blue, green, yellow, and red lines represent the optical paths at 10, 13, 15, 17, and 20μm, respectively. Measurements are given in mm. The spectrometer detector has 1000×1000(1k × 1k) pixels. φ: Diameter.

The average (mean) and maximum (i.e., worst) values of instrumental systematic error that can be caused by pointing jitter of ±0.1arcsecond root mean square (for a case where the flat fielding accuracy is 0.07%) are given in Table 1.¹⁰ Since the photometric stability of our system is much better than 10ppm, our concept can potentially provide an opportunity to spectrally characterize the emissions from temperate super-Earths around nearby late-type stars. In addition, our system can be used to study the atmospheres with transmission spectroscopy at a resolution of 20km (i.e., the thickness of the ozone and carbon dioxide layers in the Earth's atmosphere).¹¹

In summary, we have proposed densified pupil spectroscopy as a new method for the spectral characterization of transiting exoplanets. According to our numerical calculations, our system can be used to reduce instrumental systematic noise (caused by pointing jitter) down to 10ppm. Our methodology can also potentially enable the characterization (by transmission spectroscopy and secondary eclipse) of temperate super-Earths with thin atmospheres orbiting nearby late-type stars. In the next stages of our work we will start to build a test model based on our optical design (see Figure 2) so that we can investigate the stability of the real system.

The author is grateful for all the people who supported this high-precision spectrophotometry project.