Hiroaki Imada

Development of high-throughput silicon lens and grism with moth-eye antireflection structure for mid-infrared astronomy

We have been developing high-throughput optical elements with the moth-eye structures for mid-infrared optical systems. The moth-eye structures are optimized for the wavelength of 25-45μm. It consists of cones with a height of 15-20μm arranged at an interval of 5μm. They are formed on silicon substrate by electron-beam lithography and reactive ion etching. As a verification of the usefulness of moth-eye, a double-sided moth-eye silicon plane was fabricated. It shows a transmittance increase of 60% compared with the unprocessed silicon plane. As the first trial of the moth-eye optical element, two silicon lenses with single-sided moth-eye were fabricated. One is a plane-convex lens with the moth-eye on the convex surface. The size of the moth-eye formed region is 30 mm x 30 mm. Its focal length is 186 mm. The other one is a biconvex lens with moth-eye formed region of Φ 33 mm and a focal length of 94 mm. Uniform moth-eye pattern was fabricated especially for the second lens sample. Imaging test with the first sample showed that neither image degradation nor focal length variation was induced by the moth-eye fabrication. As a step to grism with moth-eye, a moth-eye grating sample was fabricated. The grating pattern (Grating constant: 124.9μm, Blaze angle: 4 deg) was successfully fabricated with anisotropic etching. Moth-eye patterns were fabricated on the grating surface. Although the resulted moth-eye was successfully fabricated in the most regions, some non-uniformity was found. It can be attributed to unevenness of resist coating, and improvement of coating method is needed.

Fabrication and tolerances of moth-eye structures for perfect antireflection in the mid-infrared wavelength region

Mid-infrared, 25 - 45 microns, is a very important wavelength region to investigate the physics of lower temperature environments in the universe. There are few transparent materials in the range of mid-infrared except silicon. However, the reflection on a silicon surface reaches 30 % because of its high refractive index (~3.4). To apply silicon to mid-infrared astronomical instruments, we need a way of antireflection and have adopted a moth-eye structure. This structure keeps durable under cryogenic environments, which is advantageous to mid-infrared instruments. We have fabricated three samples of the moth-eye structure on plane silicon surfaces by electron-beam photo-lithograph and reactive ion etching. The structures consist of many cones standing on silicon surfaces. We have substantiated the transmittance of 96 % or higher in the wide range of 20 - 50 microns and higher than 98 % at the maximum. The transmittance of moth-eye surfaces, however, is theoretically expected as 100 %. We have examined the discrepancy between the transmittance of the theory and fabrications with electromagnetic simulations. It has been revealed that shapes of the cones and gaps at the bottom of the cones seriously affect the transmittance. We have estimated a few tolerances for manufacturing the moth-eye structures achieving sufficient transmittance of nearly 100 %.

Condition of Optical Systems Independent of Frequency for Wide Field-of-View Radio Telescopes

In this paper, we present a condition of optical systems to form images independent of frequency. The condition independent of frequency in case of a single Gaussian beam on an optical axis has been known, but that in case of a beam propagated off the axis or tilted beam, which appears in a wide field-of-view (FOV) telescope, has not been known. We first show relations between an arbitrary electric field on an object plane and an induced one on an image plane after passing through a lens with calculating Fresnel diffraction integrals. If the lens formula is met, there is a one-to-one correspondence between points on the object and image plane. This result enables to use geometrical optical methods. The condition and relations derived here are confirmed by simulations. We also applied them to a wide-FOV telescope.

Design of wide-field Nasmyth optical system for a submillimeter camera

Abstract. A wide-field Nasmyth optical system that connects a planned 10-m Ritchey-Chrétien telescope to a submillimeter camera is reported. This diffraction-limited system has a 1-deg field of view at 850 GHz, filled with a more than 20,000-pixel camera. The system enables us to carry out large field surveys of distant galaxies within reasonable time scales. The size of the Nasmyth optics is reasonably compact and its cryogenic part including the vacuum window, cryogenic lens, and IR block filters can be built using existing technologies at a reasonable cost. This type of optical system can be applied for the optical design of millimeter, terahertz, and other submillimeter instruments.

Real-time point-diffraction interferometer and its analytical formulation.

We propose a novel wavefront sensor and study its performance with an analytical formulation. The sensor has a polarizing point-diffraction beam splitter. Using transmitted and reflected beams, we can build a real-time point-diffraction interferometer with high precision and efficiency. Our analytical studies reveal that wavefront errors might be measured incorrectly and that less precise estimates of wavefronts appear as the pinhole radius Rpin is increased. An investigation of propagating uncertainties shows that the wavefront measurement can be calibrated by estimating the pinhole effects and the polarizing properties with a precision of a few percent. Based on these studies, Rpin should be smaller than half of the Airy disk for better performance.

Design of wide-field Nasmyth optics for a submillimeter camera

We designed wide FoV (1 degree) Nasmyth optics which transformed the f/6 Nasmyth focus to f/1 at a 850GHz superconducting camera for a planning 10-m Ritchey-Chrétien telescope. This optical system consists of reflecting mirrors at room temperature and a refractive lens at 4K. It enables us to carry out wide FoV imaging observations at the diffraction limit (Strehl ratio < 0.89) with a more than 100,000 pixel camera equipped in a 10-m telescope. The size of this system is reasonably compact (whole size:1.6 mx3.3 mx2.6 m, cryogenic part:0.7 mx0.7 mx1.0 m). The cryogenic part of this system such as vacuum window, cryogenic lens and IR block filters can be made with existing technologies at reasonable cost. The optical system can extend to the millimeter wave and the terahertz domain.

Development of high-throughput silicon lens and grism with moth-eye anti-reflection structure

Anti-reflection (AR) is very important for high-throughput optical elements. The durability against cooling is required for the AR structure in the cryogenic optics used for mid-infrared astronomical instruments. Moth-eye structure is a promising AR technique strong against cooling. The silicon lens and grism with the moth-eye structure are being developed to make high-throughput elements for long-wavelength mid-infrared instruments. A double-sided moth-eye plano-convex lens (Effective diameter: 33 mm, Focal length: 188 mm) was fabricated. By the transmittance measurement, it was confirmed that its total throughput is 1.7± 0.1 times higher than bare silicon lenses in a wide wavelength range of 20{45 μm. It suggests that the lens can achieve 83±5% throughput in the cryogenic temperature. It was also confirmed that the moth-eye processing on the lens does not modify the focal length. As for the grism, the homogeneous moth-eye processing on blaze pattern was realized by employing spray coating for the resist coating in EB lithography. The silicon grism with good surface roughness was also developed. The required techniques for completing moth-eye grisms have been established.

Prototype design and evaluation of the nine-layer achromatic half-wave plate for the LiteBIRD low frequency telescope

LiteBIRD is a satellite project to measure the polarization of the CMB with an unprecedented accuracy. LiteBIRD observes all sky for three years at the sun-earth second Lagrange point. The goal of LiteBIRD is to observe the B-mode polarization at large angular scales and to measure the tensor-to-scaler ratio r with an accuracy less than 0.001, exploring the energy scale of the inflation. In order to mitigate the system 1/f noise and systematics, we plan to use continuous rotating half-wave plates (HWPs) as a polarization modulator at each aperture of two telescopes. One of the telescopes, called a low frequency telescope (LFT), covers the frequency range from 34 to 270 GHz, requiring the HWP to have a high modulation efficiency in the wide bandwidth. We employ a Pancharatnam-type achromatic HWP (AHWP) to achieve the broadband coverage. The AHWP consists of nine layer stacked HWPs with the optic axes mutually rotated by the angles optimized for the LFT bandwidth. In this paper, we report our development status of the nine layer AHWP and measurement results on the modulation efficiency and the phase as a function of frequency.

Trade-off studies on litebird reflectors

The LiteBIRD satellite aims at detecting a signature imprinted on the cosmic microwave background (CMB) by the primordial gravitational wave predicted in inflation, which is an exponentially expanding era before the hot big bang. The extraction of such weak spiral polarization patterns requires the precise subtraction of our Galaxy’s foreground emission such as the synchrotron and the dust emission. In order to separate them from the CMB by using their spectral shape differences, LiteBIRD covers a wide range of observing frequencies. The main telescope, Low Frequency Telescope (LFT), covers the CMB peak frequencies as well as the synchrotron emission. Based on the required sizes of optical elements in the LFT, an order of one meter, the telescope will consist of reflectors rather than lenses since the latter is limited in size availabilities of the corresponding materials. The image quality analysis provides the requirements of reflector surface shape errors within 30um rms. The requirement on surface roughness of 2μm rms is determined from the reflectance requirement. Based on these requirements, we have carried out tradeoff studies on materials used for reflectors and their support structures. One possibility is to athermalize with aluminum, with the expected thermal contract of 0.4% from room temperature to 4-10 K. Another possibility is CFRP with cyanate resin, which is lighter and has negligibly small thermal contraction. For the reflector surface shape measurements including in low temperature, photogrammetry is a strong candidate with suitable accuracy and dynamic range of measurements.

Point-diffraction interferometer for radio telescopes

We propose a novel wavefront sensor for radio telescopes with a point diffraction interferometer. A point-like object is set at a pupil plane and the electric field at the focal plane is measured. A receiver dedicated to the novel sensor is prepared which has delay lines to make interferograms. A procedure to estimate the electric field at the pupil is shown analytically. Numerical simulation reveals that the proposed system allows us to measure the phase of the electric field at the pupil with a precision of about λ/28.