2.1.

Surface relief grism

As shown in figure 3 left, a surface relief (SR) grism is consisted a transmission grating and prism, vertex angle of which is adjusted to redirect the diffraction beam straight along the direct vision direction at a specific order and wavelength. This type of grism has been used for astronomical instruments until multichannel detectors such as a CCD had developed. Especially, a replica of a blazed grating is generally used for a low dispersion grism of visible and near infrared instruments because it is moderate prices and sufficient diffraction efficiency for general purpose [4]. However, as groove period of a SR grating is close to functional wavelength, diffraction efficiency behaves peculiarly. The cause of the phenomena is an electromagnetic coupling of higher order diffraction and periodic grating structure, namely, anomaly. Figure 3 right shows calculated and measured diffraction efficiency versus normalized period of a SR transmission grating with refractive index of 1.5. The calculations are carried out by means of the analysis program valid for gratings of the rigorous coupled-wave analysis (RCWA) method [5]. The efficiency of the SR grating become oscillatory decrease below 5 and steeply drops at 2 in normalized groove period. Measured efficiencies of SR grisms (closed dots) are compatible with the efficiency cave of the RCWA calculation.

Fig. 3

Schematic representation (left) and diffraction efficiency (right) of surface relief grism.

The grism with higher order diffractions, that is, Echelle type grism are used for the high dispersion spectrograph on astronomical observations. High index material is employed for the prism of a high dispersion grism if the grism size is limited by space of an instrument since dispersion is proportional to optical path difference caused by the grating (Fig. 1). However when a grism consists of a high index prism and replicated grating, the vertex angle of the prism is limited by a critical angle between the high index material and resin of replica. Refractive indices of the prism and replica of a SR grism are 2.3 and 1.5 respectively for example, and a ray enters vertically from the prism side, the critical angle is 40.7 degree, that is, a vertex angle of the prism has to be smaller than the critical angle. In the case of the grism tilts to clockwise in figure 3 left, critical angle becomes larger, and optical axes are sifted in parallel between the incident and exit ray on the grism. The following optics of an instrument becomes lager to avoid the vignetting at a result of the optical axes shift. In these reason, a SR grism with high dispersion is essentially grooved directly onto a high index material that is called a solid grating.

2.2.

Volume phase holographic grism

The volume phase holographic (VPH) grism consists a thick VPH grating sandwiched between two prisms as specific order and wavelength is aligned the direct vision direction (Fig. 4 left). As show in figure 4 right, a thick VPH grating archives very high efficiency from 1 to 5 in normalized period of index modulation [5]. In the case of the VPH grism, refractive indices of prisms and VPH grating are 2.3 and 1.5 respectively α is obtained 63.6 degree from Eq.4 in Appendix A. As mentioned in subsection 2.1, the vertex angle of the prism is limited by the critical angle between a grating replica and prism. It means that a VPH grism has capability of higher dispersion spectroscopic observations compared with a SR grism. However a thick volume phase grating was very difficult to fabrication owing to recoding media. Dichromate gelatin had been the unique recording media for a thick volume phase hologram in practical use [6], preparation of recording material and development are complicated and critical because they are wet process.

Fig. 4

Schematic representation (left) and diffraction efficiency (right) of volume phase holographic grism.

We applied a photosensitive resin developed by Nippon Paint Co.Ltd. as a recording material of VPH grating. The photosensitive resin could overcome the disadvantages of dichromate gelatin [7-8]. The photosensitive resin consists of radically polymerizable monomer (RPM) with higher refractive, cationically polymerizable monomer (CPM) with lower refractive index, dyes, and photo-initiator. By accepting the radical from dyes absorbed visible light (470-600nm), the RMP is polymerized (Fig.7). Consequently, the monomer of RMP produces the concentration gradients at the boundary between the polymerized part and the unpolymerized part. Because of monomer diffusion, the refractive index of the polymerized part becomes higher. RPM and CPM are simultaneously polymerized by the photo-initiator with ultraviolet irradiation, and the refractive index modulation is fixed.

Fig. 5

Schematic representation (above) and picture (below) of optical system for VPH grating exposure.

2.3.

Grisms for Subaru Telescope

Several types of diffraction grating are developed for instruments of the 8.2m Subaru Telescope on Mauna Kea, Hawai [9-11]. Trispec grisms for visible, J-H band and K band were made by replication. The solid grism of Cytop (fluorocarbon polymers) for the Coronagraphic Imager with Adaptive Optics (CIAO) with the resolving power of 600 at near infrared had been successfully fabricated by using a 3D profiling machine with nano-precision and diamond turning method. The Cytop is transparent from 200 to 2,500 nm. Moreover, a solid grism of gallium arsenide (GaAs) or ZnSe with higher dispersion for CIAO ranging from 0.9 to 5 μm are under developing. The Faint Object Camera And Spectrograph (FOCAS) is providing eleven grisms with the resolving power from 250 to 7,000 [12-16].

2.4.

FOCAS grisms

The physical size of a FOCAS grism is 110 by 106 in mm, the maximum thickness along the optical axis is 106 mm. Five FOCAS grisms among eleven were made by replication onto a prism of conventional optical glass (Fig.6 right to center left) and residual six are VPH grisms (Fig.6 left). Grisms of high dispersion with the first diffraction order were fabricated by replication. However, measured efficiencies of the grisms are 45 to 48 % at the each blazed wavelength as the result of anomaly (Fig. 3 left, Normalized period: 2.70 and 2.78). The value could not be sufficient for the specifications of FOCAS.

Fig. 6

FOCAS grisms. From right, replicated grisms with low dispersion (R=500 with 0.4” slit), middle dispersion (R=1,400) and Echelle type (higher order diffraction) with high dispersion (R=3,000), VPH grism with high dispersion (R=3,000)

We employed VPH grisms (Fig. 4 left) for the high (R=3,000) and very high (R=7,000) dispersion grisms of FOCAS with the first diffraction order because a VPH grating is suitable for a higher dispersion application as shown in figure 4 right [5]. The VPH grism with high dispersion consist of a VPH grating two prisms of a conventional optical glass (Fig. 6 left). The very high dispersion grisms with the first order diffraction consist of a VPH grating and two high-index prisms of zinc selenide (ZnSe, n=2.6) as shown in figure 7.

Fig. 7

ZnSe VPH grism for FOCAS with very high dispersion (R=7,000).

2.5.

Quasi-Bragg grism

The VPH grating inheres ideal diffraction efficiency on a higher dispersion spectroscopy at a specific wavelength region, otherwise, diffraction efficiencies decrease on higher order diffractions. We propose an grism consists a comb like grating (Fig. 8), we called quasi-Bragg grating, and two high-index prisms. The quasi-Bragg grism has both advantage of VPH and Echell type grism (Fig. 9) [17-18]. We are developing a comb like grating by means of semiconductor process.

Fig. 8

Schematic representation of “Quasi-Bragg grating”.

Fig. 9

Calculation result of diffraction efficiencies of Quasi-Bragg grating [18]. (Al refractor, d=15.27 μm, A =5.71 μm, w=0.029 μm, n_g = 1.50, Bragg angle: θ_B = 20.51deg)

3.1.

Mid-infrared high dispersion spectrograph

IRHS is under planning design study as a next generation instrument for the 8.2m Subaru telescope. IRHS is aiming resolving power of R= λ/Δλ= 200,000 at 10μm, in order to observe vibrational transitions of molecule in circum-stellar and dark clouds for instance. Such a high dispersion spectrograph requires a dispersing element or moving mirror with minimum 2m in an optical path difference. A Fourier transform spectrometer (FTS) is usually applied as a high dispersion spectrometer for laboratory use from middle to far infrared because of the small size and low cost of the instrument compared with a grating spectrometer. Although FTS has disadvantages with background noise and atmospheric turbulence, only several tens or hundreds astronomical objects in the total sky can be observed around 10 μm. On the other hand, a midinfrared high dispersion spectrograph with a conventional grating of reflection type (Fig. 1a) as the dispersing element requires a large optical installation. Since a collimated beam of 40cm in diameter should be used for the conventional grating spectrograph with a resolving power of 200,000 at 10μm, the total volume of the instrument covered with a cooled vacuum chamber (below 50K) is nearly 100m³. It is huge enough even for the Nathmith focus of the Subaru telescope.

3.2.

Trial fabrications for solid gratings

The germanium immersion grating for instance could reduce 1/64 as the total volume of a spectrograph with a conventional reflection grating since refractive index of germanium is over 4.0 from 1.6 to 20μm. The size of IRHS become 2m³ covered with a cooled vacuum chamber [19]. The immersion grating is not only a powerful dispersion element for grand-based applications, but also an ideal dispersion element for space applications (Fig.10).

Fig. 10

Mid-infrared high dispersion spectrograph with R=100,000@10μm for SPICA (3.5m space infrared observatory)

In order to fabricate a solid grating with a high index material, numerous studies on micro-machining methods have been carried out by researchers and engineers. These include a precise ruling-engine, anisotropic chemical etching and so on [20-24]. To our knowledge, the KRS-5 grism used for near to middle infrared can be fabricated by using a precise ruling-engine [23]. However, since KRS-5 is a mixed crystal of TlBr and TlI, a homogeneous and large block is difficult to grow.

We had also performed trials of various methods for grating fabrications, resinous bonded diamond grinding, ion etching (Fig. 11) and laser ablation (Fig. 12) [25-27], for example. However solid gratings with deep grooves exceed 1μm in depth, are difficult to fabricate with these methods. Finally, we had successfully fabricated an immersion grating for the prototype IRHS by using a 3D profile grinding/turning machine with nano precision and grinding cups of cast iron with electrolytic dressing method (Fig. 13, 14) [28-31].

Fig. 11

Lithium niobate grism fabricated by oblique ion etching (left) and cross section of the grism (right).

Fig. 12

Schematic representation of grating fabrication by laser abrasion (left) and SEM picture of germanium grooves fabricated by laser abrasion (right).

Fig. 13

Fabrication of germanium immersion grating by means of nano-precision machine (left) and picture of prototype immersion grating for IRHS (right).

Fig. 14

Grooves shape of immersion grating fabricated by grinding cups of cast iron and electrolytic dressing method.

3.3.

Fabrication of immersion grating

The immersion gratings of prototype IRHS were designed for a spectrograph with a resolving power of 50,000 at 10μm or 250,000 at 2.0μm. The sizes of the prototype immersion gratings are 30 x 30 mm, 72mm in length and vertex angle of 68.75 degree. Groove spacing are 100μm for the first, 250μm for the second and third, 600μm for the forth and fifth fabrications. The grooves are slightly tilted to the incident aperture of the gratings to avoid influence of reflection at the incident aperture. The material of the immersion grating was germanium single crystal except the third fabrication. At the third fabrication, GaAs single crystal was chosen for the immersion grating because it was planed to use for a near infrared spectrograph, and GaAs is transparent from 0.9μm and its refractive index is about 3.4 at 1.0μm.

The wave front error of the fourth and fifth grating are acceptable for a prototype immersion grating at 10 μm if the maximum value of wave front error inside germanium is set up one eighth wave in rms, that is, 312.5nm in the air. We had obtained doubtful values of transmittance measured by using a conventional spectrophotometer because grooves are tilted about 0.8 degree to the incident aperture, and an incident and exit ray are angled about 3.2 degrees at a groove. We could say that the diffraction efficiency of the third, fourth and fifth gratings are at least 30% from 2 to 16 μm. Accurate diffraction efficiencies of gratings will measure by the prototype IRHS of under construction.

Figure 15 shows measurement for far field images of a diffraction beam. A beam of the CO₂ laser as a light source at 10.6 μm was transformed to a Gaussian beam by means of a spatial filter. Figure 16 shows the cross sections of the far field images of an incident aperture and the diffraction beams of the gratings mentioned above. The dotted line is a far field image of the reflected beam of the incident aperture. The solid lines are the far field images of diffracted beams of immersed grooves. The FWHM of the ideal image for the measurement system is 220μm. The FWHM of the images of the third, fourth and fifth gratings are 280, 259 and 302μm respectively. The far field image of the third grating has side lobes with large amplitude caused by fatal wave front error. The FWHM of far field images of the fourth grating expands 18% which is compared with the ideal image, and it is seen a Roland ghost which amplitude is about 17% of the main lobe. The FWHM of the fifth grating expands 37%, and it is seen a Roland ghost which amplitude is about 14% of the main lobe. The expansion and Roland ghost implies a wave front error with large scale of a grating, that is, a deviation of the groove interval.

Fig. 15

Measurement of far-field image of immersion grating.

Fig. 16

Cross section of far-field image of immersion gratings. No. 4: R=44,000@10μm.