SPICA (Space Infrared Telescope for Cosmology and Astrophysics) is an infrared astronomical mission led by the Japan Aerospace Exploration Agency (JAXA) in collaboration with the European Space Agency (ESA) and international consortiums in Japan, Europe, United States, the Republic of Korea and Taiwan . In early 2020s, SPICA will be launched into a halo orbit around the second Lagrange point of the Sun-Earth system. The mission lifetime is 3 years (minimum) or 5 years (design). SPICA has a Ritchey-Chretien telescope composed of monolithic mirrors with 3.0m effective pupil diameter/3.2m physical diameter in the current design. The payload modules of SPICA are cooled down to less than 6K by multiple mechanical cryocoolers without a liquid Helium cryostat in order to reduce thermal background radiation emitted by itself. Cryogenic temperature will make SPICA more sensitive than passively cooled satellites of the James Webb Space Telescope and the Herschel Space Observatory in mid- and far-infrared region. Primary scientific goal of SPICA is understanding how galaxies, stars and planets form and evolve as well as the interaction between the astrophysical processes that have led to the formation of our own Solar System.
To achieve above scientific objectives, the Focal-Plane Instruments Assembly (FPIA) of SPICA is designed as shown in Fig. 1. FPIA consists of focal plane instruments (FPIs) and the Instrument Optical Bench (IOB). The FPIs for SPICA will be equipped to achieve significant progress for these main scientific objectives. Proposed instruments are a Mid-infrared Camera and Spectrometer (MCS), an imaging Fourier-transform spectrometer operating in far-infrared (SAFARI), a coronagraphic instrument (SCI) and focal plane cameras used for fine guidance (FPC). United States may provide another instrumentation.
MCS is a general purpose instrument for mid-infrared imaging and spectroscopy, covering the wavelength region of 5 – 38µm with Si:As and Si:Sb detectors. We have been studying the MCS optics toward the SPICA international review which defines instruments and functions onboard. Taking account of the wide wavelength coverage of 5 – 38µm, we adopt reflective optical system for the most part of MCS to minimize problems due to chromatic aberration as well as changes in physical properties of materials from ambient temperature to cryogenic temperature. Under rigid limitations of size and weight assigned to MCS in FPIA, high optical specifications, such as wide field of view, small F-number and large spectral resolving power, are required for scientific goals. In order to realize the specifications, we employed an optical design method proposed by Araki  for compact reflective optics.
In this paper, we firstly summarize the specifications of constituent optical modules of MCS. Secondly, we briefly describe the optical design method based on Araki’s technique. Finally, we show optical layouts, expected optical performance and tolerance analysis of each optical module of MCS.
Fig. 2 shows the structure of the MCS optics. MCS consists of 2 relay optics and 4 scientific optical modules. Table I summarize the specifications of the scientific modules. Field of view (FOV) and field definition assigned to each module is in Fig. 3. Each module of MCS has its own field in the telescope focal plane. Selection of module will be done by telescope pointing.
SPECIFICATIONS OF SCIENTIFIC OPTICAL MODULES OF MCS
Short and Long Fore-optics are optics relayed to following scientific optical modules. Those two Fore-optics are mirror-image symmetric to each other with optically equivalent performance. Fore-optics compensates geometrical ray aberrations induced by the telescope and provides diffraction-limited images with the scientific optical modules. The telescope secondary is adopted as a pupil, and a filter wheel can be installed at an image conjugate of the pupil inside Fore-optics. Each scientific optical module has two channels (-S for short wavelength and -L for long wavelength) to cover wide wavelength ranges. WFC (Wide Field Camera) has two 5 arcminutes square FOVs. WFC-S covers the wavelength range from 5 to 25 micron and WFC-L covers the wavelength range from 20 to 38 micron. LRS (Low Resolution Spectrometer) adopts prism dispersers and covers the wavelength range from 5 to 38 micron (optional: 5 to 48 micron) with spectral resolving power, R, of 50 – 100. It also has two channels, LRS-S and LRS-L. These channels share the same FOV by means of a dichroic beam splitter. MRS (Mid Resolution Spectrometer) has integral field units by image slicer and echelle gratings with cross-disperser gratings. It covers the wavelength range from 12.2 to 23.0 micron with R ∼ 1000 by MRS-S and the wavelength range from 23.0 to 37.5 micron with R ∼ 2000 by MRS-L. HRS (High Resolution Spectrometer) covers the wavelength range from 12 to 18 micron with R ∼ 20000 - 30000 (HRS-L), and we also have studied optional short wavelength channel which covers the wavelength range from 4 to 8 micron with R ∼ 30000 (HRS-S). HRS realizes high spectral resolution using immersed echelle gratings and refractive optics.
All optical modules except for HRS adopt reflective optical system. It is beyond the scope of this paper to argue the refractive optics of HRS in detail. For further description of HRS, see Kataza.
OPTICAL DESIGN METHOD
We have carried out the design of the MCS reflective optics using the aberration analysis proposed by Araki and an automatic design technique based on the method of damped least square with a commercial ray-tracing software.
In conventional design of reflective optics, with the idea of so-called “de-centered optical systems”, we often face the problem that we cannot optimize the optical systems with a fixed optical framework. Araki redefined “off-axial optical systems” as an extended concept of co-axial optical systems, where deflection surfaces are arranged along the folded reference axes. Fig. 4 shows the concept of the off-axial optical systems. In the off-axial optical systems, a reference ray, originating from an object plane on an optical axis and traveling along the optical axis, strikes vertexes of all subsequent reflection surfaces. As a matter of course, a reflection angle of the reference ray against a surface normal at a vertex equals a corresponding incident angle. As shown in Fig.4, z-directions of local reference axes are parallel to surface normals at the reflection surfaces or traveling directions of the reference ray between the reflection surfaces. In the aberration analysis for the off-axial optical systems, each constituent surface is expressed in the following equation on a local coordinate:
Using this expression, we can optimize the surface configuration without changing the framework of the reference axes. Since mirrors can be placed freely as designer’s intent, it is suitable for design of compact reflective optics such as head mount displays.
Here is the outline of the design method.
1) Design an optical power distribution of an optical system with desired focal length using conventional paraxial analysis for co-axial optical system.
2) Arrange flat mirrors in the optical system with consideration of surface interference and interspace limitation. Each flat mirror corresponds with a optical power determined above. A separation distance between the flat mirrors is fixed with a distance between corresponding optical powers in the paraxial design.
3) Add optical powers to the flat mirrors without azimuthal dependence of paraxial quantities by the following formulas:
where Φ is the optical power assigned to the mirror and θ is the incident angle of the reference ray against the surface normal of the mirror.
4) Optimize higher order terms of the free-form surfaces using the automatic design of the software under required constraints to achieve specifications.
5) Confirm as-built optical performance by tolerance analysis based on the Monte Carlo method.
Fig. 5 shows a bird’s view of the Short Fore-optics layout. Long Fore-optics and Short Fore-optics are mirror-image symmetrical with respect to a plane including the optical axis of the telescope. The optics consists of 6 free-form surface mirrors, a pick-off flat mirror, a folding flat mirror and a hyperboloid mirror. We adopted the optical power distribution of Three-Mirror Korsch Objective  to achieve wide FOV and moderately fast F-number. In order to use optical filters of ϕ30mm, the pupil image diameter was reduced to ϕ24.44mm. At the position of the intermediate pupil image, we can install a disk-shaped filter wheel of ϕ260mm×50mm. During optimization process, there is a trade-off between the size and the wavefront error of the pupil image. We assigned high priority to minimization of the pupil image size. Consequently, the wavefront errors at the pupil image position are larger than a wavelength unit at wavelength, λ, of 5 micron. The hyperboloid mirror is located after the folding flat mirror to pick up beams and make F-number slower for MRS or HRS. The effective F-numbers of Fore-optics are f/7.3 (WFC/LRS) and f/8.0 (MRS/LRS).
Fig.6 shows a top view of the combination of Short Fore-optics and WFC-S. f/7.3 output beams of Short Fore-optics deflect off the final folding mirror into the compartment of WFC-S. The angle between reference axes of Short Fore-optics and WFC-S on the top view is 115 degrees. Fig.7 shows a side view of WFC-S only. WFC-S consists of 5 free-form surface mirrors and a folding flat mirror. Like Fore-optics, the size of the intermediate pupil image inside WFC-S was reduced to ϕ24.26mm for the use of ϕ30mm optical filters with a ϕ260mm×50mm filter wheel. The effective F-number of WFC-S is f/11.7 which realizes 5’x5’ FOV and Nyquist sampling of diffraction-limited images at λ = 5µm on the 2KX2K Si:As detector with pixel size of 25µm.
Fig.8 shows a top view of the combination of Long Fore-optics and WFC-L. The angle between reference axes of Long Fore-optics and WFC-L on the top view is 115 degrees. Fig.9 shows a side view of WFC-L only. WFC-L consists of 6 free-form surface mirrors. Like Fore-optics and WFC-S, the size of the intermediate pupil image inside WFC-L was reduced to ϕ23.90mm for the use of ϕ30mm optical filters with ϕ260mm×50mm filter wheel. The effective F-number of WFC-L is f/4.2 which matches 5’x5’ FOV. Nyquist sampling of diffraction-limited images is achieved at λ > 7µm on the 1K × 1K Si:Sb detector with pixel size of 18µm.
Fig.10 shows a top view of the combination of Long Fore-optics and LRS. The final folding mirror of Fore-optics reflects f/7.3 output beams into the compartment of LRS. Fig. 11 shows a side view of LRS only. LRS consists of 15 free-form surface mirrors, 4 folding flat mirrors and 2 dispersion prisms. The LRS optical bench is in the back of the optical bench of Long Fore-optics. The first 3 folding flat mirrors after the focal plane of Long Fore-optics make dispersion direction of prisms parallel to the plane of the optical bench. The dichroic beam splitter after the first collimator optics reflects λ < 20µm beams into LRS-S and refracts λ > 20µm beams into LRS-L. 2.5 ‘slits are installed at re-imaging planes formed by the first camera optics for both LRS-S and LRS-L. After the second collimators, a KBr prism with apex angle of 62deg and a CsI prism with apex angle of 58deg are installed for LRS-S and LRS-L respectively. Finally, f/5.0 and f/1.7 camera optics make Nyquist sampling of diffraction-limited images at λ = 10µm on the 2Kx2K detector of LRS-S and at λ = 20µm on the 1Kx1K detector of LRS-L respectively.
Fig. 12 shows a top view of the combination of Long Fore-optics and MRS. The hyperboloid mirror of Long Fore-optics reflects f/8.0 output beams into the compartment of MRS. Fig. 11 shows a side view of MRS only. MRS consists of 16 free-form surface mirrors, 2 folding flat mirrors, 2 integral field units, 2 cross-dispersion gratings and 2 echelle gratings. The optical bench of MRS are placed on the outside wall of IOB. After the focal plane of Long Fore-optics, 2 free-form mirrors and a folding flat mirror make collimated beams traveling parallel to the optical bench. The dichroic beam splitter reflects λ < 23µm beams into MRS-S and refracts λ > 23µm beams into MRS-L. The integral field units (IFUs) follow the first camera optics for both MRS-S and MRS-L. The optics of both MRS-S and MRS-L IFUs was based on the idea of the advanced image slicer proposed by Content . Fig.14 shows a bird’s view of the MRS-L IFU for instance. The IFUs place multiple reflective slits at the refocus position of the first camera optics. The multiple slits are placed almost in parallel but slightly tilted to each other. Then, light rays reflected at the different slits travel into different directions, where different camera optics of spherical mirror are placed, and re-imaged on a pseudo slit position being arranged to be laid in a line. Multiple tilted mirrors are placed on the pseudo slit position to improve telecentricity for design of following spectrometers. Folding flat mirrors and the second collimator optics follow IFUs. Cross-dispersion gratings with pitch of 51µm (MRS-S) and 78.6µm (MRS-L) and echelle gratings with pitch of 110µm (MRS-S) and 380µm (MRS-L) are placed near the pupil image made by the second collimator optics. Finally, f/3.3 and f/1.9 camera optics form echellograms of pseudo slit images on the 2Kx2K detector of MRS-S and the 1Kx 1K detector of MRS-L respectively.
Expected Optical Performance
Fig. 15 shows footprint diagrams and spot diagrams of some representative field images on the focal plane of Fore-Optics. Strehl ratios of all field images at λ = 5µm are larger than 0.825. The maximum distortion expressed as a percentage of the paraxial image height at the WFC/LRS focal plane is 4.7%. It does not have a significant impact on the subsequent optical system. In the calculation of the Strehl ratio, we did not take a diffraction effect by obscuration of a baffle of the telescope secondary mirror into consideration.
Fig. 16 shows footprint diagrams and spot diagrams of some representative field images on the focal planes of WFC-S and WFC-L. Strehl ratios of all field images at λ = 5µm are larger than 0.872 for both WFC-S and WFC-L. The maximum distortions the focal planes are 5.45% and 5.79% for WFC-S and WFC-L respectively. We can correct the image distortions in data reduction processes. Although operating wavelength of WFC-L is larger than 20µm, we have designed the WFC-L optics to achieve diffraction-limited image resolution at λ = 5µm for a back-up use from WFC-S.
Fig. 17 shows footprint diagrams and spot diagrams of some representative field images on the focal planes of LRS-S and LRS-L. Because there is a trade-off between image quality and distortion, we set high priority on the imaging performance. Thus, the distortions are relatively large, but we can correct the distortions in data reduction processes. Strehl ratios of all images field of LRS-S at λ > 10µm, which realizes Nyquist sampling, are larger than 0.875. At λ < 10µm, the LRS-S detector is in undersampling condition, i.e. the pixel size of the detector determines its spectral resolution. Strehl ratios of all field images of LRS-L at all wavelength are larger than 0.938. Fig. 19 shows spectral resolving power, R, of both LRS-S and LRS-L, which mostly satisfies the goal value of R = 50-100.
Fig. 18 shows echellograms and spot diagrams of some representative field images on the focal planes of MRS-S and MRS-L. Strehl ratios of MRS-S images at λ = 12 − 23µm and all diffraction orders of m = 5 − 8 are lareger than 0.823. Strehl ratios of MRS-L images at λ = 23 − 37µm and all diffraction orders of m = 10 − 15 are lareger than 0.916. Fig. 19 shows spectral resolving power, R, of both MRS-S and MRS-L, which satisfies the specification values.
We have evaluated as-built image performance with consideration of assembling errors by the tolerance analysis based on the Monte Carlo method. As shown in Fig. 20, we defined shift decenters in X,Y,Z and tilt decenters in α,β,γ for all mirrors and sub-optical benches. We assigned tolerances of ±0.05mm or more to shift decenters and tolerances of ±0.001radians or more to tilt decenters. We applied uniform probability distributions to the tolerances. For LRS and MRS, we assumed that constituent sub-optics of pre-optics with dichroic beam splitter, IFUs and spectrometers are assembled on corresponding sub-optical benches, which allows us to perform laboratory testing of each sub-optics separately.
As shown in the left panel of Fig. 21, we assumed that the SPICA telescope or a telescope simulator provides incident lights with Fore-optics, i.e. we took ray aberration introduced by the telescope into account. We defined the tilt decenters of α and β at the fourth free-form surface mirror of Fore-optics as compensators in the tolerance analysis. We assumed that geometrical spots of the field images for the mirror alignment defined in Fig. 3 can be evaluated in visible wavelength by small CCD detectors installed at the Fore-optics focal plane. Firstly, we generated 1000 optical models with random displacements on the probability distribution to the decenters of mirrors and sub-optical benches. Secondly, for each model with random perturbation, we minimized RMS spot diameters of the field images for mirror alignment by changing α and β angles of the fourth free-form mirror. Finally, we evaluated Strehl ratios of the field images of scientific FOVs at λ = 5µm for 1000 models and calculate their cumulative probabilities. The right panel of Fig. 21 shows the cumulative probability distribution of Strehl ratio for Short Fore-optics. As previously explained, since Long Fore-optics is mirror-image symmetric to Short Fore-optics, Long Fore-optics has the same cumulative probability as Short Fore-optics. Diffraction-limited performance with Strehl ratio of more than 0.8 will be achieved more than 20% of the time for all field images of scientific FOVs. According to the result, it is not difficult to realize actual Fore-optics with diffraction-limited image resolution if we carefully designed opto-mechanics and built the optics.
Next, we generated 500 perturbed models of WFC-S and WFC-L with the random displacements. We connected them to random perturbed models of Short and Long Fore-optics respectively after optimization of the tilt of the fourth free-form mirror. Then, we evaluated Strehl ratios of the field images at the focal planes of WFC-S and WFC-L at λ = 5µm for the 500 combined models and calculate their cumulative probabilities. Fig.22 shows the cumulative probability distributions of Strehl ratio for WFC-S and WFC-L. Like Fore-optics, diffraction-limited performance with Strehl ratio of more than 0.8 will be achieved more than around 20% of the time for all field images. It probably has no issue with actual optics of WFC-S and WFC-L if we carefully developed them.
We performed tolerance analyses for LRS and MRS in the same way as WFC. Fig. 23 and 24 show to the cumulative probability distributions of Strehl ratio for LRS and MRS respectively. LRS-S is expected to achieve diffraction-limited performance more than 20% of the time at λ = 10 – 20µm. At λ < 10µm, LRS-S has undersampled images with 25µm pixel size and its spectral resolving power is determined by the pixel size. LRS-L, MRS-S and MRS-L can easily achieve diffraction-limited image resolution over their whole wavelength range.
We have designed 2 relay optical modules of Short and Long Fore-optics, the wide field cameras of WFC, the low-resolution spectrometer of LRS and the mid-resolution spectrometer of MRS using free-form surface mirrors for the mid-infrared instrument of MCS onboard SPICA. We adopted the optical design method proposed by Araki which allow us to construct optical frameworks freely and apply conventional paraxial analysis to determination of optical power distribution. We have succeeded in deriving optimal solutions to achieve the high scientific requirements, such as bright F-number, wide FOV and high spectral resolution with compact size. We also have carried out the tolerance analysis based on the Monte Carlo method and demonstrated as-built performance of diffraction-limited image resolution with just 2 compensators assigned to the fourth free-form surface mirror of Fore-optics.
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