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The design and realization of a stigmatic grazing-incidence instrument for space applications to solar imaging spectroscopy is presented. We propose an optical layout in which imaging and spectral capabilities are decoupled by the use of crossed cylindrical mirrors. The design consists of a double telescope and a spectrograph: telescope I consists of a single cylindrical mirror with parabolic section, focusing the radiation on the entrance slit of the spectrograph in the spectral dispersion plane; telescope II consists of two cylindrical mirrors with aspherical section in Wolter configuration focusing the radiation on the spectrograph focal plane in the direction perpendicular to the spectral dispersion plane; the spectrograph consists of a grazing-incidence spherical variable-line-spaced grating with flat-field properties. Telescope II is crossed with respect to the grating and telescope I, i.e., is mounted with its tangential planes coincident with the grating equatorial plane, to decouple spectral and spatial focusing properties. The spectral resolution is preserved also for off-axis angles. The instrument that has been realized operates in the 4-26 nm spectral range and has a field of view of 0.5 deg to image the full Sun disk.
©2013 Optical Society of America
1. Introduction
Imaging and spectroscopy are the traditional techniques for the analysis of the solar surface and the coronal plasma. Both have been implemented on several solar missions in the last decades culminating in the instrumentation on board SOHO [1] and in other more recent missions like TRACE [2], HINODE [3], STEREO [4] and SDO [5].
Naturally the physical conditions of the emitting regions, mainly the temperature, determines the preferred spectral band of operation. While the photosphere emits mostly in the visible (400-700 nm) and near ultraviolet (200-400 nm) regions, the transition region and even more the corona emit in the far or in the vacuum ultraviolet (100-200 nm). The hottest part of the corona like flares and active regions have their emission mostly in the extreme-ultraviolet (10-100 nm) or soft X-rays (0.1-10 nm) regions.
The power of diagnostics by imaging is mainly in the very high spatial resolution that can be obtained even in the extreme-ultraviolet (XUV). Moderate spectral resolution, i.e. broad-band XUV spectroscopy (λ/Δλ ≈100), can be obtained through the use of filters and multilayer coatings on the optics for the XUV region. Another characteristic of imaging systems is the simultaneous coverage of a large spatial region on the Sun surface; this propriety is very important for fast dynamical events and for limited observational time. It is worth to mention that for several features on the Sun, as the spatial resolution of observations increases, so does their dynamics. The design of XUV telescopes with multilayer-coated mirrors working at normal incidence in a narrow spectral band is well established, since several solar missions have been flown using such type of instruments, among which we can cite EIT on SOHO [6], TRACE [7], EUVI-SECCHI on STEREO [8] and AIA on SDO [9].
On the other hand, high-resolution spectroscopy provides information impossible to obtain with other means: essential parameters of any emitting plasma such as elemental composition, temperature, density and velocity of moving jets. Present plasma diagnostic techniques allow to evaluate the amount of matter which is present in the source at any temperature, using the line intensity of elements in different degrees of ionization [10]. The observation of lines of different elements supplies the elemental composition of the plasma and its variations looking at different sources on the Sun. Density is determined again through intensity ratio of proper lines; for instance whose upper levels present populations that depends critically from collisional excitation or de-excitation and therefore are sensitive to density. Velocity fields of moving plasma is directly measured through Doppler effect; high spectral resolution is needed to achieving a good sensitivity. Spectral lines emitted by the various species abundant in the solar atmosphere fall in all spectral regions. The XUV region is particularly rich of lines of high ionization stages, representative of high-temperature plasmas [11].
Spectroscopic XUV instruments are generally dispersive, i.e. they use a grating and an entrance slit to separate the spectral from the spatial information. Therefore, contrary to XUV imaging systems that give in a single acquisition a two-dimensional image in the spectral band that is limited by the multilayer spectral response, a grating spectrometer has intrinsic spatial resolution capability only in the direction perpendicular to the spectral dispersion plane.
In the case of stigmatic configurations, both spectral and spatial aberrations are corrected, so that a point-like monochromatic source placed at the input is imaged on the focal plane as a point. In case of an extended source that illuminates the entrance slit, the image acquired by the detector has both spectral and spatial information: the spectral content of the source is imaged in the direction perpendicular to the slit, the intensity spatial distribution along the slit is imaged in the direction parallel to the slit itself. Therefore, a complete map of a two-dimensional region is obtained by one-dimensional scanning in the direction perpendicular to the slit. The acquisition of a two-dimensional spectroscopic image is therefore more lengthy than the corresponding image obtained by an imager. Stigmatic configurations are obtained by using the optical elements, i.e. the focusing telescope and the grating, at normal incidence. Several instruments have been flown to obtain imaging spectroscopy of the Sun in the XUV. For operations at long wavelengths in the XUV (λ > ≈50 nm), the optics are using standard coatings, as platinum, iridium or silicon carbide, and the instrument may be operated in an extended spectral region. E.g. we can cite the SUMER [12] and UVCS [13] spectrometers on SOHO. For operations at wavelengths shorter than ≈40 nm, the optics are multilayer-coated and the spectral band of operation is limited by the multilayer response. E.g. we can cite the EIS [14] spectrometer on HINODE working in the intervals 17-21 nm and 25-29 nm. The advantage of the normal-incidence operation is the effective corrections of the spatial aberrations even in an extended field-of-view (FOV) [15, 16], that make these configurations very useful for solar imaging spectroscopy.
In the case of astigmatic configurations, only spectral aberrations are corrected, so that a point-like monochromatic source placed at the input is imaged on the focal plane as a narrow and slightly curve line parallel to the slit itself. This is most often the case when the optics are operated at grazing incidence. Such a configuration is not able of providing imaging spectroscopy, i.e. simultaneous observations of extended regions, since the intensity distribution along the slit is not maintained on the focal plane. In this case the entrance slit must be reduced to a pinhole and the image of extended sources, such as the Sun or the solar corona, is obtained scanning over the whole region to be observed point by point. Therefore, long acquisition time to acquire a complete image, often longer than the time evolution of the region to be investigated, and complex scanning mechanisms are required.
The spectroscopic instruments on SOHO, that has been operated since 1996, exemplify the classification above presented: they consist of a normal-incidence (SUMER) and a grazing-incidence (CDS) configuration. SUMER operates in the band 50-200 nm with ≈20000 spectral resolution and 1-arcsec spatial resolution over a FOV of 64 arcmin, where it is fully stigmatic. CDS [17] consists of a grazing-incidence telescope (Wolter II type) and a grazing-incidence grating in the Rowland configuration [18], operated in the 8-50 nm region. The system is astigmatic, therefore the scanning of a region on the Sun needs to be done point by point.
It is possible to design grazing-incidence configurations that are stigmatic for sources that are placed on the optical axis of the instrument. When using spherical gratings, that do not provide almost any focusing capability in a plane perpendicular to the dispersion one, the astigmatism is usually corrected by an additional mirror with focusing capability also in the plane perpendicular to the dispersion one. The classical designs for grazing-incidence spectrometers, such as CDS, adopt the Rowland configuration with spherical uniform-line-spaced gratings: the slit, grating and detector are placed on a circle with diameter equal to the radius of the grating. The spectrum is acquired by a detector that is mounted tangent to this circle, therefore the length of the exit arm changes as the cosine of the diffraction angle. It is impossible to correct for the astigmatism with a fixed mirror in an extended spectral region because of this rapid variation; the variable exit arm gives large defocusing far from the stigmatic wavelength [19].
An almost flat focal surface at near normal incidence on the detector is obtained by using spherical variable line-space (VLS) gratings, where the groove spacing changes among the surface following a polynomial law: in such a system the aberrations can be controlled by the ruling parameters for groove space variation [20]. By choosing a proper distribution of the line spacing, the spectral focal curve can be brought to be the closest to the detector plane [21]. Furthermore, unlike the Rowland design, the exit arm of a spherical VLS grating is almost constant in an extended spectral region, making easier to correct for the astigmatism in the whole region to be acquired. Stigmatic designs with spherical VLS gratings often use an additional toroidal mirror with the tangential focus on the entrance slit and the sagittal focus on the focal plane [22–25]. The image of an on-axis point-like source, but it broadens in both directions for off-axis points, therefore both spectral and spatial resolutions decrease far from the optical axis. Different designs at grazing incidence, such as a plane VLS grating illuminated in converging light coming from a focusing mirror, have similar performance, therefore the spectral resolution is not preserved for off-axis points [26–28]. A different approach is the correction of the astigmatism by an additional mirror that is crossed with respect to the grating, i.e. it is mounted with its tangential plane coincident with the equatorial plane of the grating in the Kirkpatrick-Baez configuration [29–31]. In this case, the design has been proved to have a moderate spatial resolution capability for extended sources [32], although not high enough compared to what is normally required for space applications. Finally, a five-element design has been recently proposed for a sounding rocket experiment, the Marshall Grazing Incidence X-ray Spectrograph (MaGIXS) [33]. The instrument consists of a Wolter telescope and a slit spectrograph, comprising a pair of paraboloid mirrors acting as collimator and reimager and a planar VLS grating for the 0.6-2.4 nm spectral region.
Our approach to the design of a stigmatic grazing-incidence telescope-spectrometer for XUV imaging spectroscopy of extended sources is based on the property of the Kirkpatrick-Baez configuration to demand to different optics the focusing in the two directions [34]. The telescope is divided into two sections: 1) telescope 1 consists of a cylindrical mirror with parabolic section that focuses the radiation on the entrance slit of the spectrometer only in the direction perpendicular to the slit itself; 2) telescope 2 consists of two cylindrical mirrors with aspherical section in Wolter configuration that focus the radiation on the spectrometer focal plane in the direction parallel to the slit, i.e. perpendicular to the spectral dispersion plane. The spectrometer consists of a SVLS grating with flat-field properties. Finally, the spectrum is acquired by an image detector mounted at near normal incidence with respect to the direction of the exit beam. The two sections of the telescope are crossed, i.e. the mirrors of telescope 2 are mounted with their tangential planes coincident with the equatorial plane of the mirror of telescope 1 and of the grating. Therefore, the focusing properties in the plane of the spectral dispersion and in the plane perpendicular to this are fully uncoupled: the spectral aberrations are corrected by the grating, while the aberrations in the plane perpendicular to the dispersion plane are corrected by the telescope 2. It has been shown that the image of an extended source has a negligible spectral broadening even far from the optical axis and a spatial broadening that depends only on the design of telescope 2. The design gives a relatively large FOV in the direction parallel to the slit with constant spectral resolution and slightly degrading spatial resolution. Therefore, imaging spectroscopy of extended regions is performed by a one-dimensional scanning, as the case of normal-incidence instrumentation. The advantage of adopting an all-grazing-incidence design is the operation on a broad spectral band in the XUV and soft X-rays, definitely more extended than what is obtained by using normal-incidence multilayer-coated optics.
In this paper, we present the design, realization and characterization of a telescope-spectrometer adopting the configuration proposed in [34] by Poletto and Tondello, working in the 4-26 nm spectral region with a FOV of 0.5 deg, corresponding to the angular extension of the solar disk as seen from the Earth. The design of the instrument and the expected performance are presented in Par. 2, the realization is presented in Par. 3, finally the characterization in Par. 4.
2. Optical design of the instrument
A schematic view of the instrument is shown in Fig. 1. It consists of five optical elements, namely four mirrors and a grating. The first element is a grazing-incidence plane mirror that is used to perform the one-dimensional scanning in the direction perpendicular to the slit by rotating around its center. This mirror, although essential for the image scanning, does not introduce any modification in the optical performance and has not been installed in the prototype. Figure 2 illustrates the ray propagation in the two orthogonal planes: red rays propagates in the spectral plane (tangential plane); blue rays in the spatial plane (sagittal).
Fig. 2 Optical layout showing the propagation of tangential (red) and sagittal (blue) rays: a) full path; b, c) propagation up to the slit; d, e) propagation from the slit to the focal plane.
The two sections of the telescope consist of cylindrical mirrors with aspherical section mounted in the Kirkpatrick-Baez configuration. Telescope 1 consists of a cylindrical mirror with parabolic section (PP1) that focuses the radiation on the entrance slit (SL) of the spectrometer only in the direction perpendicular to the slit itself (red rays in Fig. 2), i.e. the spectral dispersion plane. The parameters of the parabola are calculated as
where f is the focal length, q the exit arm, i.e. the distance from the center of the mirror to the slit, and θp1 is the incidence angle. The spatial resolution on the slit, that is the width of the region in the direction perpendicular to the slit that is imaged by the instrument, is calculated as the ratio between the slit width and the exit arm, while the effective collecting area of the mirror is maximized by the proper choice of the incidence angle. Telescope 1 is realized by a single mirror at grazing incidence, since it is required to focus light that is coming only on-axis.Differently from telescope 1, telescope 2 has an extended FOV, therefore it consists of two cylindrical mirrors with respectively parabolic and hyperbolic section in Wolter configuration, that focus the radiation on the spectrometer focal plane only in the direction parallel to the slit, i.e. perpendicular to the spectral dispersion plane. Telescope 2 limits the useful spatial FOV of each spectral image. It is crossed with respect to telescope 1, i.e. it is mounted with its tangential plane coincident with the equatorial plane of telescope 1. A detailed schematic is shown in Fig. 3. When working at grazing incidence, two reflecting surfaces are necessary to give a useful FOV obeying to the Abbe condition. Almost aberration-free images in an extended FOV are given by systems with two confocal conical mirrors in Wolter configuration [35]. Three different designs have been presented by Wolter [36] and the choice of the configuration depends on the spectral region of operation. Since the instrument is operated in the 4-20 nm region, we have adopted the Wolter II configuration, that adopts a paraboloid and a hyperboloid with internal-external reflections. The mirror are arranged coaxially to have a coincident common focus which makes the system focus.
The parameters that have to be chosen to design the telescope 2 are the incidence angle on the parabolic and hyperbolic mirrors θp2 and θh2, the separation between the two mirrors Δ, and the length of the exit arm p”. The relations between the parameters are defined through the following equations [37]:
where α and β are the angles formed with the optical axis respectively by the central ray between the two mirrors and by the central ray on the focal plane, p’ is the virtual entrance arm of the hyperbolic mirror, fp and fh are the focal lengths respectively of the parabolic and hyperbolic mirrors, a and b are the parameters of the hyperbola, h is the distance between the center of the first mirror and the optical axis, and L is the distance, measured along the optical axis, from the center of the first mirror to the focal plane. Equations (2)-(8) allow to completely design the Wolter II telescope.The choice of the design parameters of telescope 2 is driven by the required effective focal length, feff, which determines the angular resolution on the focal plane. Let us consider a ray inclined with respect to the optical axis by an angle δ, which is focused on the focal plane displaced by an amount S with respect to the focus of the central ray, as shown in Fig. 4.
The effective focal length is calculated as feff = S/δ [38]:
In the case of small δ, Eq. (8) is simplified asthat in our case is about 1200 mm.The effective focal length of the telescope 2 is determined by the requirements on the angular resolution, while the incidence angles are determined to maximize the effective area. Once feff and α are given, another parameter has to be fixed to solve Eqs. (2)-(8): we have chosen to fix p’. Table 1 summarizes the instrumental parameters. As usual for Wolter configurations, feff varies across the FOV, since it depends on δ. In the case here discussed, the minimum feff is 1148 mm and the maximum 1285 mm, corresponding to a variation of ± 5% with respect to the nominal value. The variation of feff has to be taken into account in the spatial calibration of the instrument. Tables 2 and 3 summarize the performance in terms of spatial and spectral resolution and effective area. The latter has been calculated as the physical area that collects the photons at the input of the instrument, decreased by the mirror reflectivity, the grating efficiency and the detector efficiency. The latter quantities (i.e., reflectivity and grating and detector efficiencies) have been previously measured in the facilities available at CNR-IFN using well-consolidated procedures for instrumental calibration [39, 40].
Table 1. Parameters of the spectro-imager
Table 2. Spatial and spectral resolution
Table 3. Effective area at 5, 10 and 20 nm
The performances in the focal plane are summarized in Figs. 5 and 6, that show the ray-traced spot sizes at four wavelengths inside the spectral band both on axis and at the edges of the FOV. The aberrations are well confined within one pixel.
Fig. 5 Spots diagram matrix. The box area is 2 × 2 pixels. Three fields (0°, ± 0.25°) and four wavelengths (4, 6, 10, 20 nm) are shown within the working ranges of the instrument.
In the evaluation of the performance of any grazing-incidence optics, a careful attention must be paid to the influence of the tangential slope errors in the surfaces of the various optical elements, since the quality of the focus is primarily determined by the slope distribution on the surface of the mirrors [41]. The mirrors have been provided by the manufacturer (Zeiss, Germany) with slope errors lower than 4 arcsec in the tangential direction. Their effects on the optical performance have been calculated through ray-tracing simulations. For the telescope 1, the effects of the slope errors are negligible both on the spatial resolution on the entrance slit, that is 100-μm wide, and on the spectral resolution, that is limited by the pixel size of the detector. For the telescope 2, the slope errors on the two mirrors give a FWHM response of about 30 μm, i.e., 1.5 pixels, for a collimated beam. Considering both the effects of the slope errors and the spatial aberrations already shown in Fig. 6, the ultimate spatial resolution is limited to about two pixels.
3. Characterization of the instrument
The instrument has been realized as shown in Fig. 7. The optical components are mounted on a breadboard that is accommodated in a vacuum vessel. The detector is mounted in a movable stage that permits to move it at the desired position along the spectral plane. The instrumental characterization has been performed using two laboratory sources: a hollow-cathode lamp filled with helium for wavelengths longer than 23 nm and a microfocus soft-X-ray source with interchangeable anodes for wavelengths as short as 4.4 nm.
Fig. 7 a, b) Pictures of the optical supports installed on the breadboard; c) mechanical realization of the vacuum vessel for the telescope (top view).
The beam emitted by the sources has been collimated through a toroidal mirror placed in front of the instrument. The spatial extension of the source, i.e., the extension in the direction parallel to the entrance slit of the spectrometer, has been limited by a variable aperture from 25 μm to 1 mm, in order to simulate an extended source and demonstrate the decoupling of the focusing properties in the two directions. Furthermore, the source and the collimating mirror can be tilted respect to the telescope by ± 0.25 deg, in order to illuminate the instrument within the full FOV.
4.1 Spectral characterization
Some of the spectra that have been acquired are shown in Fig. 8. They have been taken with the slit closed at 100 μm and the instrument illuminated on axis. Figure 8(a) shows the spectrum measured with the hollow-cathode lamp. The width of the spectral lines is about 0.05 nm (3 pixels), that is in good agreement with the slit aperture and the demagnification factor due to the grating anamorphism. Figure 8(b) shows the emission of the microfocus soft-X-ray source with the aluminum anode. The Al L-edge at 76 eV is sharp and well defined as expected. Finally, Fig. 8(c) shows the emission of the microfocus source with the carbon anode. The three diffraction orders of the C-Kα line are clearly identified.
Fig. 8 On-axis spectra obtained with: a) the hollow-cathode lamp filled with He; b) the microfocus source with Al anode; c) the microfocus source with C anode.
4.2 Spectral-spatial decoupling
To verify the decoupling of the focusing properties in the tangential and sagittal planes, we have acquired some spectra with the spatial aperture in front of the source open at different apertures between 50 μm and 1 mm, to simulate an extended source. The results are shown in Fig. 9. Figure 9(a) shows a mosaic of seven images of the He 25.6 nm spectral line, Fig. 9(b) shows the spectral and spatial width of the images. The spectral width of the lines is almost constant, therefore is clearly not influenced by the spatial extension of the source.
Fig. 9 Measurements of the spectral-spatial decoupling: a) He II spectral line at 25.6 nm acquired with seven spatial apertures, from 50 μm to 1 mm; b) spectral (cross) and spatial (circle) width of the images. The spatial width is increasing linearly with the spatial aperture, the slope of the line being the magnification factor of the system, that is the ratio between the effective focal length feff and the focal length of the toroidal mirror used to collimate the beam after the source.
4.3 Off-axis imaging
To test the focusing within the FOV the source and its collimating mirror have been tilted with respect to the optical axis of the telescope. The results are presented in Figs. 10 and 11. The spectral and spatial focusing are maintained within the whole instrumental FOV.
Fig. 10 He spectra with the source on axis and tilted at 0.125 deg. The spectrometer slit is 100 μm wide, the source spatial aperture 100 μm. The spatial separation is 2.7 mm, as expected from the instrumental focal length.
Fig. 11 C spectra at 4.4. nm with the source on axis and tilted at ± 0.25 deg. The spectrometer slit is 100 μm wide, the source spatial aperture 100 μm.
4. Conclusions
The design, realization and characterization of a stigmatic grazing-incidence telescope-spectrograph for space applications to solar imaging spectroscopy has been presented. The design purpose is to separate on different optical elements the focusing properties in the two directions, to preserve the spectral aberrations also for off-axis points in the direction parallel to the entrance slit of the spectrograph and to give an extended spatial field-of-view. Imaging spectroscopy is obtained by scanning the object in a single direction, therefore simplifying the mechanisms. The instrument that has been realized covers the 4-26 nm spectral region in a 0.5-deg field-of-view. Experimental tests have confirmed the theoretical expected performances. Space solar spectroscopic observations in a broad spectral band requiring grazing-incidence operations may benefit of the proposed design both for rocket or satellite observations.
Acknowledgments
We would like to thank prof. Giuseppe Tondello for many useful discussions during the realization and test of the instrument. The work has been funded by the Italian Space Agency under the contract ASI/INAF I/015/07/0 in the framework of the program “Studies for the exploration of the solar system”.
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