Sliced pupil gratings: a compact solution for increased spectral resolution
A novel astronomical spectrograph design enhances instruments with multiple resolutions, strong envelope constraints, or that are predesigned to use compact dispersive elements.
Spectrographs are the main tool in astronomical instrumentation, providing information about the physical and chemical processes of gas and stars. In recent decades, observational astronomers have wanted to improve the spectrographs built onto their telescopes, either by increasing the spectral resolution of their instruments or by combining different regimes of spectral resolution in the same instrument. But redesigning such systems while remaining within the spatial constraints of already-built instruments has proven difficult. We developed a spectrograph design that bypasses problems with more conventional approaches to increasing spectral resolution.
A spectrograph is composed of a slit (at the entrance focal plane) followed by collimating optics, then a pupil where the dispersive elements are placed. At this point, the light is separated by wavelength then passed through camera optics that focus the dispersed beam onto the detector. The optical design of a spectrograph is driven by the spectral resolution requirement, which determines the instrument's ability to distinguish spectral lines. It is set by the resolving power, R, which is the ratio between the wavelength (λ) and the spectral resolution element (Δλ), which in turn is related to the number of pixels on the detector on which the image of the entrance slit is projected with the required image quality. The design parameters to be considered are the entrance aperture (slit width), the pupil size, and the geometry required to operate at the optimum configuration, such as the Bragg angle for Littrow-based spectrographs. Maintaining the Bragg angle is especially important to optimize efficiency when using volume phase holograms (VPHs), because although VPH gratings are more efficient than ruled gratings at the Bragg angle, they lose efficiency very quickly away from it.1 Increasing the spectral resolution in an already-built instrument implies either operating with a smaller slit width or changing the angle of light at the pupil.
The first approach was used during the last 20 years but has a major drawback: decreasing the slit width reduces the amount of light that enters the spectrograph, in a situation where light is already limited. To avoid loss of light flux, optical designers used different techniques for dividing the focal plane object (slit) into smaller sub-slits, for which individual images were produced on the detector and later combined by software, producing the final target spectrum. This division at the entrance focal plane has been implemented in two ways: one could use either image slicers—a set of adjustable mirrors that cut the object image in sub-images that then become the new slits—or, alternatively, optical fibers whose cores limit the slit width.
The alternative to decreasing the slit width is increasing the exit angle from the pupil. This led designers to propose other solutions like the articulated camera, a mobile camera system in combination with the grating rotation to recover the Bragg condition. However, the results are not completely satisfactory, and important calibration and operation problems arise. This kind of design also implies large instrument envelopes.
Our approach consists of dividing the optical beam at the pupil into sub-beams whose images are focused on the same detector position by the instrument camera. This ‘sliced-pupil grating’ design is based on ‘cutting’ the pupil into a given number of slices, each produced by placing a prism on either side of a VPH grating. The independent beams are guided through a very precise optomechanical assembly to assure stacking of the individual images on the detector within the available error budget to produce a single spectrum with the desired performance. If the images are not stacked accurately, the image quality degrades and spectral resolution is lost. Increasing the number of slices raises the spectral resolution but also increases the complexity of the instrument.
To demonstrate the feasibility of this concept we built a prototype (see Figure 1) for Elmer, an already-built spectrograph for the Gran Telescopio Canarias (GTC) 10m telescope in Spain, to increase the spectral resolution around the Balmer Hα line at 656nm. The instrument had been designed to produce R=2500 in Littrow configuration and with 0° angle between the collimator and the camera. To obtain the high angle of incidence (AOI) on the grating for the required resolution, we used three prisms to slice the beam into portions at the pupil. Total internal reflection (TIR) on the upper faces of these prisms supplied the required AOI on the grating. A gap between the prisms, seated on the gel-coupled VPH window, was used to avoid tunnel transmission. The grating is a hologram of 3400lines/mm sandwiched between two fused silica flat windows providing R=10, 000 at first order. Once the light is diffracted, the beam is redirected again to the camera using TIR through the second set of prisms. The unit is placed at the pupil (89mm Ø size). The arrangement results in unfortunate but unavoidable pupil vignetting (38% in this prototype). Note that this loss is typically lower (and of different nature because it does not sacrifice field of view) than that commonly associated with narrowing of the slit in long-slit spectrographs, which is needed to produce the same increase in spectral resolution.
The difficult part of our design lies in stacking the three images from the different slices (which travel different paths) onto the detector. Note that the images can be incoherent and that we are working far from the diffraction limit. To place the optical elements in accurate positions within the instrument optical path, the optical elements are held in a complex mount (see Figure 2). We designed this mount to absorb the differential thermal dilatations of the optics with respect to the aluminum elements while maintaining performance and preventing surface stress that could affect the transmission. Figure 2 shows a 3D model of the mount and the real element after assembly. Optical and opto-mechanical design publications2 give all the technical details.
We carried out a complete set of tests on the prototype.3 The results show that our built sliced pupil grating could increase spectral resolution by a factor of 3.5. The experience gained has allowed us to recommend registering the image in real time while gluing the prism to improve beam stacking.
We are in the midst of manufacturing the next device, a two-slice grating for MEGARA,4 a fiber-fed multi-object spectrograph also destined for the GTC telescope. The instrument provides spectral resolution ranging from about 5600 to a high of roughly 17,000, made possible by the sliced pupil grating (see Figure 3).
The sliced pupil grating allows us to increase the spectral resolution of spectrographs while maintaining their geometry. Although our initial aim was to design innovative gratings for large telescopes, we realized that these devices can be used in all kinds of spectrographs that need higher spectral resolution, combinations of different spectral resolution regimes, or small envelopes (for example, portable or space-borne instruments).
The sliced-pupil grating is a collaborative project between the SME FRACTAL and the Complutense University of Madrid. The first prototype received funds from the Madrid Regional Government (CAM) through grant 22/2009 for Aero-spatial Innovation. The development for large telescopes (VIENTOS project) has been co-funded by CDTI (the Centre for Industrial Technological Development under the Ministry of Economy and Competitiveness, Spain) through the Industry for Science program IdC-20101106. The authors also acknowledge support received from the Consolider-Ingenio 2010 Program grant CSD2006-00070 First Science with the GTC and Spanish National Plan for Astronomy and Astrophysics grant AyA2009-10368. The Laboratory for Advanced Scientific Instrumentation at the Complutense University of Madrid is funded by the Moncloa Campus de Excelencia Internacional.
Maria Luisa García Vargas received a PhD in astrophysics from the Autonomous University of Madrid (UAM) in 1991. She is the director and founder of the company FRACTAL. For nine years she headed the instrumentation group of the GTC 10m telescope. She also spent eight years as a professor at UAM and is the author of many SPIE papers on astronomical instrumentation.
Ernesto Sánchez-Blanco Mancera is an optical engineer. For eight years he was a member of the instrumentation group of the GTC telescope. He has worked for FRACTAL since 2006 and has participated in most of the company's projects. He is the author of many SPIE papers on astronomical instrumentation.
Manuel Maldonado Medina is an industrial engineer. He was a member of the instrumentation group of GRANTECAN, the public company responsible for constructing and managing the 10.4m GTC, for seven years. He joined FRACTAL in March 2008 and has worked as an optomechanical engineer in most of the projects developed by FRACTAL.
Ana Pérez-Calpena received her telecommunications engineering degree from the Polytechnic University of Madrid. She has been the head of systems engineering at FRACTAL since 2008. Formerly she worked as a system engineer for the GTC telescope for seven years and before that as a spacecraft engineer at the European Space Astronomy Centre, the European Space Operations Centre, and the European Organisation for the Exploitation of Meteorological Satellites. She has authored many SPIE papers on astronomical instrumentation.
Ismael Martínez-Delgado has a PhD in astrophysics and works as an optical test engineer at FRACTAL. Formerly, he worked two years for the Center for Astrobiology in Madrid and five years at the Astrophysical Institute of the Canary Islands. He is the author of many SPIE papers on astronomical instrumentation.
Armando Gil de Paz has a PhD in astrophysics and is a professor of astrophysics. He is the principal investigator of the MEGARA spectrograph for the GTC and has also authored several SPIE papers on astronomical instrumentation.
Jesús Gallego-Maestro has a PhD in astrophysics. He is a professor of astrophysics and head of the Group for Extragalactic Astrophysics and Astronomical Instrumentation (GUAIX). He is also the author of several SPIE papers.
Jaime Zamorano-Calvo has a PhD in astrophysics and is a professor in the Department of Astrophysics. He is an expert in light pollution and dark sky preservation, and the author of many SPIE papers on astronomical instrumentation.
