The CASTLE is a small robotic telescope designed for the observations of ultra-low surface brightness objects and the search and detection of transient objects. The telescope is designed and built at Laboratoire d’Astrophysique de Marseille and will be installed at the Calar Alto Observatory. In the present work we consider a possibility to implement a low-resolution slitless spectroscopy mode for CASTLE in order to provide a fast spectrum of the transient immediately after the first detection. Such an additional observation mode could be realized by introduction of a grism in the pre-focal position at the filter wheel. The grism can create spectral images with a minimal decentering and a small defocusing, so the same detector and focusing mechanism can be used. Use of a volume-phase holographic grating as the main dispersing part of the grism allows to reach a high diffraction efficiency together with the low level of scattered light. The value of the spectral resolving power is R=163- 698 over the extended spectral range of 350-950 nm, while telescopes nominal f/#=2.5 is maintained and an extended field of view of 9’x14’ is covered. Due to the limitations set by the telescope optical design the grism will be placed in a converging beam far from the pupil, so that its aberrations and diffraction efficiency will vary notably across the clear aperture. In order to compensate for these variations we consider using a composite holographic component, which represents a mosaic of zones. In each of them such parameters of the hologram as the photosensitive layer thickness, refraction index modulation depth and aberrations of the recording wavefronts can be optimized separately. We estimate the performances of such an innovative element and compare it with that of an ordinary grism. The comparison demonstrates gain up to a factor of 3 in the image quality and up to a factor of 4.2 in the diffraction efficiency.
Waveguide-type displays with volume phase holograms are notable for their small size, large eyebox and high transmission in both the projected image and see-through channels. However, as the aperture, field of view and working spectral range grow, the variation of the hologram replay conditions across its’ surface increases and sets a performance limitation in terms of resolution and diffraction efficiency. In order to overcome it, we propose to use a composite hologram, i.e. a volume phase grating split into sub-apertures with independently varying parameters as the fringes tilt, their pattern, the holographic layer thickness and modulation depth. This approach allows to increase the number of free variables in the design drastically, without introducing any additional optical components. We present the optical design and modelling algorithm for a display with a composite outcoupling hologram. The algorithm relies on simultaneous raytracing through auxiliary optical systems and the diffraction efficiency computations with the coupled waves theory equations. We demonstrate its’ application on an example of polychromatic display with extended field of view. It operates in the spectral range of 480-620 nm and covers the field of 6° × 8° with 8 mm exit pupil diameter. The output hologram has a uniformized diffraction efficiency over the field and the spectral range varying from 26.0% to 65.3%, thus providing throughput around 50% for the projected image and its’ optimal overlapping with the see-through scene. At the same time, the image quality is high and uniform with the PTV angular size of the projected spot better than 1.88′ for the entire image. We compare the results for the initial design using a single classical grating with that for a composite hologram comprising of 4 sub-apertures and show the achieved gain in performance – the gain in DE is up to 13.8% and that in aberration is 0.4 ′ . Also we demonstrate that the computed parameters are feasible and provide a brief sensitivity analysis for them.
Aberration-corrected holographic gratings are widely used in spectral instruments. They allow to achieve high resolution and uniformly distributed diffraction efficiency as well as to combine several functions in a single optical element. However, their performance is limited. In particular, when the optical system has a large aperture the hologram replay conditions vary significantly across its’ surface. Due to this variation the hologram aberration properties and its efficiency change locally thus leading to decrease of the resolution and efficiency of the entire system. In the present research we consider a composite volume phase holographic optical element used as a disperser in a spectrograph design. Such an optical element represent a hologram recorded by stitching of several elementary fields or zones. The refraction index modulation depth, the fringes tilt and the hologram spatial frequency may vary locally in each of the elementary fields to match the changing reconstruction conditions. This approach allows to implement a better aberrations correction and to maximize the overall diffraction efficiency. We demonstrate an exemplary spectrograph design with a composite hologram for the visible range of 400-800 nm. It is shown, that in the design as fast as f/2.1 the maximum aberrations can be decreased by factor of 1.19 and 2 in the X and Y directions, respectively, while the average diffraction efficiency increases by 15.6% at shorter wavelenghts. We continue the study by investigation of the composite hologram technological feasibility and demonstrate that it can be recorded with a standard precision of the moving sources positioning, achievable stroke of the auxiliary deformable mirror and reasonably high accuracy of the photosensitive layer’s parameters.
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