In the present study we consider an approach to design and tolerance analysis of a spectrograph with a complex dispersive unit. The design uses a mosaic dispersive unit consisting of two VPH gratings imposed on the same substrate. This solution allows to detect spectra in two intervals – visible (375-625 nm) and near infrared (600-1000 nm) simultaneously. The modeling results show that the spectra resolution reaches 0.78 and 1.25 nm in the visible and NIR channel, respectively. The diffraction efficiency varies between 74.3% and 99.7% for the entire working range. However, the design is sensitive to the manufacturing and assembly errors. Some design parameters have influence on both the image quality and the diffraction efficiency. We developed a set of design tools allowing to include diffraction efficiency data into the tolerance analysis process. The analysis performed with these tools shown that maintenance of the nominal efficiency together with the image quality requires special control over the holographic layer parameters and also tightening of the tolerances on the lenses parameters. The developed analysis approach and tools may be useful in the future for design of spectral instruments with VPH gratings, especially when they are used to build a complex dispersive element.
We demonstrate the approach of using a holographic grating on a freeform surface for advanced spectrographs design. We discuss the surface and groove pattern description used for ray tracing. Moreover, we present a general procedure of diffraction efficiency calculation, which accounts for the change of hologram recording and operation conditions across the surface. The primary application of this approach is the optical design of the POLLUX spectropolarimeter for the LUVOR mission project, where a freeform holographic grating operates simultaneously as a cross disperser and a camera with high resolution and high dispersion. The medium ultraviolet channel design of POLLUX is considered in detail as an example. Its resolving power reaches (126,000 to 133,000) in the region of 118.5 to 195 nm. Also, we show a possibility of using a similar element working in transmission to build an unobscured double-Schmidt spectrograph. The spectral resolving power reaches 4000 in the region 350 to 550 nm and remains stable along the slit.
In the present paper we consider an optical design of a head-mounted display with a free-standing holographic image combiner. The optical system works with a 24°×18° field of view and a 6mm pupil providing energy concentration up to 89% for a 20μm-pixel. The combiner represents a volume-phase reflective hologram recorded by two point sources. We demonstrate that the recording and replay angles for the hologram considerably vary across the surface, that causes perturbation and overall decrease of the diffraction efficiency. A revised optical design is presented. It provides a higher hologram efficiency together with a better image quality and decreased decenters of the components. The resultant gain in the median efficiency is factor of 5.3.
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