A transmission hologram for slitless spectrophotometry on a convergent telescope beam. Optimisation and characterization

TL;DR

The study addresses converting a converging-telescope imager into a slitless spectrograph using a holographic optical element, aiming to outperform periodic gratings in both focusing and first-order transmission. It presents a rigorous optimization pipeline—from phase-hologram prototyping and optical bench testing to a physics-based model of recording and reading the hologram—and demonstrates that the final AuxTel hologram achieves diffraction efficiency near the theoretical maximum for thin holograms, with $N_{eff}\approx150\,\text{lines/mm}$ and $D_{CCD}\approx200\,\text{mm}$, across $\sim350$–$1050\,\text{nm}$. On-sky validations at Pic du Midi and commissioning on AuxTel show stable focusing, predictable dispersion, and robust performance with field-star masking and fiducial-domain extension, enabling precise slitless spectrophotometry for atmospheric transmission monitoring. The work provides a scalable approach to turning imaging telescopes into low-cost, high-performance slitless spectrographs and outlines future enhancements such as dedicated beam projectors for continuous transmission calibrations.

Abstract

This article details the optimisation and the characterisation of the hologram described in a companion paper published in 2021, which showed the superiority of a holographic optical element over a periodic grating as a disperser installed in the path of a converging beam on an on-axis detector (unbent spectrograph) for slitless spectroscopy. In this article, we describe in detail the development and optimisation of the final optical holographic element installed on the spectrograph of the auxiliary telescope (AuxTel) at the Rubin-LSST observatory. After recalling the general principle of a hologram used as a dispersing and focusing element, we describe the technical resources - optical bench and sky measurements - and modeling tools that enabled us to determine the optimum production parameters for the AuxTel hologram after 4 prototyping phases. We also describe the on-sky verifications and measurements carried out with various telescopes. Thanks to these various techniques, we have succeeded in obtaining a diffraction efficiency in the first order close to the maximum theoretically possible with our thin-type hologram. This hologram has been in place on AuxTel's spectrograph since February 2021, and has since given full satisfaction, coupled with analysis software adapted to slitless spectroscopy.

Figures (19)

• Figure 1: (Top) Recording of a specific holographic element as a disperser adapted to a convergent telescope beam for an on-axis spectrograph (left): The intensity interference pattern of two illuminating point sources A (reference wave) and B (image wave), produced by a laser splitted beam ($\lambda_R=639nm$), is recorded on the holographic sensitive plate emulsion. After the emulsion processing, the iso-transmission lines are confocal hyperboloids (middle left) ; here only 1 line every 400 is represented (and zoomed). Scale is in mm. (Bottom) Image restitution: a monochromatic conic beam with wavelength $\lambda_R$ converging on $S_0$ (reference wave) through the holographic element produces a first order point-image at $S_1(\lambda_R)$ (image wave) such that $S_0S_1(\lambda_R)=AB$ if $D_{CCD}=D_R$. For any $\lambda \ne \lambda_R$ the image is focused near the line $S_0S_1(\lambda_R)$. The coordinate frames attached to the hologram $(w,l,\zeta)$ centered on $C'$, and to the focal plane $(u,v,\zeta)$ centered on $S_0$, are represented. In all figures, the red lines are the symmetric axis of the interference pattern, and the black dotted lines are centered on the incident telescope beam.
• Figure 2: Pictures of the holographic bench. (up) General view seen during assembly (the microscope objective missing on the right, and the optical paths are not equalized). (down) Detail of the assembled production optical bench showing the microscope objectives, the $30\mu$m filtering holes, the prism-mirror and the illuminated plate.
• Figure 3: Optical test-bench (side view). The Quartz Tungsten Halogen lamp and the monochromator sit above the dark enclosure and are not drawn. The light from the monochromator exit slit is conveyed through a liquid light guide (Newport 77639 Liquid Light Guide, 2 m long, 8 mm diameter) that feeds the small (cubic) integrating sphere. Exposure time is controlled through a mechanical shutter attached at the exit of the optical beam simulator (see below).
• Figure 4: The AuxTel optical beam simulator (see text). The light emerges from the integrating sphere through a $20\,\mu\text{m}$ diameter pinhole, hits successively two off-axis parabolic mirrors (optical relay), then converges on the CCD to form point-like image with a $f/D=18$ converging beam.
• Figure 5: A simple phase grid model with periodic square wave index variations $\delta n$, resulting in optical path variations of $\Delta=e\delta n$. A, B and C are separated by the semi-period of the local grid $a/2$. The direction of the emerging light-rays corresponds to the first diffractive order. If the optical index step $\delta n$ is such that the optical path $BB'B"$ equals the path $AA'A"$ (modulo $\lambda$), then the light transmitted from the plane wave incident underneath is maximal in the direction of the first diffraction order.