2- The optical formula

UVEX is a spectrograph based on a relatively simple and well known Czerny-Turner design. The right figure shows the optical formula in its basic form. There are two spherical concave mirrors (M1, M2), a diffraction grating (R) to spectrally disperse the light, an input slit (F), and of course, a camera (D) to record the spectrum

In the particular case of UVEX, a cylindrical lens is added just in front of the detector to correct the astigmatism inherent in this optical formula (a cylindrical lens has a finite CURVATURE radius on an axis and an infinite curvature radius on the other axis).  The special feature of UVEX is that the design uses almost entirely mirrors, hence its property of achromatism (the absence of chromatic aberration), which allows us to observe a very wide range of wavelengths without refocusing. To preserve this achromatism, it is absolutely vital to avoid using UVEX on a telescope equipped with a focal length reducer or a field corrector. The best place is always at the direct focus of a mirror telescope (the SCT entrance corrector plate is tolerated, but absorb some UV).

More specifically, UVEX is a “crossed” Czerny-Turner spectrograph (see right figure) to facilitate the physical design (interface with the telescope and camera, compactness). As indicated above, a cylindrical lens is added, facing the detector. Its purpose is to correct the very strong astigmatism which the Czerny-Turner suffers.  Without this lens, the trace of the spectrum of the stars would be excessively wide along the spatial axis, which would greatly affect the efficiency of the instrument when observing low-brightness stars. This lens has no effect along the spectral axis (in that dimension it behaves like a simple parallel glass plate, without optical power) while along the perpendicular axis (spatial) it has a focusing effect. In the final version of UVEX (so-called Version 3), the lens is also strongly inclined relative to the average axis of the ray beam.  This design standardizes the correction of astigmatism along the spectrum – this inclination corrects the clean chromaticism of the cylindrical lens. It is made of BK7, a very transparent optical glass in the ultraviolet.

All optical elements are available from ThorLabs. The references for the order are indicated on the optical opposite drawing. Note that spherical concave mirrors are used in dedicated mounts (brackets), which are available from ThorLab. The focal length of the mirrors is 100 mm, with a diameter of 25 mm. The dimension of the cylindrical lens is 22 mmm x 20 mm.

The catalogue number in the figure is for a grating with 300 lines/mm blazed at 500 nm. The size is 25 mm x 25 mm x 6 mm.  The ThorLabs catalogue has gratings with different line densities (the maximum density usable on UVEX is 1800 lines/mm). For example, the grating of 1200l/mm blazed at 500 nm is GR25-1205, while the one blazed at 400 nm (special UV) is GR25-1204.

The slits used are those provided for the Shelyak Alpy 600 spectrograph (either printed on glass or clear slit version).

The detail of the optical scheme is given in the figures below (note: the orientation of the grating indicated corresponds to an etching density of 300 lines / mm, with the wavelength 510 nm positioned in the center of the detector):

And the following diagrams give the dimensions for the camera interfaces (for ATIK and ZWO):

Remember, since the optical elements are mostly mirrors, UVEX is not affected by chromatic aberration, the spectral range potentially covered is therefore very wide, with no need to adjust image. For example, on the ultraviolet side, the wavelength limit is the spectral cutoff induced by the Earth’s atmosphere (the ozone layer at high altitude), as shown in the figure below:

It would be necessary to go into space to do better! Another characteristic of UVEX is the high optical efficiency, which reaches 35% in the green (excluding the losses at the slit related to the enlargement of the star image because of seeing) – see the detail in the following figure:

This 35% value is a particularly high photon efficiency for a spectrograph (the final result depends on the intrinsic quantum efficiency of the detector and the wavelength). This result comes from the relatively simple optical scheme.  This is a conscious design choice, which has the tradeoff of an increase in the difficulty of adjustment compared to a more traditional spectrograph, as we will see later.

One thought on “2- The optical formula”

  1. Hi,

    I your document, you mention the use of a cylindrical lens.

    What is the focal length of the cylindrical lens?

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