What is a pupil slicer, and how does it work with anamorphic optics in VLT's ESPRESSO Echelle spectrograph? This excellent answer points to ESPRESSO, - Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations. From there I looked at the Instrument Description and Performance page.

The page describes three parts or th esystem:


Coudé Trains (transporting light from each of the VLT's four telescopes)
Front Ends (corrections, stabilizations, fiber pick-up) 
Spectrograph (fiber output, pupil slicer, Echelle grating, collimator, dichroic splitter, Red and Blue cameras)


I'm wondering what the pupil slicer is, and how it works exactly.


  At the entrance of the spectrograph, an anamorphic pupil slicing unit (APSU) shapes the beam in order to compress the beam in cross-dispersion direction but not in main-dispersion direction, where high resolving power needs to be achieved. In the latter direction, however, the pupil is sliced and superimposed on the echelle grating to minimize its size. The rectangular white-pupil is then re-imaged and compressed by the anamorphic VPH grism.


I'm familliar with the basics of how an Echelle spectrograph works, and as far as anamorphic optics, I understand this to mean that not all of the elements are not cylindrically symmetric so that the size and divergence changes in one plane is different than in the perpendicular plane. (Classic example is Anamorphic format).

Question: What is a pupil slicer, and how does it work with anamorphic optics in VLT's ESPRESSO Echelle spectrograph?

below: The Spectrograph itself. Light enters from the right from an optical fiber, and the anamorphic pupil slicer (whatever that is) forms a diverging beam to illuminate the entire Echelle grating (beam shown in gray) via the collimator. Everything else in this drawing is post-grating.
In order to reach the stability required for planet detection, the majority of high resolution echelle spectrographs are mounted off the telescope in a stable environment. This involves pressure and temperature stabilization, often by housing the spectrograph in a vacuum vessel. 

In order to feed the spectrograph with light from the telescopes, and to reduce the effect of image motion causing variations in the slit illumination and corresponding variations in the spectral line shape which would mask the tiny radial velocity changes     we are trying to measure, optical fibers are used to feed the light. However there are two disadvantages to this: 1) the fiber is now round (although octagonal fibers are the new hotness for their better image scrambling properties) and not a long slit, and 2) due to focal ratio degradation, the output of the fiber is wider (lower f/ratio) than the fiber input which decreases the spectrograph resolution.

In order to combat these effects and increase the resolution, which is needed to measure the tiny 1/1000th pixel shifts caused by low mass planets, image slicers are typically used to reformat the output fiber into a new more slit-like shape. The classic example is the Bowen-Walraven image slicer which uses a glass plate and prisms to slice the circular fiber image into 2 semi-circles and stack them on top of each other. Higher efficiency versions using mirrors or glass slabs have been made more recently; this ESO SPIE publication has some examples of alternative constructions and the resulting image shapes. There is also this page which has more details, including construction of a prototype.

I am not an expert on optical design or anamorphic optics but I suspect this is done because the beam is not the same size and shape in the spatial/cross-dispersion direction compared to the dispersion/wavelength direction and so equal power in the optical elements in each direction is not needed. Given the size of the input beam from the 8.4m VLT that will feed ESPRESSO, and the need to get the whole instrument into an affordable vacuum vessel that will keep vacuum for a long time, I would imagine the designers employed as many tricks as they could in order to keep the size of the instrument down; the Optical Design section of the ESPRESSO Overview paper talks a little more about this.