Wide-Field Corrector designs are presented for the Blanco and Mayall telescopes, the CFHT and the AAT. The designs are Terezibh-style, with 5 or 6 lenses, and modest negative optical power. They have 2.2-3 degree fields of view, with curved and telec
entric focal surfaces suitable for fiber spectroscopy. Some variants also allow wide-field imaging, by changing the last WFC element. Apart from the adaptation of the Terebizh design for spectroscopy, the key feature is a new concept for a Compensating Lateral Atmospheric Dispersion Corrector, with two of the lenses being movable laterally by small amounts. This provides excellent atmospheric dispersion correction, without any additional surfaces or absorption. A novel and simple mechanism for providing the required lens motions is proposed, which requires just 3 linear actuators for each of the two moving lenses.
We present Simulated Annealing fiber-to-target allocation simulations for the proposed DESI and 4MOST massively multiplexed spectroscopic surveys, and for both Poisson and realistically clustered mock target samples. We simulate both Echidna and thet
a-phi actuator designs, including the restrictions caused by the physical actuator characteristics during repositioning. For DESI, with theta-phi actuators, used in 5 passes over the sky for a mock ELG/LRG/QSO sample, with matched fiber and target densities, a total target allocation yield of 89.3% was achieved, but only 83.7% for the high-priority Ly-alpha QSOs. If Echidna actuators are used with the same pitch and number of passes, the yield increases by 5.7% and 16% respectively. Echidna also allows a factor-of-two increase in the number of close Ly-alpha QSO pairs that can be observed. Echidna spine tilt causes a variable loss of throughput, with average loss being the same as the loss at the rms tilt. With a natural tilt minimization scheme, we find an rms tilt always close to 0.58 x maximum. There is an additional but much smaller defocus loss, equivalent to an average defocus of 30microns. These tilt losses offset the gains in yield for Echidna, but because the survey strategy is driven by the higher priority targets, a clear survey speed advantage remains. For 4MOST, high and low latitude sample mock catalogs were supplied by the 4MOST team, and allocations were carried out with the proposed Echidna-based positioner geometry. At high latitudes, the resulting target completeness was 85.3% for LR targets and 78.9% for HR targets. At low latitude, the target completeness was 93.9% for LR targets and 71.2% for HR targets.
