In the reflecting version, the first lens collimator is replaced by a parabolic collim ator in double pass. The author modelled a simplification o f the configuration using an off-axis parabolic m irror and a flat m irror that could be tilted to the correct angle in place o f the echelle and adjacent cross disperser prism [72]. W ith the echelle near L ittrow giving negligible anamorphism, this is a valid approxim ation. The L ittrow configuration refers to an echelle in which the incident and reflected beam s are not
separated in the plane o f dispersion o f the grating. Three possible reflecting B aranne arrangem ents w ere investigated, and are detailed below.
4.3.1. Layout A: No Cross Dispersion Prior to the
Intermediate Echellogram
This arrangem ent requires the slit to be oriented in the tangential plane, with respect to the off-axis parabola. N ote that this slit orientation is not always the most desirable for minimum aberrations. In this version a beam o f f-num ber 19 diverges from the N asm yth focus, which is incident upon an off-axis parabola. The m irror collimates the beam onto an echelle grating (a plane m irror in ou r model). W e show the arrangem ent in figure 4.5.
In order for the collimated beam to correctly align w ith a grating placed immediately below the slit, an angle o f 2 degrees is required betw een the optical axis o f the telescope and the axis o f the parabola. After dispersion from the grating rays are again reflected o ff the parabola and imaged above the slit length. In such an arrangem ent no cross dispersion has been introduced prior to the form ation o f an interm ediate Echellogram above the slit.
A berrations are introduced when rays strike a parabolic m irror at significant angles w ith respect to the optic axis. It follows that w avelengths diffracted at large angles from the echelle suffer from larger aberrations. In o rd er to correctly model the echelle dispersion using a plane mirror, the mirror w as angled specifically in the tangential and sagittal planes for each individual wavelength to be investigated.
N ot to Scale 5880m m ^ 25m m 18.6mm Entrance Sli O ff A xis Parabola o O ff A xis Angle = 2 Solid Arrows = Rays Before Echelle Reflection Hollow Arrows = Rays After Echelle Reflection
Echelle Grating - M odelled by Plane Mirror
■Plane mirror angle = 0.3“ = 0.15“ Gamma angle for Echelle)
Figure 4.5 ; The Reflecting Baranne; Schematic o f the Ray Tracing M odel
The author modelled two variants o f this arrangement in order to investigate the effects o f these aberrations on slit images at different wavelengths. These tw o layouts w ere identical apart from using the dispersion characteristics o f 79g/mm and 31g/mm R2 echelle gratings respectively, each with a beam size o f 300mm. These results do not include aberration effects due to the length o f the slit, but this w as taken to be +/- 30 arc seconds to allow room for beam clearance from the intermediate Echellogram. The intermediate Echellogram was set at 25mm above the slit.
Analysis o f spot diagrams using the 79g/mm echelle model revealed that the aberrations are greater than 0.5mm at worst, equivalent to 0.65 arc seconds on the sky. This w ork assumes that complete orders up to 7000 Angstroms are
accom m odated, and this gives a field o f +/- 300mm either side o f the slit. W ith an R2 echelle o f 31g/mm the field size is reduced to +/- 120mm and the spot sizes are smaller and found to be 0.3mm or less, representing 0.4 arc seconds on the sky. The smaller levels o f aberrations o f this latter option are due to the intrinsically shorter F S R o f this type o f echelle. B oth o f these options w ere rejected due to the unacceptable effects o f geom etric aberrations on spectrograph perform ance. The author also investigated toroidal collimating surfaces, but concluded they offer little advantage in this application w here good imaging perform ance is required over a large num ber o f field positions.
4.3.2 Layout B: Cross Dispersion Prior to the Intermediate
Echellogram
The author also modelled several other variants o f this type o f collim ator arrangem ent [see docum ent 72 on page 24]. These consisted o f optical layouts in which cross dispersion is achieved in front o f the echelle, producing a 2 dimensional interm ediate Echellogram above the slit. These options require even larger incidence angles on the parabolic m irror at second pass. As a result the aberrations w orsen considerably.
4.3.3 Layout C: A Twin Off-axis Parabola Arrangement
By addition o f a second o ff axis parabolic m irror to the above arrangem ent w e can investigate another option [72]. Tw o parabolic mirrors are located face to face, w ith one collimating light onto an echelle grating and another identical m irror re- collimating it again after reflection from the first mirror. H ow ever this system requires a large physical area, and is unfeasible for HROS due to space limitations.