2.3 Inserts
2.3.3 Lenses
SPIDER’s telecentric lens design is identical to that of the BICEP2 experiment [8]. The refracting design of the SPIDER telescopes requires an objective lens and eyepiece lens, whose surfaces are described by simple conics. The lenses are separated by 550mm, with an effective focal length of 583.5mm. This yields a plate scale of 0.98 deg/cm on the focal plane and a field of view of 20◦ [78].
The lenses were machined from thick slabs of high-density polyethylene (HDPE). These slabs were annealed in a programmable oven prior to machining to relieve any internal stress in the material. This annealing step was found to be necessary by the BICEP2 team, who found that the internal stress of the lenses caused deformities during the anti-reflection (AR) coating process. The rough cutting of the lenses was done by an outside shop. The rough cut lenses were shipped back to us for another annealing cycle prior to the final machining of the lens.
The final lenses are measured on a CMM machine to ensure that final shape and surface finish are within the allowable tolerances. The final shape of each lens is described by the conic lens equation, where the surface height Z of the lens, in terms of the radius of curvatureR, is
Z(R) = cR2
1 +p
1−(1 +k)c2R2, (2.1)
wherec and kare constants that determine the curvature.
The lenses are then AR coated with porous PTFE sheets made by Porex. These sheets
(a) Eyepiece (b) Objective
Figure 2.4: Diagrams of the SPIDER lenses.
Table 2.1: Material Properties for SPIDER optics.
Thickness and indices of refraction for lenses and AR coating materials.
n d
HDPE 1.52 -
Nylon 6/6 1.75 -
PM23DR (90GHz lenses) 1.2 0.025”
PM23DR (150GHz lenses) 1.2 0.016”
PM23JR (90GHz nylon filters) 1.4 0.023”
PM23JR (150GHz nylon filters) 1.4 0.015”
are chosen to have an index of refraction close to the ideal of nAR = √
nlens. The thick- nesses are chosen such that they are nearly λ/4nAR, to within the tolerances given by the manufacturer. Table 2.1 shows the indices of refraction and the thicknesses of the PTFE sheets used for AR coating.
Adhering the PTFE sheets to the curved surfaces of the lenses requires a specialized jig. After the surface preparation of the lenses, a thin sheet of low-density polyethylene (LDPE) and a thicker sheet of Porex are lightly taped to both sides of the lens. The lens is then set in a concave Teflon mold that has the exact shape of the lens. A silicone sheet is vacuum-drawn over the top surface of the lens to press the sheets smoothly across the surface and help the lens keep its shape while in the oven. The entire jig and lens is then put into a programmable oven (still under vacuum) for approximately 10 hours at 124◦ Celsius to melt the LDPE layer while remaining below the melting point of the HDPE lenses (130◦ Celsius). The AR coating process must be must be done carefully to avoid wrinkling the Porex or the LDPE underneath. The LDPE is typically pre-stretched with a separate jig prior to being taped to the lens. Additionally, the PTFE sheets pick up dust and dirt extremely quickly, so the whole AR coating process is best done with gloves and extremely clean working surfaces.
Early on in the creation of the SPIDER lenses, we found that the AR coating process was significantly changing the shape of the lenses (see Fig. 2.5). We eventually found that this was due to the fact that the AR coating mold was made from aluminum, which had a different coefficient of thermal expansion than the lenses and thus was actually a slightly different shape than the lenses at the temperatures necessary to bond the AR coating. A new jig made from Teflon was found to alleviate this problem.
(a) (b)
Figure 2.5: Left: The results of fitting the CMM data from the X2 eyepiece to Eqn. 2.1.
Units are in inches. Right: The error between the shape of the X2 eyepiece lens as measured and the ideal shape of the eyepiece lens. The distinctive “cup-like” shape of the error indicates that the lens is being warped (too convex) by the shape of the AR coating jig.
The AR coating for all of the flight lenses for SPIDERand many of the nylon filters was my responsibility. The process seems to be working well thus far. Many of the lenses have been through multiple cool downs and have so far shown no signs of delamination.
The HDPE lenses contract much more than their aluminum mounts when they are cooled. The HDPE contracts by approximately 2%, while the aluminum contracts by only 0.4%. This works out to a radial differential contraction between the lens and its aluminum support ring of approximately 0.1”. In order to allow this contraction to happen while keeping the lens well centered (and not deforming the relatively soft plastic), we use copper flexures to attach the lens to the ring. There are eight of these flexures spaced evenly around the ring, as shown in Fig. 2.6.
(a) (b)
Figure 2.6: Copper flexures holding the objective lens (left) and eye lens (right).