The James Webb Space Telescope (JWST) Optical Simulation Testbed (JOST) is a tabletop experiment designed to reproduce the main aspects of wavefront sensing and control (WFSC) for JWST. To replicate the key optical physics of JWSTs three-mirror anastigmat (TMA) design at optical wavelengths we have developed a three-lens anastigmat optical system. This design uses custom lenses (plano-convex, plano-concave, and bi-convex) with fourth-order aspheric terms on powered surfaces to deliver the equivalent image quality and sampling of JWST NIRCam at the WFSC wavelength (633~nm, versus JWSTs 2.12~micron). For active control, in addition to the segmented primary mirror simulator, JOST reproduces the secondary mirror alignment modes with five degrees of freedom. We present the testbed requirements and its optical and optomechanical design. We study the linearity of the main aberration modes (focus, astigmatism, coma) both as a function of field point and level of misalignments of the secondary mirror. We find that the linearity with the transmissive design is similar to what is observed with a traditional TMA design, and will allow us to develop a linear-control alignment strategy based on the multi-field methods planned for JWST.
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