Design and alignment of an all-spherical unobscured four-mirror image relay for an ultra-broadband sub-petawatt laser

We describe the design and alignment of an unobscured reflective image relay for use in an ultra-broadband half-petawatt laser system in development at the University of Rochester's Laboratory for Laser Energetics. The design consists of four spherical mirrors in an unobscured configuration. We show the theoretical basis for such a four-mirror design using first-order optical matrix methods and nodal aberration theory. We also describe the process of aligning this design in a test bed and show the results of this alignment method. We were able to achieve a diffraction-limited nominal design. Upon aligning the design in our test bed, we were able to successfully align the design to achieve our target wavefront error of less than 0.3 waves peak to valley and 0.07 waves rms at the central laser-operating wavelength of 910 nm.