WE PROPOSE TO DEVELOP NEW HIGH-PRECISION X-RAY TELESCOPE MIRROR TECHNOLOGY THAT IS CRITICALLY NECESSARY FOR PLANNED NASA MISSIONS WITH SUB-ARC-SEC HPD ANGULAR RESOLUTION GOALS INCLUDING FOR EXAMPLE EXPLORER CLASS MISSIONS SUCH AS STAR-X AND FORCE PROBE CLASS MISSIONS SUCH AS AXIS TAP AND HEX-P AS WELL AS LARGE MISSIONS SUCH AS LYNX. THE PROPOSED EFFORT BUILDS ON PREVIOUS RESEARCH AT MIT AND COMPLEMENTS NASA-SUPPORTED RESEARCH AT OTHER INSTITUTIONS. WE PROPOSED WORK PLAN INCLUDES (1) IMPROVED METHODS FOR STRESS-FIELD MIRROR CORRECTION (2) COMPENSATION OF MIRROR DISTORTION CAUSED BY COATING STRESS (3) STABILIZATION AND SMOOTHING OF MIRROR COATINGS AND (4) IMPROVED MIRROR FIGURE METROLOGY. THIN SHELL MIRRORS WITH RESOLUTION IN THE SUB-ARC SECOND DOMAIN REQUIRE SIGNIFICANT ADVANCES IN MIRROR SHAPING COATING AND CORRECTION TECHNOLOGY. FOR THE PROPOSED WORK WE WILL FOCUS OUR EFFORTS ON THE POLISHED SILICON MIRRORS BEING FABRICATED BY THE NEXT GENERATION X-RAY OPTICS (NGXO) GROUP AT GODDARD SPACE FLIGHT CENTER. WE CHOSE THESE PARTICULAR MIRRORS FOR OUR RESEARCH SIMPLY BECAUSE THESE ARE THE BEST AVAILABLE AT THE PRESENT TIME. OVER THE LAST YEAR THE NGXO GROUP HAS PROVIDED MIRRORS FOR US TO DEVELOP IMPROVED MIRROR CORRECTION TECHNIQUES WHICH HAS ALLOWED US TO SUCCESSFULLY DEMONSTRATE FOR THE FIRST TIME COATED X-RAY MIRRORS WITH SUB-ARCSEC SLOPE ERRORS APPROACHING LYNX REQUIREMENT. WE PROPOSE TO FURTHER DEVELOP ON-GOING RESEARCH IN MIRROR STRESS-BASED FIGURE CORRECTION USING MEV ION BEAM SILICON MICROFABRICATION AND FEMTOSECOND LASERS. SINCE PROGRESS IN THE FIELD INTO THE SUB-ARC SEC DOMAIN IS NOW STRONGLY LIMITED BY METROLOGY ERROR WE ALSO PROPOSE TO DEVELOP RADICALLY IMPROVED METROLOGY TOOLS. WE ALSO PROPOSE TO CONTINUE WORK ON A VARIETY OF BEAM-BASED MIRROR FABRICATION COATING AND CORRECTION TECHNIQUES TARGETED SPECIFICALLY TO THE PROPOSED LYNX MISSION.