Fig. 1. CGH null test of freeform surface. (a) Test layout; (b) test surface and result; (c) CGH patterns and diffraction structures; (d) test system^[13]

Fig. 2. Ghost disturbance in CGH null test. (a) Test layout for a cylinder with tilt carrier^[17]; (b) ghost fringe resulted from reflection of CGH in null test of a cylinder^[17]; (c) ghost fringe resulted from reflection of CGH in null test of an on-axis asphere

Fig. 3. Linear mapping between pixels on the imaging plane and transverse coordinates on the virtual RS instead of the CGH plane^[23]

Fig. 4. Mapping distortion correction for CGH null test of a parabolic surface with large off-axis paraboloid^［23］

Fig. 5. Traceability chain of CGH null test^[24]

Fig. 6. CGH cross test with a calibrated sphere

Fig. 7. Three-step absolute test of cylinders. (a) W₁; (b) W₂; (c) W₃^[17]

Fig. 8. CGH multiplexing techniques for absolute test of aspheres. (a) Twin-CGH^[35]; (b) radial shearing^[38]

Fig. 9. Subaperture stitching with CGHs for measuring large convex aspheres. (a) Near-null test^[39-41]; (b) null test^[42]

Fig. 10. CGH null test of an even asphere with large aspheric departure (3.56 mm)

Fig. 11. Failure cases of CGH null test. (a) Impractical size of CGH required; (b) gull-wing asphere; (c) stitching-based interference microscopy^[46]

Fig. 12. Comparative test of a gull-wing asphere. (a) Stitching interference microscopy; (b) CGH null test; (c) null fringe interference pattern for CGH null test; (d) full aperture surface error (RMS 60.9 nm) obtained by stitching interference microscopy; (e) central convex part of stitched map (RMS 24.9 nm); (f) central convex part of CGH null test (RMS 21.8 nm)^[46]

Fig. 13. Sharing CGH null test for simultaneous measurement of primary and tertiary mirrors. (a) Without pattern overlap; (b) with pattern overlap

Fig. 14. Subaperture test enabling resolving local big error. (a) Irresolvable full aperture fringes; (b) data loss in full aperture measurement; (c) reconstructed surface error by subaperture stitching

Fig. 15. SLM-based adaptive null interferometry. (a) Unknown surface reconstruction based on iterative close-loop control of the SLM phase function^[55]; (b) fringe reduction from invisible to null fringe states^［55］; (c) measurement of bi-conic Zernike surface (setup, freeform departure, and point-to-point difference of 0.039λ RMS from cross test)^［54］; (d) hybrid refractive and diffractive null combining the SLM with high order even asphere singlet can be adapted to a large range of freeform aberrations^［57］

Fig. 16. In-situ CGH null test integrated on an ultra-precision turning machine. (a) System setup^［65］; (b) simultaneous measurement of mirror surfaces S1 and S3^［65］; (c) machined surfaces S1 and S3 sharing the same substrate^[66]