Fig. 1. Schematic optical setup of SWLI system and its image formation principle

Fig. 2. Most commonly used types of interferometers in SWLI. (a) Michelson; (b) Mirau; (c) Linnik

Fig. 3. NA cone limit of SWLI when measuring a tilted optical flat. (a) 0° tilt; (b) the tilt angle β larger than the NA cone limit angle θ

Fig. 4. Additively manufactured surfaces measured by SWLI. (a) A PBF Al-Si-10Mg sample (image courtesy of Dr Helia Hooshmand at University of Nottingham); (b) laser PBF Al-Si-10Mg sample surface; (c) laser PBF Ti-6Al-4V sample surface; (d) electron beam PBF Ti-6Al-4V sample surface

Fig. 5. SWLI measurement of a ceramic coating on a metal surface^[44]. (a) Cross-sectional slice through the 3D SWLI interferogram; (b) one-dimensional interference signal at a single surface point along the z-axis; (c) (d) topography of the top surface and the substrate, from which the coating layer thickness can be calculated

Fig. 6. Simulated measurement of films surrounded by air (central wavelength is 532 nm, bandwidth is 100 nm, NA is 0.3, and the refractive index of the film is 2). (a) Interference signal for 3 μm-thick film;(b) interference signal for 0.6 μm-thick film

Fig. 7. Stroboscopic SWLI. (a) Optical setup of the system; (b) measurement of the surface topography of a capacitive micromachined ultrasonic transducer membrane operating at 2.72 MHz^[55]

Fig. 8. Simulated SWLI measurement of a step height with sharp edges. (a) Profile of the step height (width is 8 µm, height is 0.75 µm); (b) cross-sectional interferogram; (c) difference between the simulated measurement and the ground truth, the batwing effect is obvious

Fig. 9. Schema of the optical setup of Fourier scatterometer based on SWLI and pupil imaging

Fig. 10. Interferometric objective lens design (courtesy of Zygo Corporation). (a) The “De Groot-Biegen” interferometer; (b) a 0.5× interferometric objective with the Michelson geometries

Fig. 11. Sub-aperture stitching measurement result of a single-point diamond turned sinusoidal surface^[112]

Fig. 12. Experimentally measured 3D STF of a commercial SWLI (central wavelength is 570 nm, bandwidth is 100 nm, NA is 0.55) ^[129]. The cross sections of (a)(c) magnitude and (b)(d) phase of the 3D STF; (e)(f) magnitude and phase of the in-pupil 2D STF. The 2D STF is calculated as a projection of the 3D STF along the longitudinal direction [in an aberration-free system, the phase terms in (b)(d)(f) should be zero]

Fig. 13. Simulated interferogram of a vee-groove with the dihedral angle of 70° and the depth of 10 mm using a rigorous SWLI model. The reversed interference fringe can be observed

Fig. 14. Nanometer-precision lateral distortion can be measured using an arbitrary surface based on image correlation and self-calibration^[155]. (a) An arbitrary coin surface; (b) intensity image of a local surface region under the interference microscope; (c) three measurement positions in a typical self-calibration procedure; (d) measured lateral distortion of a commercial SWLI

Fig. 15. Modeled (left column) and experimental (right column) fringes of a blazed grating at different tilts. An SWLI model based on the BEM is used. The PV amplitude of the grating is 200 nm and the frequency is 300 lp/mm^[27]. The solid blue line represents the surface profile used in the model

Fig. 16. SWLI measurement of a sinusoidal surface (pitch is 15 µm, PV amplitude is 1.35 µm) before and after the error correction. The 2π errors are effectively removed

Fig. 17. Concept of the virtual SWLI for surface topography measurement^[179]