Fig. 1. Schematic representation of the experimental setup used to generate Laguerre–Gaussian beams and characterize diffractive optical elements. The fundamental Gaussian beam, emitted by a He-Ne laser source ( nm, mW), was relay imaged and collimated onto an SPP, transformed into an optical vortex and detected by a high-resolution S-H wavefront sensor (HASO4 126 VIS, Imagine Optics, number of sub-pupils , pupil size , bit RGB color depth) placed in the Fourier plane of the SPP element. RI, collimating relay imaging system; L1–L11, plano-convex lenses; M1, M2, plane mirrors; DM, deformable mirror; BS, beam splitter; BD, beam dump; HASO, wavefront sensor; PRM, on-axis parabolic mirror; SPP, spiral phase plate; RM, reference plane mirror. The values f1–f11 and fPRM are the focal lengths of lenses L1–L11 and of the PRM.

Fig. 2. A optical profiler image with a height range of 3 m. The height was exaggerated to observe the curved background and the stitching artifacts.

Fig. 3. Relative error of the step heights across the phase plate, compared with the average value.

Fig. 4. Wavefront distortion as measured with the Shack–Hartmann setup: (a) initial wavefront; (b) wavefront after masking out the discontinuities.

Fig. 5. Starting field distribution of irradiance (a), (b) and equi-distributed phase (c). Image (d) shows the phase distortion corresponding to the fitted polynomial. The squares have a size of 80 mm. The irradiance distributions in (a) and (b) are normalized to the same power and share the same intensity scale. The unit of phase distributions is one wavelength.

Fig. 6. Simulated irradiance profiles in focus and the relative standard deviation (in percent RSD) of the circular sections through the points with the highest value. The phase jump in the initial phase distribution was, for all images calculated, in the upper left quadrant, at an angle of 36.6° with the vertical. The rows index the initial spatial distribution of the field: super-Gaussian (a)–(d) or measured in the HPLS (e)–(h). The columns index the step height distribution across the spiral: nonuniform as measured, with the wavefront background being polynomial (a), (e) or flat (b), (f); uniform between the total height difference measured (c), (g); uniform, with corrected total height (d), (h). For the last two columns, no polynomial distortion of the wavefront was applied. The images share the same range of values for the color map.

Fig. 7. Two ways of approximating a continuous phase plate of (dashed green line) with a discrete, -step plate (orange in (a) and blue in (b)) and the resulting optical path length difference (OPLD) as a function of the azimuth . The largest phase jump is in (a), but in (b) it is .

Fig. 8. Coefficient of variation of the circular section in the focus as a function of the relative lateral shift between the phase plate and the HPLS beam.

Fig. 9. Circular sections (a) through the irradiance profiles in focus for several cases, and azimuthal integration (b) of the respective profiles. The legend refers to the images from Figure 4 and their respective RSDs.