Fig. 1. Optical setup for wavefront measurement

Fig. 2. Walsh functions. (a) Segments formed by divided unit circle; (b) Walsh functions in polar coordinates (Black areas are assigned value of 1, white areas are assigned value of -1)

Fig. 3. Equivalent matrix of wavefront

Fig. 4. Mean value of absolute value of Walsh function coefficient

Fig. 5. Incident wavefront (PV is 1.43λ,RMS is 0.31λ)

Fig. 6. RMS of residual wavefront reconstructed with different number of Walsh functions

Fig. 7. Reconstructed real part of optical field

Fig. 8. Reconstructed imaginary part of optical field with selected 64 Walsh functions. (a) Absolute value of reconstructed imaginary part of optical field; (b) reconstructed imaginary part of optical field

Fig. 9. Reconstructed discrete wavefront. (a) Wrapped wavefront; (b) unwrapped wavefront

Fig. 10. (a) Wavefront after smoothing; (b) residual wavefront (PV is 0.074λ,RMS is 0.0086λ)

Fig. 11. Wavefront reconstructed with the first 256 Walsh functions. (a) Reconstructed wavefront; (b) residual wavefront (PV is 2.30×10-3λ,RMS is 1.58×10-4λ)

Fig. 12. Wavefront reconstructed results when signal-to-noise ratio of thermal noise is 30 dB. (a) Unwrapped discrete wavefront; (b) reconstructed wavefront; (c) residual wavefront between unwrapped discrete wavefront and incident wavefront; (d) residual wavefront of reconstructed wavefront (PV is 0.47λ,RMS is 0.045λ)