Recently, interferometric null-testing with computer-generated hologram has been proposed as a non-contact and high
precision solution to the freeform optics metrology. However, the interferometry solution owns some typical
disadvantages such as the strong sensitivity to the table vibrations or temperature fluctuations, which hinders its usage
outside the strictly controlled laboratory conditions. Phase retrieval presents a viable alternative to interferometry for
measuring wavefront and can provide a more compact, less expensive, and more stable experimental setup. In this work,
we propose a novel solution to freeform metrology based on phase retrieval and computer-generated hologram (CGH).
The CGH is designed according to the ray tracing method, so as to compensate the aspheric aberration related to the
freeform element. With careful alignment of the CGH and the freeform element in the testing system, several defocused
intensity images can be captured for phase retrieval. In this paper the experimental results related to a freeform surface
with 18×18mm2 rectangular aperture (its peak-to-valley aspherity equals to 193um) are reported, meanwhile, we also
have compared them with the measurement results given by the interferometry solution, so as to evaluate the validity of
To deal with the problem of phase-shifting interefrometry with different unknown phase shifts, some special designed algorithms have been put forward by former researchers, such as the advanced iterative algorithm (AIA) and the principal component analysis (PCA) demodulation algorithms. This paper proposes a novel solution for it. Firstly, the captured phase-shifting interefrograms are differentiated to remove the additive background term. Then the trigonometric functions of the modulation phase can be extracted with the blind signal separation method. Simulations and experiments have been carried out to validate the feasibility of the proposed algorithm, where both open and closed fringe patterns are involved. Besides, the comparison results with the AIA and PCA algorithms are also provided.