Measurement limitations in knife-edge tomographic phase retrieval of focused IR laser beams

An experimental setup to measure the three-dimensional phase-intensity distribution of an infrared laser beam in the focal region has been presented. It is based on the knife-edge method to perform a tomographic reconstruction and on a transport of intensity equation-based numerical method to obtain the propagating wavefront. This experimental approach allows us to characterize a focalized laser beam when the use of image or interferometer arrangements is not possible. Thus, we have recovered intensity and phase of an aberrated beam dominated by astigmatism. The phase evolution is fully consistent with that of the beam intensity along the optical axis. Moreover, this method is based on an expansion on both the irradiance and the phase information in a series of Zernike polynomials. We have described guidelines to choose a proper set of these polynomials depending on the experimental conditions and showed that, by abiding these criteria, numerical errors can be reduced.

Dual self-image technique for beam collimation

We propose an accurate technique for obtaining highly collimated beams, which also allows testing the collimation degree of a beam. It is based on comparing the period of two different self-images produced by a single diffraction grating. In this way, variations in the period of the diffraction grating do not affect to the measuring procedure. Self-images are acquired by two CMOS cameras and their periods are determined by fitting the variogram function of the self-images to a cosine function with polynomial envelopes. This way, loss of accuracy caused by imperfections of the measured self-images is avoided. As usual, collimation is obtained by displacing the collimation element with respect to the source along the optical axis. When the period of both self-images coincides, collimation is achieved. With this method neither a strict control of the period of the diffraction grating nor a transverse displacement, required in other techniques, are necessary. As an example, a LED considering paraxial approximation and point source illumination is collimated resulting a resolution in the divergence of the beam of σ φ = ± μrad.