Conclusion

We showed that fractional Fourier transforms were well adapted to analyze diffraction figures.

The intensity distribution of in-line holograms is partly described by two joint linear chirped functions.

We established a relation allowing us to link the fractional index to the position of the object during the recording.

Hence, we note that, if the frequency drift is cancelled, we focus on the object at the same time.

Finally, thanks to the definition of , we synthesized the mathematical definitions of FT, the optical definition of FRFT and the digitization of optical signals by a digital acquisition system.

* Figure 13: Representation of the order FRFT Wigner distribution of .

Acknowledgements: I want to thank my former PhD students to have taken part in this document. I also thank my colleagues Denis Lebrun and Marc Brunel to use this document in the M2 DIODE syllabus.