**4. Computer generated holograms tool**

The idea of using computers to define and generate holograms was proposed by the middle of the 60's (Brown & Lohmann, 1966). Some essential aspects of CGHs are:


in Optics 5

A Contribution to Virtual Experimentation in Optics 361

where *d* is the grating spacing, *f* is the focal length of the Fourier lens, and *λ* is wavelength of the collimated light beam. Relative intensities of the diffraction orders are proportional to the grating structure *a*/*d*. In any CGH, it is important to maximize light on the desired diffraction

DE <sup>=</sup> Light in the desired diffracted order

measures such light maximization. To this end, when the basic CGH cell is calculated, such 2D cell is repeated to form the CGH structure; spatial invariance of the Fourier transform means that every single cell produces the same diffraction pattern at the output plane, contributing to increased DE. The type of optical material in which the CGH is implemented also contributes

CGHs calculated in section 4.2 are binary-only (*i.e.* pixels have only two possible values, black or white). Depending on the type of physical object where the CGH is implemented, it can be a Binary Amplitude Hologram (*i.e.* photographic film, where black pixels correspond to dark zones and white pixels are transparent zones in the film) or a Phase-only Hologram (for instance, using a Liquid Crystal Spatial Light Modulator, where the two possible orientation

of the liquid crystal molecules correspond to phase states differing by *π*).

Total incident light (2)

Fig. 4. Main interface for laboratory experiments

to have a good DE.

order (usually +1). Diffraction efficiency DE, defined as:

(b) Picture of the actual laboratory assembly

CGHs have long been used in optical processing information, optical interconnects, interferometry and health diagnosis, to name just a few relevant applications (Yaroslavsky & Astola, 2009). Advances in computer power, together with the development of sophisticated manufacturing methods, are causing CGHs to become increasingly efficient and complex.
