Introduction
The dispersing element is a key element in modern astronomical spectrographs, since it has to provide the required dispersion and resolution with the largest possible efficiency. As dispersing element, the diffraction grating covers most of the applications, sometimes coupled with prisms both as GRISM or immersed grating (especially for the infrared).
Among the different kinds of diffraction gratings, Volume Phase Holographic Gratings (VPHGs) are extremely interesting thanks to some unique features:

• the large peak diffraction efficiency (theoretically up to 100%) also at large dispersion (line density, G, up to 5000 l/mm);
• the easy customization that is often required in the astronomical spectrographs;
• the robustness;
• the possibility to make large size elements.

Consequently, VPHGs have become the baseline in the modern astronomical spectrographs working in the visible and near infrared spectral region at low and moderate resolutions. And spectrographs are common workhorse instruments in virtually every observatory. Furthermore, large size telescopes are equipped with several instruments of that type that offer different resolving power and/or wavelength range coverages.

How a VPHG works
VPHGs work thanks to a periodic modulation of the refractive index (Δn) stored in a holographic material with a defined thickness (d) [Fig. 1, Fig. 2].
The periodic modulation is induced by means of a two laser beams interference pattern that promotes a localized photoreaction. Looking at the diffraction efficiency of the VPHGs (in the case of pure phase gratings), it depends mainly on:

• rilm thickness (d);
• Refractive index modulation (Δn);

For high dispersion gratings (high values of line density, G), the large peak efficiency and bandwidth is achieved by maximize the Δn and minimize the film thickness d. For low dispersion gratings (low values of line density, G), if we increase the refractive index modulation too much, the light will be sent more and more in different diffraction orders.
Consequently, the optimization of the efficiency by choosing d and Δn will follow different paths depending on the features of the grating and the required spectral response.

Once you have chosen the parameters, the VPHG provide a diffraction efficiency curve (blaze curve) that is peaked at the Bragg angle (angle of incidence, AOI, equal to the diffraction angle). Moreover, the blaze curve can be tuned in wavelength by changing the incidence angle obtaining the superblaze curve [Fig. 3].

The VPHG can be used in transmission alone or coupled with prisms in a GRISM configuration. The former is the classical use of diffraction gratings; the latter is suitable for instruments capable of both imaging and spectroscopy, such as focal reducers [Fig. 4].