Storage Capacity & Limits

The storage density of a hologram depends not only on the properties of the recording medium but also on the resolution of the other optical components in the system, e.g., the laser beam width, as well as lens and mirror quality. In order to be able to produce a hologram grating with a period of $\Lambda_{\mathrm{min}}$, all spatial fluctuations of the light beams must be smaller than $\Lambda_{\mathrm{min}}$. If we realistically assign the best possible resolution of a recording apparatus as $\Lambda_{\mathrm{min}}\approx \lambda$, taking the optical system into account, we get, from van Heerden [14], the maximum storage density for a 2-D hologram as:

$$N_{\mathrm{2D}}^{\mathrm{max}} = \frac{1}{\lambda^2}$$ (28)

and for a 3-D hologram

$$N_{\mathrm{3D}}^{\mathrm{max}} = \frac{1}{\lambda^3}$$ (29)

Thus, the maximum storage density depends on wavelength and dimensions as summarized in Table 2. The same diffraction limitations exist also for digital recordings. For commercial plane optical memory discs, typically it is $\sim 10^8$ bit/cm$^2$, for a total capacity of $6\times 10^9$ bit on a 130 mm diameter disc [15,2].

Table 2: Theoretical maximum storage density for given wavelength.

$\lambda$, nm	Dimensions
	2-D		3-D
650	240	Mbit/cm$^2$	3.64	Tbit/cm$^3$
600	280	Mbit/cm$^2$	4.63	Tbit/cm$^3$
550	330	Mbit/cm$^2$	6.01	Tbit/cm$^3$
500	400	Mbit/cm$^2$	8.00	Tbit/cm$^3$
450	500	Mbit/cm$^2$	11.00	Tbit/cm$^3$
400	625	Mbit/cm$^2$	15.62	Tbit/cm$^3$
350	820	Mbit/cm$^2$	23.32	Tbit/cm$^3$

There is one more limitation called structural resolution which is a property of recording medium. It depends on the atomic structure of the material (the evenness in the distribution of the photoactive centers), as well as on the macroscopic inhomogeneities (variation of $n$) in the bulk material and on the degree of surface roughness and flatness. Typical spatial resolution for commercially available photographic emulsion (Agfa-Gevaert, Eastmann-Kodak) is about 5000 lines/mm, corresponding to $d_{\mathrm{rec}}= 0.2 \mu\mathrm{m}$ (i.e. $d_{\mathrm{rec}}<d_{\mathrm{min}}$).This is physical limit for silver halide caused by grain structure of elementary light sensitive areas after development [2] The best real time recording media have a higher resolution than silver halides, e.g. $\mathrm{As_{2}S_{3}}$ thin films have $d_{\mathrm{rec}}\le 0.1 \mu\mathrm{m}$ (Sect. 3).