BRIEF DESCRIPTION OF THE DRAWINGS
For a better understanding the invention shall now be explained in more detail in the following description with reference to the figures. It is understood that the invention is not limited to this exemplary embodiment and that specified features can also expediently be combined and/or modified without departing from the scope of the present invention. In the figures:
FIG. 1 schematically depicts a holographic pickup used in a holographic storage system,
FIG. 2 depicts a further schematic view of the light beams impinging on the holographic storage medium,
FIG. 3 illustrates the positions of the reference beam and the object beam on the objective lens,
FIG. 4 schematically shows a k-sphere representation of recording and reading with an uncorrected and a corrected wavelength mismatch,
FIG. 5 depicts a k-sphere representation of angle-multiplexed recording and reading,
FIG. 6 depicts a k-sphere representation of angle-multiplexed reading with a wavelength mismatch,
FIG. 7 shows the wavelength dependency of the diffraction efficiency,
FIG. 8 shows the region of the diffraction peak for four different wavelength mismatches,
FIG. 9 depicts the diffraction peaks of holograms read with a wavelength mismatch for different defocusing values,
FIG. 10 shows the diffraction efficiency in dependence on the lens shift in z-direction, and
FIG. 11 schematically depicts a compensation method according to the invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
In holographic data storage digital data are stored by recording the interference pattern produced by the superposition of two coherent laser beams. An exemplary setup of a holographic pickup 1 for use in a holographic storage system is shown in FIG. 1. A source of coherent light, e.g. a laser diode 2, emits a light beam 3, which is collimated by a collimating lens 4. The light beam 3 is then divided into two separate light beams 7, 8. In the example the division of the light beam 3 is achieved using a first beam splitter 5. However, it is likewise possible to use other optical components for this purpose. A spatial light modulator (SLM) 6 modulates one of the two beams, the so called “object beam” 7, to imprint a 2-dimensional data pattern. Both the object beam 7 and the further beam, the so called “recording reference beam” 8, are focused into a holographic storage medium 10, e.g. a holographic disk or card, by an objective lens 9. At the intersection of the object beam 7 and the recording reference beam 8 an interference pattern appears, which is recorded in a photo-sensitive layer of the holographic storage medium 10.
The stored data are retrieved from the holographic storage medium 10 by illuminating a recorded hologram with a readout reference beam 8′ only. The readout reference beam 8′ is diffracted by the hologram structure and produces a copy of the original object beam 7, the reconstructed object beam 11. This reconstructed object beam 11 is collimated by the objective lens 9 and directed onto a 2-dimensional array detector 13, e.g. a CCD-array, by a second beam splitter 12. The array detector 13 allows to reconstruct the recorded data. In order to compensate for wavelength deviations of the readout reference beam 8′ in comparison to the recording reference beam 8′, the holographic data storage system 1 includes a wavelength mismatch compensation element 14 and a wavelength mismatch determination unit 18. Advantageously, the wavelength mismatch determination unit 18 measures the wavelength of the readout reference beam 8′ and compares this wavelength with information about the wavelength of the recording reference beam 8, which is recorded on the holographic storage medium 10. Of course, the wavelength mismatch determination unit 18 may also employ other methods for measuring the wavelength mismatch.
FIG. 2 shows a more detailed view of the exemplary holographic storage system with respect to the focusing of the recording reference beam 8 and the object beam 7 into the holographic storage medium 10 by the objective lens 9. The two beams 7, 8 interfere in, or close to, the Fourier plane of the objective lens 9 within a storage layer 16 of the holographic storage medium 10. During readout of the stored data the medium 10 is illuminated with a readout reference beam 8′ only. The reconstructed object beam 11 passes through an optional buffer layer (not shown), is reflected by a mirror layer 17, passes trough the optional buffer layer, the storage layer 16 and a cover layer 15, and is collimated by the objective lens 9. The correction element 14 is preferentially located close to the objective lens 9. It is likewise possible that the objective lens 9 is part or the correction element 14. Preferably, the correction element 14 is a lens with a variable focal length, a telescope, a diffractive optical element, or the objective lens 9 itself.
In FIG. 3 the positions of the (recording or readout) reference beam 8, 8′ and the object beam 7 on the objective lens 9 are illustrated. FIG. 3a) shows the case of the exemplary holographic storage system 1 of FIGS. 1 and 2, whereas FIG. 3b) shows a case where the reference beam 8, 8′ is located in a central circular region of the objective lens 9, while the object beam 7 is located in a surrounding ring-shaped region of the objective lens 9.
The diffraction efficiency of a volume hologram decreases when the hologram is read out with a wavelength that is different from the wavelength used during recording. At the same time the object beam quality is reduced with regard to optical aberrations. This situation is known as wavelength mismatch.
FIGS. 4
a) to c) illustrate a k-sphere representation of the situation during recording with a wavelength λ1 (FIG. 4a)), when reading with a longer wavelength λ2 without correction (FIG. 4b)), and when reading with a longer wavelength λ2 with correction (FIG. 4c)). It is to be noted that in figures the k-spheres have been normalized to a unit k-sphere. The object beam 7 and the reference beam 8 are considered as plane waves. During recording, the wave vectors R1 (reference beam) and S1 (object beam) generate a grating vector G1. As can be seen in FIG. 4b), reading the grating structure with a wave vector R2, which has a different wavelength (in this example a longer wavelength) leads to a Bragg mismatch B of a reconstructed object beam S2. According to the invention, the direction of the wave vector R2 is changed such that the resulting reconstructed object beam S2=R2+G1 fulfills the Bragg equation and the Bragg mismatch is equal to zero. In this case the direction of the reconstructed object beam S2 is also changed.
According to a first embodiment of the invention, the change of direction of the wave vector R2 is achieved by modifying the focal length of the objective lens 9 according to the following equation:
where fi is the effective focal length of the combination of correction element 14 and the objective lens 9. The subscripts 1 and 2 refer to the original wavelength λ1 and the shifted wavelength λ2. The modification of the focal length is preferentially achieved by an additional lens with a variable focal length, a telescope, or a diffractive optical element. It is likewise possible to use the lens with the variable focal length as the objective lens 9.
When the focal length is changed, the distance between the holographic storage medium 10 and the objective lens 9 is preferably also changed in such a way that the focal plane is situated on the reflective layer 17 of the holographic storage medium 10. This means that, if the focal length f1 is changed to f2, the distance between the objective lens 9 and the reflective layer 17 is also changed from f1 to f2.
From the k-sphere diagrams illustrated in FIG. 4 the wavelength selectivity can easily be derived. The wavelength selectivity can be defined as the difference between the reading wavelength and the recording wavelength where the diffraction efficiency reaches its first zero. Theoretically this is the case when
with Δλ=λ2−λ1, θs the angle of the (reconstructed) object beam, θf the angle of the reference beam and L the hologram thickness. For a hologram of thickness L=200 μm and angles θs and θf of 10°, this results for a recording wavelength of 400 nm in a selectivity of Δλ=13 nm.
FIG. 5 illustrates the k-sphere diagrams for the case of a spherical recording reference beam 8, as used for example for shift multiplexing. The spherical recording reference beam 8 can be understood as a sum of plane waves with different angles. The diagram in FIG. 5a) shows three exemplary plane waves R1,i of this sum of plane waves. The resulting grating vectors are indicated by short dashed lines G1,i.
When reading the hologram with the same wavelength each plane wave, e.g. the one which has recorded the ‘central’ grating vector, simultaneously reads all recorded grating vectors. However, due to the Bragg mismatch of all other gratings only the ‘central’ grating is read out with a high diffraction efficiency, as illustrated in FIG. 5b).
The situation encountered in case of reading with a different wavelength is shown in FIG. 6. FIG. 6a) shows the case of a longer wavelength λ2, FIG. 6b) the case of a shorter wavelength λ2. Since the readout reference beam 8′ consists of different plane waves, there will be always one plane wave which fulfills the Bragg condition for one of the gratings. However, in contrast to the case of reading with the correct wavelength λ2=λ1, the reconstructed object beam 11 exhibits some deficiencies:
- 1. The angle of the reconstructed object beam 11 is different from the angle of the original object beam 7.
- 2. Since the grating vectors G1,i do not meet at the same point of the k-sphere, the reconstructed object beam 11 consists not only of a single plane wave, but of a set of plane waves with different angles. This results in an aberration of the reconstructed object beam 11. A more detailed discussion of this aspect will be given below.
- 3. Not all the gratings G1,i can be read with a different wavelength, as not all of the necessary reference beam angles are available. In FIG. 6 it can be seen that the fans of the reference beams R2,i of the second wavelength (solid lines) and the reference beams R1,i of the first wavelength do not overlap completely. Therefore the total diffraction efficiency is lower.
FIG. 7 shows the wavelength dependency of the diffraction efficiency η (intensity of the reconstructed signal beam) obtained from beam propagation simulations for a setup with a spherical recording reference beam and readout reference beam. The underlying parameters are:
λ1=405 nm
n=1.5, Δn=0.00002
hologram thickness: d=200 μm
distance of spherical wave origin from center of hologram: z=500 μm
numerical aperture of readout reference beam: NA=0.30, 0.4
object beam angle (outside medium): θ=10°
As can be seen, a higher numerical aperture results in a higher wavelength selectivity.
Apart from the diffraction efficiency η it is also interesting to study the aberrations of the diffracted light. As discussed before, the reconstructed beam will differ from a plane wave if a wavelength mismatch is present. Therefore, the peak representing the signal beam of a single SLM pixel imaged on the detector will be distorted in case of a wavelength mismatch. This could have the negative effect of an increased crosstalk between neighboring pixels of the SLM imaged on the detector.
FIG. 8 shows the region of the diffraction peak for four different wavelength mismatches of Δλ=−50 nm (FIG. 8a)), Δλ=−25 nm (FIG. 8b)), Δλ=0 nm (FIG. 8c)), and Δλ=+20 nm (FIG. 8d)). The simulation is based on the parameters as in FIG. 7 with NA=0.3. As expected, the peak shows large distortions in case of large wavelength differences. The distortion of the beam could be more critical for reading the hologram than the lower diffraction efficiency, since the smearing of the peak occurs already at relatively small wavelength mismatches.
As described with reference to the k-sphere diagram in FIG. 6, the wavelength mismatch causes a ‘fan’ of reconstructed plane waves. According to a further aspect of the invention the readout reference beam 8′ is defocused in order to compensate for the aberrations resulting from wavelength mismatches. In FIG. 9 the diffraction peaks of holograms read with a wavelength mismatch of Δλ=−25 nm are shown for different defocusing values, i.e. different distances zread of the origin of the spherical reference wave. The underlying distances zread are zread=480 μm (FIG. 9a)), zread=500 μm (FIG. 9b)), zread=520 μm (FIG. 9c)), and zread=540 μm (FIG. 9d)), which corresponds to offsets from the nominal position of −20 μm, 0 μm, +20 μm, and +40 μm, respectively. The diffraction peak becomes sharp if the focus is adjusted to zread=520 m instead of the correct focus where the hologram was recorded, i.e. zread=500 μm.
This means that a wavelength mismatch can be corrected by displacing the lens 9 producing the spherical readout reference beam 8′ in z-direction. In other words, the beam distortion caused by a wavelength mismatch is corrected by defocusing the readout reference beam 8′. This is preferentially done with the focus servo itself. Additional error signals are preferably generated from the detector image so that the displacement of the lens 9 is automatically adjusted to achieve an optimal peak shape. Of course, also an additional optical element may be used for defocusing.
FIG. 10 shows the diffraction efficiency η in dependence on the shift Δzread in z-direction. It can be seen that also the total diffraction efficiency η is increased if the wavelength mismatch is compensated by a z-shift of the readout reference beam 8.
In FIG. 11 a compensation method according to the invention is schematically depicted. In a first step 20 a wavelength mismatch Δλ is determined 20. In the next step 21 the necessary compensation for the determined wavelength mismatch Δλ is determined. The wavelength mismatch Δλ is the compensated by either defocusing 22 the readout reference beam 8′ or by adjusting 23 the focal length of the objective lens 9.
Patent Application
20070242326
