1. Introduction

Recently, holographic storage has received increasing attention owing to its potentially high storage capacity and fast data access rate. Its large storage capacity is realized by means of multiplexing schemes, such as angular multiplexing, wavelength multiplexing, shift multiplexing and phase-code multiplexing [1, 2]. Most of them relate to the Bragg selective reconstruction of specific holograms out of an entire ensemble of holograms except phase encoding techniques.

In the last decade, V. Markov proposed the speckle multiplexing scheme [3, 4], which is based on the spatial autocorrelation character of speckle field and realized by using the same speckle reference beam and shifting the storage material. It can be called the static speckle multiplexing scheme [5, 6]. In our last paper, Q.S He ets. proposed a novel dynamic speckle multiplexing scheme [7, 8], which generates different speckle fields by moving the random phase diffuser, instead of the storage crystal as implemented in the static speckle multiplexing scheme. One advantage of dynamic speckle multiplexing is that it can be combined with other multiplexing schemes easily. Subsequently, we incorporated both the dynamic speckle multiplexing and static speckle multiplexing schemes for high capacity holographic storage. As can be seen from Fig. 1, the idea of this hybrid multiplexing scheme is to record some holograms by first shifting a holographic diffuser in the reference beam as a random-phase modulator and then shifting the LiNbO₃:Fe crystal to record another serious of holograms. We call this multiplexing scheme “Dynamic-Static speckle multiplexing (DSSM)”, a holographic data storage method chosen for its simple setup and the potential to offer further data storage capability. Each reference beam interferes in the crystal with object beam carrying information. To retrieve the data, the object beam is blocked and the phase modulator reproduces the specific phase code to which the required data has been addressed.

 

Fig. 1. Geometry of DSSM holographic storage.

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In this paper we propose a recording schedule for DSSM holographic storage. The theoretical analysis is applied to the recording of multiplexed holograms that reconstruct with equal diffraction efficiencies. Experimental results demonstrating the validity of this schedule are presented for holograms recorded in both LiNbO₃:Fe and LiNbO₃:Fe:In crystals.

As is well known, each newly recorded hologram has tiny effect on the retrieval, but partially erases all previously stored images. Therefore, if uniform recording time and uniform exposure intensity are applied to record all the holograms, each hologram recorded previously must have a lower diffraction efficiency than that recorded at a later time [9, 10]. Burke and Psaltis proposed a recording schedule called sequential exposure that effectively compensates the erasure of the later-recorded holograms [11, 12]. But all these conclusions were obtained by using a collimated light as the reference beam, so some basic experiments in our DSSM system were implemented to demonstrate that it is still valid when we use a speckle reference beam. According to the experimental results, the recording and erasing process can also be drawn as an exponential curve like using a collimated light. So the recording schedule can be applied directly in the dynamic speckle multiplexing process.

In the next section, we propose a novel exposure schedule that can optimize DSSM holographic storage scheme. Before our analysis, two assumptions should be considered for DSSM: one is that all the holograms in one position of the crystal are governed by the dynamic speckle multiplexing; the other is that erasing effect between every two positions is proportional to the superposed area of every two recording faculae. When these two positions are completely overlapped, the schedule is the same as that of the dynamic multiplexing storage. Along this way, our overriding goal will be to explore: for a sequence of DSSM holograms, how long should each frame be recorded to achieve uniform image playback intensity?

2. Principle

As stated earlier in the paper, the DSSM recording process records M frames of holograms in one position by shifting the holographic diffuser in the reference beam and then to record another M frames of holograms by shifting the storage material. Finally, M×N holograms can be recorded in the crystal as shown in Fig. 2.

 

Fig. 2. Schematic diagram of the DSSM holograms.

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According to the two assumptions above, if the facular point radius of the reference beam is r, and the shift distance between two points is l (l<2r), the superposition area can be calculated as follows.

 

Fig. 3. Relationship diagram of the overlapped holograms.

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The shaded area showed in Fig. 3 can be calculated as:

We can now define an overlap-factor γ_overlap, which represents the proportion of overlapped areas

This factor can be regarded as a constant to compensate for the erasure effect of the static speckle multiplexing scheme. So we can adopt the sequential exposure schedule here in our DSSM system by introducing a factor γ_overlap. Since the diffraction efficiency of each hologram is roughly proportional to the square of the refractive-index modulation depth, the formulae can be derived. First, the recording and erasing process can be respectively written as:

where Δn_s is the saturated steady-state index of refraction modulation, Δn and Δn’ are the refractive-index modulation after being exposed for time t and erased for time t’ respectively and τ_r, τ_e is the recording and erasure-time constants. γ_uv is the overlap-factor between the uth hologram and the vth hologram. The function of the overlap-factor is to increase the erasure-time constant and weaken the erasure effect.

When M holograms are recorded in one recording position, and then N positions are implemented by shifting the crystal in the DSSM storage system. Every hologram must be partially erased by all other holograms recorded after it. Here Δn_g is defined as the refractive-index modulation of the gth (g=1,2,…, NM) hologram.

Generally, the recording- and erasure-time constants are not the same, and we equate the index of refraction modulation of every hologram,

In this model, it is reasonable to expect uniform diffraction efficiency if a recording sequence satisfies the criterion that Δn_ij=Δn _i′j′.

To simplify the recursion formula of the exposure schedule, the numbers of the two-dimension holograms here are converted to one-dimension 1,2…M × N. Substitute Eq. (6) into Eq. (4), then the exposure schedule can be obtained as an inverse recursion formula,

Where t_N×M is the exposure time of the last hologram in the last point.

Where t _(i-1)×M+k represent the exposure time of the kth hologram in the ith point. Finally, the exposure time of the first hologram can be expressed by,

Now, we deduced the exposure schedule, which is an inverse recursion formula. It is similar with the schedule of the dynamic speckle multiplexing, but with an erasure factor γ_overlap to compensate for the erasure effects of the DSSM scheme. Some experiments are executed by using an iron-doped lithium niobate. The validity of the exposure schedule of the DSSM has been validated and the diffraction efficiencies of the recorded holograms are comparatively uniform.

3. Experiment

We used a diode pumped laser at 532 nm as the light source. The hologram recording medium is a LiNbO₃:Fe crystal of 45° cut, and its dimensions are 10×10×10mm. The laser was collimated and split into two parts. One was the signal beam modulated by a resolution chart incident on the crystal. The other beam was incident on a diffuser, with the passing wave as the reference beam. The signal and the reference beams were incident on adjacent surfaces of the crystal. Thus the incident angle is approximately 90°. Two accurate motion stages are used in this system to execute the DSSM process. Stage.1 is used to control the vertically lateral movement of the diffuser, and stage 2 is used to control the horizontal movement of the crystal. The experimental setup is shown in Fig. 4.

 

Fig. 4. Experimental setup.

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It should be emphasized that the result is valid only if τ_w and τ_e are all constants for every frame in the recording sequence. This requires precise survey of the writing- and the erasure-time constants of the crystal. Another practical problem arises from the fact that we cannot directly measure τ_w and τ_e, but must deduce these constants (under our exposure conditions) from experimental observations.

We adopted Eq. (8) to generate different series of recording time schedules. By using this schedule, we obtained DSSM storage with 10×10 holograms. This means that 10 holograms are recorded in one position and 10 positions are recorded in a LiNbO₃:Fe crystal doped with 0.03wt%Fe. Generally, the intensity of the gray scale is proportional to the diffraction efficiency of the hologram. The experiment result is shown in Fig. 5(a). To reduce the scattering noise in the reconstructed figures and increase the recording rate, a second type of crystal (LiNbO₃:Fe:In which is doped with 0.03wt%Fe and 1.0mol%In) is employed to record 10×10 holograms with the same scheme. The experiment result has a less than ±6.2% fluctuation and is as shown in Fig. 5(b). The result also demonstrates the validity of the schedule.

 

Fig. 5. Experimental result (a) in a LiNbO3:Fe crystal; (b) in LiNbO3:Fe:In crystal.

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The demonstrative experiment with 20×20 holograms was executed in a LiNbO₃:Fe:In crystal. The expected uniformity in diffraction efficiency with ±7.67% fluctuation can be observed, as shown in Figs. 6(a) and (b).

 

Fig. 6. Experimental result in a LiNbO3:Fe crystal with 20×20 holograms.

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4. Conclusion

An accurate theoretical model for the exposure-schedule in DSSM holographic storage has been developed. An erasure factor γ_overlap is introduced to compensate for the erasure effect. Experimental results demonstrating the validity of this approach are also presented. Using this schedule, 400 holograms with uniform diffraction efficiencies were recorded in a LiNbO₃:Fe:In crystal. We realize the dynamic-static speckle multiplexing scheme with uniform diffraction efficiency experimentally, which offers the best potential to realize super-high storage density.