homodyne readout on dc-removed coaxial holographic data storage

Homodyne readout on dc-removed coaxialholographic data storage

Shin Yasuda,* Yasuhiro Ogasawara, Jiro Minabe, Katsunori Kawano,and Kazuhiro Hayashi

Research and Technology Group, Fuji Xerox Company, Ltd., 430 Sakai,Nakai-machi, Ashigarakami-gun, Kanagawa 259-0157, Japan

*Corresponding author: [email protected]

Received 21 May 2009; revised 1 November 2009; accepted 13 November 2009;posted 16 November 2009 (Doc. ID 111699); published 10 December 2009

Multiplexing characteristics of a dc-removed coaxial holographic storage system were evaluated for whatis believed to be the first time. Our dc-removed coaxial system achieved 3.5 times higher raw data densitythan a conventional coaxial system that involved dc recording. The increase of the data density was duenot only to lessM=# consumption but also to the effects of signal amplification and noise reduction by useof the positive and negative images reconstructed from the same holograms. © 2009 Optical Societyof America

OCIS codes: 210.2860, 210.4680, 090.0090.

1. Introduction

Coaxial holographic data storage [1,2], in which thesignal and reference beams propagate along a com-mon optical axis, has been one of the most promisingconfigurations that achieve high data capacity andhigh data transfer rates because the optical setup notonly can be compact but also can tolerate environ-mental disturbances such as mechanical vibration.However, this configuration has some issues to con-sider with regard to the optical noise and the dy-namic range M=# (Ref. [3]) of the media, where M=#is the sum of the square root of the diffraction effi-ciency of the corresponding multiplexed hologram.The issue of M=# is concerned with the recording

process in which data pages are recorded as Fourierholograms in the medium. It is reported that theusable M=# for Fourier holograms of data pages isat least 2–10 times lower than that for holograms re-corded with plane waves [1]. This loss is attributed tospatially nonuniform intensity distributions of therecording beams inside the medium. In particular,the dc components of the recording beams, which

are much higher in intensity than other Fourier com-ponents, produce the nonuniformity and consume alarge amount of M=#.

To avoid exposure of the high-intensity dc compo-nent, we have proposed a method of removing the dccomponents on recording and adding the phase-modulated dc component of the signal beam togetherwith the readout reference beam on reading [4]. Thephase modulation of the additional dc component ispossible by utilizing the nature of the liquid crystalsconstituting the spatial light modulator (SLM) used.That is, the phase matching of the additional dc com-ponent with the reconstructed dc-removed signalbeam can be made by controlling the gray level of theuniform image expressing the additional dc region onthe SLM. The reconstructed image is formed by in-terference between the additional dc component andthe reconstructed dc-removed signal beam. Becauseboth of the beams have the same frequency, this read-ing method is regarded as homodyne detection,which is well known in the fields of communicationtechnology and so forth. With this method, we havedemonstrated that recording energy was saved sothat M=# consumption was reduced.

As for the optical noise, coaxial configurations aremore vulnerable to optical noise that results from

0003-6935/09/366851-11$15.00/0© 2009 Optical Society of America

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nonuniformity of the medium and optics, leading todegrading the reconstructed images [5,6]. This isbecause, upon readout, optical noise attributed to re-ference beam can enter the detector more easily com-pared with off-axial configurations such as angularmultiplexing.To solve the problems of both M=# and the optical

noise, we have developed the method in Ref. [4] andproposed amethod of removing the dc components onrecording and reconstructing both positive and nega-tive images on reading [7]. The reconstruction of thecontrast-reversed image is possible by using a con-trast-reversed reference pattern without changingthe additional dc component of the signal beam. Thisis because the contrast-reversed reference patternprovides the reconstructed dc-removed signal beamwith a phase difference of π compared with the recon-struction by use of the original reference pattern. Inthis method, we have demonstrated that comparisonbetween both images reduced optical noise, i.e., bothM=# consumption and optical noise were reduced.Incidentally, it seems that reconstruction of the

contrast-reversed image would also be possible withthe method in Ref. [4] by modulating the phase of theadditional dc component. However, that would be dif-ficult in practice because the phase and intensity ofthe additional dc component cannot be controlled in-dependently by the SLM. Moreover, it is not alwayspossible to reconstruct both positive and negativeimages because of the dynamic range limitation ofthe phase shift provided by the SLM. Therefore, themethod in Ref. [7] is more suitable for practical use.Although we have demonstrated the advantages of

the above-mentioned dc-removal methods by em-ploying a single hologram, a detailed analysis of themethods and the multiplexing characteristics arestill unavailable.In this paper, we describe an analysis of homodyne

readout on dc-removed coaxial holographic datastorage and indicate that signal amplification andnoise reduction can be realized. We also present themultiplexing characteristics of dc-removed coaxialholographic data storage and show that more holo-grams can be recorded compared with the con-ventional method, which involves recording the dccomponents. Moreover, we show that both signal am-plification and noise reduction were verified experi-mentally by comparison of positive and negativereconstructed images.

2. Principle

We describe the principle of reconstructing positiveand negative images from the same Fourier holo-grams that have been recorded without the dccomponents. Let us consider an arbitrary two-dimensional amplitude distribution sðx; yÞ as a signalpattern. As sðx; yÞ expresses black-and-white distri-butions, sðx; yÞ is defined as 1 for ON (white) pixelsand 0 for OFF (black) pixels as shown in Fig. 1(a).sðx; yÞ can be expressed by superposing its dc compo-nent sdc and higher order (ac) components shðx; yÞ,

i.e., sðx; yÞ ¼ sdc þ shðx; yÞ, where sdc is a positiveconstant.

Fourier transforming sðx; yÞ, we obtain its Fouriercomponents Sðμ; νÞ ¼ F½sðx; yÞ�, where F½ � denotesthe Fourier transform. Sðμ; νÞ may be separated tothe dc component sdcδðμ; νÞ and the higher order com-ponents Shðμ; νÞ, i.e., Sðμ; νÞ ¼ sdcδðμ; νÞ þ Shðμ; νÞ,where Shðμ; νÞ ¼ F½shðx; yÞ�. Since the dc componentis removed on recording, only Shðμ; νÞ is recordedas a hologram. The higher order component shðx; yÞis shown schematically in Fig. 1(b).

In most cases of holographic data storage systems,a low-pass filter such as the Nyquist filter is placed atthe Fourier transform plane for decreasing the re-cording region, i.e., for increasing the data density. Inthe analysis below, however, the effect of the low-passfilter on the pixel spreading is neglected and the fillfactor of the SLM is assumed to be 100%.

The following are descriptions of four differentreading methods. In these descriptions, we pay at-tention to the homodyne readout principles and de-scribe the signal amplification and noise reduction ofthe data pages reconstructed by our homodyne read-out methods.

A. Positive Image Reconstruction Method

In order to reconstruct a positive image that has asimilar contrast to the original signal pattern, theoriginal reference pattern is used as a readout refer-ence pattern. By following the same proceduredescribed in Ref. [4], the reconstructed image is ex-pressed by

Fig. 1. Schematics of the amplitude distributions of (a) the origi-nal signal pattern sðx; yÞ, and (b) the dc-removed signal patternshðx; yÞ that is to be recorded as a hologram.

6852 APPLIED OPTICS / Vol. 48, No. 36 / 20 December 2009

Ipðx0; y0Þ ¼��adcðΔφÞ

��expðiðΔφ −ΔθÞÞ þ tshðx0; y0Þ��2;

ð1Þ

where jadcðΔφÞj is the amplitude of the additional dccomponent of the signal beam, Δφ is a phase shift ofthe additional dc component from the readout refer-ence beam, Δθ is a phase shift of the reconstructedsignal beam from the readout reference beam, t isa coefficient depending on the diffraction efficiencyand the intensity of the readout reference beam,and ðx0; y0Þ is the coordinate of the inverse Fouriertransform plane, i.e., the image sensor plane. Δφcan be controlled by the nature of liquid crystals con-stituting the SLM.Δφ is determined so that jadcðΔφÞj is phase

matched with tshðx0; y0Þ at the image sensor plane,i.e., Δφ ¼ Δθ. In the case of phase holograms whoserefractive index modulations are in phase withrespect to the intensity fringe patterns, Δθ ¼ π=2is satisfied [8,9]. This is true of the photopolymersthat are currently most prospective holographicmaterials.Consequently, Eq. (1) can be rewritten as

Ipðx0; y0Þ ¼ jjadcj þ tshðx0; y0Þj2; ð2Þ

where jadcj stands for the additional dc componentthat satisfies Δφ ¼ Δθ. Because the dc and the high-er order components are phase matched to eachother, the intensity distribution is the square of thecoherent sum of these amplitudes.Assuming that IpON and IpOFF are the intensities of

ON and OFF pixels of the image sensor, respectively,these intensities are represented, with reference toFig. 2(a), by

IpON ¼��adc

��þtð1 − γÞ��2; ð3Þ

IpOFF ¼��adc

��−tγ��2; ð4Þ

where γ is a white rate that is the ratio of the numberof ON pixels to that of the total pixels consisting ofthe signal pattern when the fill factor of SLM is100%. In the above equations, we use γ in place ofsdc by utilizing the relation γ ¼ sdc.Thus, the signal component Δμp of Ipðx0; y0Þ is ex-

pressed by

Δμp ¼ IpON − IpOFF ¼ 2t��adc

��þt2ð1 − 2γÞ: ð5Þ

In order that Ipðx0; y0Þ forms a positive image lookingsimilar to the original signal pattern, Δμp > 0 mustbe satisfied. In this case, jadcj should satisfy the fol-lowing relation:

��adc

��> tð2γ − 1Þ=2: ð6Þ

When 0 < γ < 1=2, the right-hand side of relation (6)is negative. In this case, relation (6) is always satis-fied. Therefore, relation (6) is the condition to be sa-tisfied when 1=2 ≤ γ < 1. In usual cases, t can beregarded as t ≪ 1. Therefore, Eq. (5) can be rewrittento be

Δμp ≈ 2t��adc

��: ð7Þ

Relation (7) indicates that Δμp increases almost lin-early with increasing jadcj.B. Negative Image Reconstruction Method

Next, we will describe how to reconstruct negative(contrast-reversed) images from the same Fourierhologram from which the positive image has been re-constructed by the above method. Contrast reversalof the reconstructed images can be carried out simplyby reversing the contrast of the readout referencepattern. This method utilizes the effect that the con-trast-reversed readout reference pattern produces aphase difference of π from the reference pattern usedon recording, while the spatial frequency distributionis unchanged (see Appendix A). Therefore, the recon-structed signal beam is represented by −tshðx0; y0Þ,which is π out of phase with respect to tshðx0; y0Þ.

By following the same procedure obtaining Eq. (2),the reconstructed image is expressed by

Inðx0; y0Þ ¼��adc

��−tshðx0; y0Þ��2: ð8Þ

Assuming that InON and InOFF are the intensities ofON and OFF pixels of the negative (contrast-reversed) reconstructed image Inðx0; y0Þ, respectively,these intensities are represented, with reference toFig. 2(b), by

Fig. 2. Schematics of the intensity distributions of the (a) positiveand (b) negative reconstructed images. Higher order componentsof both images are π out-of-phase with respect to each other.


InON ¼��adc

��þ tγ��2; ð9Þ

InOFF ¼��adc

��−tð1 − γÞ��2: ð10Þ

Thus, the signal component Δμn of Inðx0; y0Þ is ex-pressed by

Δμn ¼ InON − InOFF ¼ 2t��adc

��−t2ð1 − 2γÞ: ð11Þ

In order that Inðx0; y0Þ forms a negative image,Δμn >0 must be satisfied. In this case, jadcj should satisfythe following relation:

��adc

��> −tð2γ − 1Þ=2: ð12Þ

When 1=2 < γ < 1, the right-hand side of relation(12) is negative. In this case, relation (12) is alwayssatisfied. Therefore, relation (12) is the condition tobe satisfied when 0 < γ ≤ 1=2.As is the same in Δμp, t can be regarded as t ≪ 1.

Therefore, Eq. (11) can be written as

Δμn ≈ 2t��adc

��: ð13Þ

Relation (13) indicates thatΔμn increases almost lin-early with increasing jadcj, which is the same asin Δμp.By comparison of relations (6) and (12), reconstruc-

tion of both positive and negative images requiresthe satisfaction of relation (12) when 0 < γ ≤ 1=2 andthe satisfaction of relation (6) when 1=2 < γ < 1.In the above descriptions on positive image recon-

struction (PIR) and negative image reconstruction(NIR) methods, we take for granted that all the high-er order components of the signal beam are recorded.However, in most optical systems, a low-pass filtersuch as the Nyquist filter is employed for reducingthe hologram size, i.e., for increasing the data den-sity. Thus, some of the higher order componentsare removed by the low-pass filter. In this case,the requisite dc components for creating positiveand negative images, which depend on the filter size,are a little less than those in relations (6) and (12),respectively. Therefore, satisfaction of relations (6)and (12) is sufficient for creating positive and nega-tive images, respectively, regardless of the filter size.According to relations (7) and (13), the signal com-

ponents Δμp and Δμn increase almost linearly withjadcj. Therefore, increase of jadcj would always seemadvantageous for enhancing signal components de-tected by the image sensor. However, this is not al-ways true because a dynamic range of the imagesensor is finite. When too much jadcj is provided,the dc offset generated by IpOFF and InOFF, which con-sume the dynamic range of the image sensor in vain,also increase. To appreciate the enhanced signalcomponents, the dynamic range of the image sensor

is desired to be wide. In this manner, the maximumjadcj is confined practically by the dynamic range lim-itation of the image sensor.

C. Postprocessing by Use of Positive and NegativeImages

Here, we will show two kinds of processing methodsto improve the reconstructed image Ipðx0; y0Þ with thehelp of Inðx0; y0Þ; One is the difference image (DI)method and the other is the subtraction image (SI)method. For describing the both methods, Eqs. (3),(4), (9), and (10) are used.

In order that both the DI and SI methods are car-ried out, both the reconstructed images Ipðx0; y0Þ andInðx0; y0Þ should be converted by an image sensorinto digital images, namely, luminance distributions.However, when confusion does not occur, we ex-press the luminance distributions of the both recon-structed images by use of the same notations as de-noting the corresponding intensity distributions forsimplicity.

1. Difference Image Method

In the DI method, the processed image is obtained bycomputing the difference between the luminance ofeach pixel on the positive image Ipðx0; y0Þ and thatof the corresponding pixels on its negative imageInðx0; y0Þ. Thus, the dynamic range of the differenceimage is nearly doubled compared with both positiveand negative images. For example, if a dynamicrange (gray-level range) allocated for the positiveand negative images is from 0 to 255, the range of thedifference image is from −255 to 255.

We denote IdiffON and IdiffOFF as the intensity of theON and OFF pixels of the difference image obtainedin the DI method, respectively. IdiffON and IdiffOFF areexpressed by

IdiffON ¼ IpON − InOFF ¼ 4tjadcjð1 − γÞ; ð14Þ

IdiffOFF ¼ IpOFF − InON ¼ −4tjadcjγ: ð15Þ

Therefore, as is shown in Fig. 3, the signal compo-nent Δμdiff of the difference image is expressed by

Δμdiff ¼ IdiffON − IdiffOFF ¼ 4tjadcj: ð16Þ

As is shown in Eq. (16), Δμdiff is independent of γ.In this analysis, we have assumed that the inten-

sities of ON and OFF pixels in each of the re-constructed images Ipðx0; y0Þ and Inðx0; y0Þ are, respec-tively, the same regardless of the position on theimage plane. In reality, however, the intensity of eachpixel varies, depending on the position of the imagesensor. This is because each ON pixel of the signalpattern displayed on the SLM is not uniform dueto the intensity distribution of the illuminatingbeam. Furthermore, the reconstructed image isaffected by optical noise such as the scatter from


the medium. As a result, the intensity of each of theON and OFF pixels of the reconstructed imagevaries.We describe the effect of the DI method on the im-

provement of the reconstructed image Ipðx0; y0Þ. To doso, we take the signal-to-noise ratio (SNR) by consid-ering the above-mentioned intensity distribution inthe cases with and without optical noise such asthe scatter noise. SNR is defined by

SNR≡μON − μOFFffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiσON

2 þ σOFF2

p ; ð17Þ

where μON and μOFF are the average signals of ONand OFF pixels, respectively, and σON and σOFF arethe standard deviations of ON and OFF pixels, re-spectively. The numerator of the right-hand side ofdefinition (17) corresponds to the signal componentdescribed in this section.First, we consider a virtual case that no optical

noise exists. By comparison of Eqs. (5) and (16),Δμdiff is approximately 2 times more than Δμp.Hence, the DI method would seem more advanta-geous than the PIR method. However, from the view-point of SNR, it is not important because thestandard deviations of ON and OFF pixels on the dif-ference image also expand by a factor of∼2 due to theexpansion of the dynamic range of the intensity (lu-minance). Thus, in the absence of optical noise, theSNR of the difference image remains the same asthat of the positive reconstructed image Ipðx0; y0Þ.This means that even if the expanded dynamic

range is shrunk back to the original dynamic range,the SNR remains the same. In this case, the signalcomponent and the two standard deviations becomehalf and are also the same as those of the originalpositive reconstructed image Ipðx0; y0Þ. That is, theactual signal component becomes Δμdiff ¼ 2tjadcj,which is almost equal to Δμp in Eq. (7).In summary, expansion or contraction of the dy-

namic range is irrelevant to the SNR if no opticalnoise exists. Hence, the DI method would not seembeneficial to improve the SNR when no optical noiseexists. However, this is not the case when optical

noise exists in the reconstructed image. In the pre-sence of optical noise in Ipðx0; y0Þ, the noise can be re-duced by the DI method, the reason for which ismentioned below.

Typical noise components in coaxial configurationsare scatter from the medium and interference fringesdue to multiple reflections in the optics. These noisecomponents cause local (intrapage) variations of in-tensity at the inverse Fourier transform plane, lead-ing to increasing standard deviations σON and σOFF ofthe reconstructed image. Consequently, the SNR ofthe reconstructed image is degraded.

However, the influence of the local variations canbe reduced by utilizing the fact that two recon-structed intensity distributions Ipðx0; y0Þ and Inðx0; y0Þcontain the common noise components. This is be-cause the negative image reconstruction process re-verses only the contrast of the signal components byinterference, not the contrast of the noise compo-nents. Therefore, comparison of the two intensity dis-tributions Ipðx0; y0Þ and Inðx0; y0Þ can reduce the noisecomponents. The advantage of the DI method lies inthis noise reduction, i.e., the standard deviations σONand σOFF can be reduced. As a result, the SNR can beincreased.

2. Subtraction Image Method

Next, we describe the other processing method, i.e.,the SI method. In this method, the processed imageis obtained by subtracting a negative reconstructedimage Inðx0; y0Þ from its corresponding positive imageIpðx0; y0Þ. In this case, the equation IdiffOFF ¼ 0 is sa-tisfied, so that the signal component Δμsubt of thesubtraction image is represented, with reference toFig. 3, by

Δμsubt ¼ IdiffON ¼ 4tjadcjð1 − γÞ: ð18Þ

We should note that the dynamic range of the sub-traction image is the same as that of the positive im-age Ipðx0; y0Þ. Thus, by comparison of Δμp, we can seethat Δμsubt is amplified by a factor of ∼2ð1 − γÞ when0 < γ < 1=2. In the case of γ ¼ 1=2,Δμsubt ≈Δμp is sa-tisfied so that the signal amplification is notachieved. In the case of 1=2 < γ < 1, Δμsubt < Δμp issatisfied so that the signal is reduced. However, evenin this case, by taking the signal component by sub-tracting the positive image from the correspondingnegative image, the signal component can be ampli-fied by a factor of ∼2γ. If this γ is replaced byγ0ð¼ 1 − γÞ, both factors are identical to each otherso that the signal components can be amplified tothe same degree. Thus, we restrict our descriptionbelow to the case of when 0 < γ ≤ 1=2.

We can also see that optical noise in the OFF pixelsof Ipðx0; y0Þ decreases to null because of IdiffOFF ¼ 0.Consequently, the SI method can amplify the signalcomponent except when γ ¼ 1=2 and reduce the opti-cal noise in the positive reconstructed image Ipðx0; y0Þ.

Fig. 3. Schematic of the difference intensity distribution pro-duced by the positive and negative images. This distribution formsa difference image. Only the positive intensity values form a sub-traction image.


In order to satisfy Δμsubt > Δμp, the following rela-tion must be satisfied:

��adc

��> t=2: ð19Þ

This relation is easily satisfied since t is much lessthan 1.Similarly to the DI method, the SI method can in-

crease the SNR due to signal amplification and noisereduction. Improvements of SNR by the DI and SImethods have been demonstrated experimentallyand will be described in Section 3.

3. Experiments

A. Optical Setup

Figure 4 shows our coaxial configuration. We used afrequency-doubled Nd:YVO4 laser with a wavelengthof 532nm as the light source. After its emitting beamwas expanded and collimated with a beam expander,it was incident on a reflective SLM. Our SLM wasconstituted with a liquid-crystal array that consistedof 1024 × 768 with 28 gray scales=pixel. The pixelpitch and the linear fill factor of the SLM were19 μm and 93%, respectively. The SLM modulatedthe signal and reference beams according to the datapage displayed on it. In our experiment, 2 × 2 pixelsin the SLM were utilized as a single pixel block toexpress data pages. Figure 5 shows three data pagesthat were used in our experiment. Figure 5(a) wasused in recording. Figures 5(b) and 5(c) were usedfor reading positive and negative images, respec-tively. Our recording and reading processes are de-scribed in order below.In the recording process, the data page of Fig. 2(a)

was displayed on the SLM. The data page was com-posed of two parts, an inner part (signal pattern) andan outer part (reference pattern). The inner part hadthe data, whose capacity was 17:76kbits. As a codingmethod, we employed a modulation code [10,11] ofrate 5=9 code that expressed 5 bits by 2 ON pixelblocks (8 pixels) in 3 × 3 pixel blocks (36 pixels). Inthis code, the white rate γ was 0.22. Symbol error rate(SER) was defined as an error rate of the 5 bit dataunit. The outer part was formed by a random patternwith only ON and OFF pixels. The diameters of

its inner and outer circles were 520 and 768 pixels,respectively.

The SLM produced the signal beam from the innerpart and the reference beam from the outer part.These two beams were Fourier transformed by lensL1, and the dc components of both beams were re-moved by the dc stop located at the Fourier transformplane. The size of the stop was 200 μm × 200 μm.After the signal and reference beams without the dccomponents were inverse Fourier transformed bylens L2, these were Fourier transformed again bylens L3. The dc-removed beams were spatial filteredby circular aperture A1, whose inscribed square was1:2× linear Nyquist size. After that, the beams wererelayed by lenses L4 and L5, and a hologram was re-corded in the medium. The hologram size on theFourier plane was estimated to be 343 μm in dia-meter. As a medium, we used a 1mm thick photopo-lymer film that formed phase holograms. The dc-removed signal beam to be recorded is shown inFig. 6. Since the dc component was removed, the con-trast of the signal pattern is degraded.

For reading a positive image similar to the originalsignal pattern, the pattern shown in Fig. 5(b) wasdisplayed on the SLM and the dc stop was removedfrom the optical path. The pattern of Fig. 5(b) con-sisted of two parts: the outer part was the same re-ference pattern that had been used in recording, andthe inner part had the same luminance of a gray le-vel, the area of which covered the signal patternarea. The inner part was used for adding the dccomponent to the reconstructed signal beam. Theluminance of the inner part was determined to pro-vide the additional dc component with a phase shift

Fig. 4. Experimental setup: SH, shutter; HW, half-wave plate;PBS, polarizing beam splitter; SLM, reflective spatial light mod-ulator; L1–L10, lenses; A1–A3, apertures. Focal lengths of L1–L10in units of mm are 90, 90, 150, 105, 10, 10, 105, 105, 105, and 105,respectively.

Fig. 5. Patterns used on (a) recording and (b) reading positive re-constructed images and (c) reading negative reconstructed images.The reference patterns in (b) and (c) are contrast reversed to eachother while the gray level for the additional dc component isidentical.


of π=2 from the readout reference beam, so that theadditional dc component was in phase with the re-constructed signal beam. The reconstructed signalbeam and the additional dc component were inverseFourier transformed by lens L6 and relayed by lensesL7–L10. Circular aperture A2 was used for removingthe reference beam, and the inscribed square of cir-cular aperture A3 was of 1:2× linear Nyquist size.The reconstructed image was detected by the compli-mentary metal oxide semiconductor (CMOS) camera(2 × 2 pixels of the signal pattern were sampled by3:86 × 3:86 pixels of the CMOS camera).For reading a negative (contrast-reversed) image,

the pattern shown in Fig. 5(c) was displayed on theSLM and the dc stop remained removed from the op-tical path. The pattern of Fig. 5(c) consisted of twoparts similar to that in Fig. 5(b). The only differencebetween them was the pattern of the outer part; thereference pattern in Fig. 5(c) was contrast reversed tothe reference pattern that had been used in record-ing. Hence, the additional dc component and the re-constructed signal beam were π out of phase witheach other.In performing the DImethod, the dynamic range of

the postprocessed image was decreased by half sothat its dynamic range of the luminance was thesame as those of the PIR and SI methods, i.e., 28 graylevels.

B. Multiplexing Scheme

Figure 7 shows the multiplexing scheme we em-ployed, which is a raster scan method [12]. In thismethod, holograms are recorded along the shift di-rection first, and then along the track direction. Theshift pitch was set to 8 μm. The track pitch was chan-ged in accordance with the recording data density.We evaluated the central hologram that was over-

lapped by all the other holograms. The experimentalconditions are summarized in Table 1.

The recording energy for multiplexing each dc-re-moved hologram was 1:9mJ=cm2. For comparison,we also multiplexed conventional (dc-contained) ho-lograms, the recording energy of each of whichwas 3:3mJ=cm2.

The reading energy for each dc-removed hologramwas 221 μJ=cm2, in which the energies of both the ad-ditional dc and the reference beam’s dc componentswere included. As these dc components did not workfor reconstructing holograms, the effective energy forreconstruction was that of the only higher order com-ponents of the reference beams. The effective readingenergy was estimated to be 58 μJ=cm2.

In addition, the energy of the additional dc com-ponent was 129 μJ=cm2, which was 2.2 times greaterthan the effective reading energy. Thus, it is reason-able to assume that relations (12) and (19) weresatisfied.

On the other hand, we employed two kinds ofreading energies for conventional (dc-contained)holograms: one was 92 μJ=cm2, and the other was690 μJ=cm2. The former was obtained when theilluminating energy for the SLM was the same asin reading the dc-removed holograms. The formerand the latter were 1.6 and 11.9 times higher thanthe effective reading energy for dc-removed holo-grams, respectively.

4. Results and Discussion

A. Single dc-Removed Hologram Reconstruction

Figures 8(a) and 8(b) show the images from a singledc-removed hologram reconstructed by use of thepatterns of Figs. 5(b) and 5(c), respectively. As is seenin these figures, positive and negative images weresuccessfully obtained, which indicates that the addi-tional dc component was large enough to satisfy re-lations (12) and (19). The diffraction efficiency of thedc-removed hologram was estimated to be 9 × 10−2.

Since exposure scheduling was not performed onmultiplexing holograms, diffraction efficiency of amultiplexed hologram should be smaller than thatof the single hologram. Therefore, relations (12)

Fig. 6. Dc-removed signal pattern that was detected by CMOScamera. This pattern was recorded as a hologram.

Fig. 7. Multiplexing sequence: the central hologram thatwas overlapped by all the other holograms was evaluated as arepresentative.


and (19) should also remain to be satisfied in the caseof multiplexed holograms.The diffraction efficiency of the single dc-contained

hologram for which the reading energy was92 μJ=cm2 was almost the same as that of the dc-removed hologram.

B. Symbol Error Rate Characteristics

Figure 9 shows the SER dependence on raw datadensity. The PIR method shows that SER increasedmost quickly. However, the degradation of the SERwas improved by the DI and the SI methods. The DIand the SI methods show similar behavior andachieved the raw data density of 28:5Gbit=in:2 withan SER of less than 10−1, which can be corrected with40–50% error correcting codes [12].The reason that SER of the PIR method increased

most quickly would be attributed to the scatter fromthe medium generated by the additional dc compo-nent. Because the additional dc component was atleast 10 times higher in intensity than the recon-structed dc-removed signal beam, the considerablescatter would have been generated. Furthermore,as the raw data density or the number of multiplexedholograms increased, various noise sources attribu-ted to the medium itself and adjacent holograms alsoincreased. Therefore, the additional dc componentgenerated more optical noise as the number of holo-grams increased.However, as is explained in Subsection 4.C, the

optical noise mentioned above was reduced signifi-cantly by the DI and the SI methods. Furthermore,the SI method realized signal amplification. As a re-sult, SER was reduced so much that the achievableraw data density was greatly increased.As for the conventional method, the reconstructed

image for the data density of 8:2Gbit=in:2 was notrecognized with the reading energy of 92 μJ=cm2,

though this reading energy was higher than thatof PIR method. The reason would be that M=# of themedium was consumed more because the recordingenergy was higher. As a result, the reconstructed sig-nal beam would not have had a sufficient intensity tobe recognized by the CMOS camera. Thus, we em-ployed the higher reading energy of 690 μJ=cm2 forreconstruction for the data density of 8:2Gbit=in:2and more.

As shown in Fig. 9, the SER for conventionalmethod increased very quickly. The raw data densitywhose SER was less than 10−1 was 8:2Gbit=in:2,which was 3.5 times lower than that of the DI andthe SI methods.

C. Signal Amplification and Noise Reduction

Figure 10 shows the dependence of the signal compo-nents on raw data density, where the signal compo-nent is the difference between the average signals ofON and OFF pixels. The signal components of the SImethod were the highest in all the data densities. Bycomparison of the SI and the PIR methods, we con-firmed that the SI method amplified the signal com-ponents of the PIR method.

As was mentioned in Subsection 2.C.2, the maxi-mum amplification ratio was ∼2ð1 − γÞ, i.e., approxi-mately 1.6. However, above the data density of15:3Gbit=in:2, the amplification ratio was more than1.6. The excessive amplification would be attributedto the effect of the noise reduction made by the SImethod.

Figure 11 shows the variance dependence on rawdata density: Figs. 11(a) and 11(b) are for σON

2 andσOFF

2, respectively. As is shown in these figures, σON2

and σOFF2 for the SI method were smaller than those

for the PIR method. This means that the SI method

Table 1. Experimental Conditions

Number of Tracks Raw Data Density ðGbit=in:2Þ Number of Holograms Shift Pitch ðμmÞ Track Pitch (μm)

1 8.2 1 × 85ð85Þ —

3 15.3 3 × 85ð255Þ 1725 28.5 5 × 85ð425Þ 8 857 41.1 7 × 85ð595Þ 579 53.7 9 × 85ð765Þ 43

Fig. 8. (a) Positive and (b) negative images reconstructed fromthe same dc-removed hologram. Fig. 9. SER dependence on raw data density.


reduced the noise embedded in the positive recon-structed images. In other words, the positive recon-structed images had its signal components buried inthe noise, which made the intrinsic signal compo-nents appear small. This would be the reason thatthe excessive amplification ratio was obtained.

By comparison of the DI and the PIR methods inFig. 10, both methods had similar behavior until thedata density of 15:3Gbit=in:2. Above that data den-sity, however, the DI method had its signal compo-nents higher than the PIR method. The reasonwould be the same as that for the excessive signalamplification by the SI method. Namely, the noise re-duction by the DI method would make the signalcomponent buried in the positive image emerge. Thiswould be supported by the fact that σON

2 and σOFF2

for the DI method were smaller than those for thePIR method, as shown in Figs. 11(a) and 11(b).

The effect of noise reduction made by the DI andthe SI methods can be elucidated by investigatingthe change of the histogram of the positive recon-structed image. As an example, the reconstructedimages as well as their postprocessed images forthe case of 8:2Gbit=in:2 are shown in Fig. 12. Also,their corresponding histograms are shown in Fig. 13.

By comparison of the positive reconstructed image[see Fig. 12(a)] with the difference image [seeFig. 12(c)] and the subtraction image [see Fig. 12(d)],the contrast of the positive reconstructed image wasgreatly improved by the DI and the SI methods. Theeffect of the difference between the DI and the SImethods is depicted in the difference between theircorresponding histograms shown in Fig. 13. The DImethod caused the distributions for both ON andOFF pixels to become narrowed, which means thatthe noises on the ON and OFF pixels on the positivereconstructed image were reduced. On the otherhand, the SI method made both the distributions,especially the one for OFF pixels, become narrowed,which means that the noise especially on the OFF

Fig. 10. Dependence of signal components on raw data density.

Fig. 11. Variance dependence on raw data density: (a) and (b) arefor ON and OFF pixels, respectively.

Fig. 12. Reconstructed images and their postprocessed imagesfor the case of 8:2Gbit=in:2: (a) positive reconstructed image,(b) negative reconstructed image, (c) difference image, (d) subtrac-tion image.


pixels of the positive reconstructed image was re-duced. The difference of these noise reduction effectscan be understood reasonably by considering the dif-ference between these postprocessing methods de-scribed in Section 2.As wementioned the reason of realizing the optical

noise reduction in Section 2, both positive and nega-tive images reconstructed from the same hologramcontained the common noise components. Therefore,the common noise components were reduced by useof the two reconstructed images. In other words, theexperimental fact that the noise of the positive recon-structed image was reduced significantly by the DIand the SI methods indicated that the main causeof degradation of the positive image was the commonnoise components that had been generated by the ad-ditional dc component. This is because the additionaldc component was common to reading both the posi-tive and the negative images and also because theenergy of the additional dc component was as muchas 2.2 times higher than that of the higher order com-ponents of the reference beam. As a result, somesignificant noise components, especially the scatterfrom the hologram, should have been generatedand then degraded both the positive and negative re-constructed images.The high energy of the additional dc component

mentioned above should have also wasted the dy-namic range of the CMOS camera due to a high dcoffset generated. This dc offset was a restrictionfor increasing the exposure energy of the higher or-der components of the readout reference beam. If theadditional dc component is small but satisfies rela-tion (12), then the positive reconstructed image aswell as the other images would be improved. Onthe other hand, the higher additional dc componentamplifies the signal component more. Therefore, the

additional dc component should be designed by bal-ancing the signal amplification effect and the dy-namic range of the image sensor.

As for the conventional method, its σOFF2 shown in

Fig. 11(b) remained low. Although the reason is notfully understood, it might be due to a noise-removaleffect of apertures A2 and A3 shown in Fig. 4. On theother hand, its σON

2 shown in Fig. 11(a) were highestuntil the data density of 8:2Gbit=in:2 and, abovethat, decreased steeply. The initial increase of σON

2

until the data density of 8:2Gbit=in:2 would be be-cause diffraction efficiency for each ON pixel was di-verse to a great degree due to spatially nonuniformM=# consumption that was caused by irradiation ofhigh-intensity dc component. Above the data densityof 8:2Gbit=in:2, the steep decline of σON

2 would bebecause the reconstructed signal beam became weak-ened as shown in Fig. 10.

D. Signal-to-Noise Ratio Characteristics

Figure 14 shows the SNR dependence on raw datadensity. SNR behaviors on the DI and the SI methodslook similar to each other. This indicates that thenoise reduction by the DI method had a similar effectto the signal amplification and the noise reduction bythe SI method.

With reference to SER behaviors on the DI and theSI methods shown in Fig. 9, their SER behaviorscorrespond well with their SNR behaviors. This im-plies that there was no significant difference betweenthese two methods for improving SNR and SER inthe experimental conditions we employed.

However, there is a possibility that SNR behaviorwould not correspond well with SER behavior whenthe white rate and additional dc component are chan-ged. This is because the white rate and additional dccomponent affect an amplification ratio by the SImethod as written in Eq. (18). Moreover, the whiterate affects the energy of the dc component to beremoved on recording, which also affects M=# con-sumption. Therefore, to determine which methodshould be chosen for practical use, we have to

Fig. 13. Histograms of the (a) positive reconstructed image,(b) difference image, and (c) subtraction image, respectively.The histograms in (a), (b), and (c) correspond to the images inFigs. 12(a), 12(c), and 12(d).

Fig. 14. SNR dependence of raw data density.


consider the white rate and the additional dc compo-nent together with various decoding methods such aserror correction techniques. This is reserved for fu-ture study.

5. Conclusions

We have demonstrated that dc-removed coaxial holo-graphic data storage by use of positive and negativereconstructed images contributes to increasing thenumber of multiplexed holograms. We have shownthe multiplexing characteristics of dc-removed co-axial holographic data storage and experimentallyverified signal amplification and noise reduction byuse of positive and negative reconstructed images.Furthermore, it has been demonstrated that,because of these effects as well as less M=#consumption due to dc removal, 3.5 times moreraw data density was achieved compared with theconventional method that involved recording thedc components.

Appendix A: π Phase-Shift of a Reference Beam by Useof the Contrast-Reversed Reference Pattern

Let us assume that rðx; yÞ is the amplitude distribu-tion of the reference pattern used. Fourier transform-ing rðx; yÞ, we obtain its Fourier components Rðμ; νÞ,which can be separated into its dc componentrdcδðμ; νÞ and the higher order components RHðμ; νÞ,i.e., F½rðx; yÞ� ¼ rdcδðμ; νÞ þ RHðμ; νÞ. Because the dccomponent is removed on recording, the RHðμ; νÞworks as a reference beam on recording. When read-ing a positive image, RHðμ; νÞ produced by the origi-nal reference pattern rðx; yÞ works as a readoutreference beam.On the other hand, when a contrast-reversed (ne-

gative) image is read out, the contrast-reversed refer-ence pattern is used. The amplitude distribution ofthe contrast-reversed reference pattern is expressedby 1 − rðx; yÞ. Fourier transforming 1 − rðx; yÞ, we ob-

tain F½1 − rðx; yÞ� ¼ ð1 − rdcÞδðμ; νÞ − RHðμ; νÞ. The−RHðμ; νÞ works as a reference beam to reconstructthe signal beam.

By comparison between −RHðμ; νÞ and RHðμ; νÞ,the only difference is their sign. This means that−RHðμ; νÞ has the same spatial frequency distributionas RHðμ; νÞ, while −RHðμ; νÞ has the phase differenceof π from RHðμ; νÞ.

We thankM. Shimizu andM. Furuki at our labora-tory for encouragement.

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