This content has been downloaded from IOPscience. Please scroll down to see the full text.
Download details:
IP Address: 140.113.38.11
This content was downloaded on 25/04/2014 at 15:43
Please note that terms and conditions apply.
Gray Apertures for Holographic Data Storage System
View the table of contents for this issue, or go to the journal homepage for more 2008 Jpn. J. Appl. Phys. 47 5957
(http://iopscience.iop.org/1347-4065/47/7S1/5957)
Gray Apertures for Holographic Data Storage System
Jenn-Hwan TARNG, Chien-Fu TSENG, Chih-Ming LIN1, and Feng-Hsiang LO1
Department of Communication Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
1Electronics and Optoelectronics Research Laboratories, Industrial Technology Research Institute, Hsinchu 310, Taiwan
(Received November 30, 2007; accepted January 31, 2008; published online July 18, 2008)
In this paper, we propose the idea of gray optical apertures in contrast to the conventional binary apertures for holographic data storage (HDS). A gray aperture can be realized by a liquid crystal display or a binary aperture with a coating near the edge. In our simulation, HDS with a gray aperture shows a better page signal-to-noise ratio and modeling accuracy than HDS using a binary aperture. [DOI:10.1143/JJAP.47.5957]
KEYWORDS: optical storage, holographic, aperture, filter
Holographic data storage (HDS) is a strong contender for next generation optical data storage. It can achieve terabyte capacity by multiplexing, which enables the recording of multiple holograms in same volume.1)The optical aperture, acting as a spatial frequency filter, can lead to increased storage density by limiting the holographic recording to specific regions in the medium. In this paper, we employ the idea of gray optical apertures in contrast to the conventional binary apertures for HDS. A gray aperture can be realized by a liquid crystal display or a binary aperture with a coating near the edge. A similar design was proposed by Karpati et al.2)for coaxial HDS systems, and an optical apodization
filter is suggested to reduce the diffraction noise caused by the reference beam in the object area. In this paper we model the aperture as a Fourier-plane filter in the HDS channel, so as to investigate the effects induced by the aperture design. The analysis is performed from the viewpionts of signal processing and channel design. The simulation results show that HDS with a gray aperture gives a better page signal-to-noise ratio (SNR)3)and modeling accuracy than HDS using a binary aperture.
We consider some optical aperture functions (OAF), as shown in Fig. 1. For a 4-f HDS system with a focal length of 20 mm and laser wavelength of 405 nm, corresponding point spread functions (PSFs) are calculated and shown in Fig. 1. Equation (1) below, connecting a½p; q, the data for spatial-light-modulator (SLM), to r½k; l, the output from the charge-coupled device (CCD), is obtained by modifying
the well-known HDS simulation equation.4) In eq. (1),
g1ðu; vÞ represents the SLM pixel function, D1 is the SLM pixel pitch, g2ðu; vÞ represents the shape function of CCD pixel, D2is the size of the CCD pixel, and hðx; yÞ denotes the PSF. Also, no and nedenote the electronic noise and optical noise, respectively. r½k; l ¼ Z Z1 1 ( " XN p XM q a½p; q g1ðx pD1; y qD1Þ # hðx; yÞ þ no½x; y 2 g2ðx kD2; y lD2Þ ) dx dy þ ne½k; l ð1Þ
We simulated HDS with several different gray apertures (parameterized by ) and we briefly discuss the numerical
results. In our simulation, the pixels of SLM and CCD are rectangular with a 64% fill ratio. The Nyquist aperture (W) is 1013 mm.
We define the effective aperture size as the aperture width through which 95% of the laser power passes. The effectiveness of gray apertures can be evaluated using SNRpage3)vs effective aperture plots, as shown in Fig. 2. SNRpage is a good measure of the separability between the zeros and ones. HDS with gray apertures ( ¼ 0:25 and 0.5)
has a better SNRpage than HDS with a binary aperture
( ¼ 0).
In Fig. 2, Zone 2 is close to the Nyquist aperture; thus, e a threshold detector can be applied and the performance is satisfactory. Our simulations yield the distributions of zeros and ones shown in Fig. 3 and the bit error rate (BER) vs SNRelectronic. plots in Fig. 4. The BER of the gray aperture ( ¼ 0:5) is better than that of the binary aperture.
The HDS with an aperture in Zone 1 has significant interpixel interference (IPI); hence, it requires advanced
(a) (d) (b) (e) (c) (f)
Fig. 1. (Color online) Gray apertures and corresponding PSFs. (a) 800 800 mm2 binary aperture, (b) 800 800 mm2 raised-cosine ( ¼ 0:50)
aperture, (c) 800 800 mm2Gaussian aperture, (d) 400 400 mm2binary
aperture, (e) 400 400 mm2 raised-cosine ( ¼ 0:50) aperture, and
(f) 400 400 mm2Gaussian aperture.
E-mail address: chienfu.cm94g@nctu.edu.tw Japanese Journal of Applied Physics Vol. 47, No. 7, 2008, pp. 5957–5959 #2008 The Japan Society of Applied Physics
5957
detectors, such as a decision-feedback equalizer, and a maximum-likelihood detector. In order to utilize these advanced detectors, we need a precise channel model. We can use intensity-modeling and amplitude-modeling schemes4)to approximate eq. (1), and we then evaluate the
modeling accuracy by calculating the normalized mean square error (NMSE)3)between them.
The modeling accuracy is compared in Fig. 5 (intensity modeling) and Fig. 6 (amplitude modeling), for three kinds of apertures. The Gaussian aperture has the best accuracy, probably because its PSF has no negative amplitude and
there is less phase variation in each CCD pixel. For a Gaussian aperture size of 500 mm, we can achieve accurate modeling (NMSE is only 6:5 104).
By applying a gray aperture, we obtain a more accurate channel model to generate detectors. We performed two kinds of application. One was to generate a zero-forcing (ZF) equalizer using the channel model. The ZF equalizer is still effective under a severe IPI, as shown in Fig. 7, because
200 400 600 800 1000 1200 1400 -4 -2 0 2 4 6 8 10 SNR page
Effective Aperture Size (0.95 Power) of OAF (um) Comparison between gray and binary apertures
Zone 2 Zone 1 Zone 3 β=0.00 β=0.10 β=0.25 β=0.50 β=0.75 β=1.00
Fig. 2. (Color online) Aperture size vs SNRpage.
0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 x 104
Intensity of data received from CCD
Counts
Distribution (Effective Aperture size = 1.1W) "0" bits,the binary aperture (β = 0) "1" bits,the binary aperture (β = 0) "0" bits,the gray aperture (β = 0.5) "1" bits,the gray aperture (β = 0.5)
Fig. 3. (Color online) Distributions of ‘‘1’’s and ‘‘0’’s.
5 10 15 20 10-4 10-3 10-2 10-1 SNR electronic (dB) BER
Threshold Detector ( Effective Aperture = 1.1W ) the binary aperture (β = 0) the gray aperture (β = 0.5)
Fig. 4. (Color online) SNRelectronicvs BER.
0.6 0.8 1 1.2 1.4 10-4 10-3 10-2 10-1 NMSE
Aperture Size Normalized by Nyquist Aperture (W) Intensity Modeling
Binary Aperture Raise-cosine (β=0.5) Gaussian
Fig. 5. (Color online) Accuracy of intensity modeling.
0.6 0.8 1 1.2 1.4 10-4 10-3 10-2 10-1 NMSE
Aperture Size Normalized by Nyquist Aperture (W) Amplitude Modeling
Binary Aperture Raise-cosine (β=0.5) Gaussian
Fig. 6. (Color online) Accuracy of amplitude modeling.
5 10 15 20 25 30 10-4 10-3 10-2 10-1 100
Zero-Forcing Equalizer (Effective Aperture = 0.8W)
BER SNRelectronic β=0 without ZF-Eq. β=0 with ZF-Eq. β=0.5 without ZF-Eq. β=0.5 with ZF-Eq.
Fig. 7. (Color online) Effectiveness of HDS with gray aperture and ZF equalizer.
Jpn. J. Appl. Phys., Vol. 47, No. 7 (2008) J.-H. TARNGet al.
the HDS with the gray aperture has more accuracy than HDS with the binary aperture. The other was to generate a partial response channel for a two-dimensional (2D) PRML detector. For the HDS with the 0.5 W Gaussian aperture,
the channel model is close to ½1 2 1T ½1 2 1, as
illustrated in Fig. 8; thus, the 2D PRML detector can be utilized.5)
We presented the idea of gray apertures and showed their effectiveness in terms of SNRpage. When the aperture size is
near that of the Nyquist aperture and a threshold detector is adopted, we recommend the use of a raised-cosine aperture ( ¼ 0:5). Because HDS with this gray aperture exhibits a high SNRpageand more concentrated distribution of ‘‘1’’ bits, the use of some post processors can be expected to result in superior performance. When a small aperture (<0:7 W) is adopted for achieving high capacity, we suggest the use of a Gaussian aperture. Because they can be used for accu-rate modeling, we can expect superior performance from advanced detectors.
Acknowledgements
The authors thank Professor B. V. K. Vijaya Kumar of Carnegie Mellon University and Dr. P. C. Chen of the Industrial Technology Research Institute for helpful sugges-tions regarding this paper.
1) K. Anderson and K. Curtis:Opt. Lett. 29 (2004) 1402.
2) Z. Karpati, K. Banko, G. Szarvas, S. Kautny, and L. Domjan:Jpn. J. Appl. Phys. 46 (2007) 3845.
3) L. Ramamoorthy, S. Nabavi, and B. V. K. V. Kumar: Lasers and Electro-Optics Society, LEOS 2004, 17th Annu. Meet. IEEE, 2004, Vol. 2, p. 997.
4) V. Vadde and B. V. K. V. Kumar:Appl. Opt. 38 (1999) 4374. 5) K. H. Lai, C. F. Tseng, P. C. Chen, F. H. Lo, T. R. Jeng, and S. C. Hsu:
ISOM Tech. Dig., 2007, p. 272.
(a) (b) 0.01763 0.13503 0.26558 0.13503 0.01763 0.13503 1.0341 2.0338 1.0341 0.13503 0.26558 2.0338 4 2.0338 0.26558 0.13503 1.0341 2.0338 1.0341 0.13503 0.01763 0.13503 0.26558 0.13503 0.01763
Fig. 8. Partial-response channel of HDS with 0.5 W Gaussian aperture: (a) image and (b) value.
5959
