Ординатура / Офтальмология / Английские материалы / Handbook of Optical Coherence Tomography_Bouma, Tearney_2002

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386 Chinn and Swanson

lengths can be focused to smaller spot sizes [2], allowing more closely spaced data. Another, more recent and complementary approach to exploit volumetric storage has been to use several layers of data on the same disk [3–5]. The latest commercial advance, digital video disk (DVD), shortens the wavelength slightly to 635–780 nm and offers the option of having two layers per side, on two sides (the disk must be turned to change sides) [6]. The track pitch is reduced from 1:6 m (CD) to 0:74 m, and the minimum pit length is reduced from 0:83 m to 0:4 m [7]. If the dual layer option is used, an important parameter for later comparison is the layer separation, 35–55 m [6,8]. The net improvement in storage capacity is from 650 MB (conventional CD) to a maximum of 17 GB (DVD, two layers on each of two sides) [6].

In this chapter we will discuss a new readout concept [9] using optical coherence domain reflectometry that can extend the capability of reading multilayer disks with a number of layers an order of magnitude greater than previously achieved. Although this is not a quasi-static imaging application, we will refer to the technique as optical coherence tomography (OCT), for consistency with the rest of this volume. Much of the material in this chapter is based upon our previously published work [10,11] with the addition of more detailed analyses and explanations and new experimental data on multilayer disks. Figures 1–9, 11, 12, 14 and 15 are adapted from Refs. 10 and 11.

Optical coherence tomography uses broadband light from a source such as continuous wave (cw) superluminescent light-emitting diode (LED), with interferometric detection [12–15], and is capable of high resolution three-dimensional imaging inside partially transparent media, as has been demonstrated in various biomedical imaging applications described in other works and elsewhere [16] in this volume. This method’s high sensitivity with good lateral and depth resolution make it an excellent candidate for reading optical data stored in many closely packed layers. Because diffraction-limited imaging of local regions is used (as opposed to volumetric holography), much of the existing single-layer disk technology can be employed.

Another simpler but related method for improving multilayer readout simply replaces the laser diode in a conventional CD system with the same type of broadband source [11,17], with no other changes to the system except for possibly improving the intensity detection sensitivity. Improvements from the broadband source replacement in this direct-detection (DD) system arise from the reduction of coherent interlayer cross-talk signal fluctuations. Although this method does not have the depth resolution or sensitivity of the OCT system, it does provide improved performance over laser-based systems and provides an interesting comparison to the OCT method. Its main virtue is that required modification of existing system design is reduced.

Section 14.2 contains a more detailed description of the multilayer readout concept using OCT. In Section 14.3 we present analytical descriptions of beam propagation through multilayer media, which has a direct influence on optical signal quality. Similarly, in Section 14.4 we discuss the signal degradation arising from reflective cross-talk among the layers. System sensitivity issues and limits are presented in Section 14.5. Experimental methods and results on imaging one-, two-, and three-layer disks are given in Section 14.6. A summary and conclusions are given in Section 14.7. Throughout this chapter, the emphasis is on readout of multilayer media, which could be most easily produced by mass replication methods adapted from current technology. Other possible media fabrication issues and alternatives will be discussed in Section 14.7.

disk. Because their optical pathlengths will be different from that of the reference path to the desired layer, the spurious heterodyne signals will be greatly reduced by the combination of smaller coherent interference and increased optical defocusing.

The broadband direct detection (DD) version would be similar to a conventional CD system and would lack the reference path and interferometer used with OCT. The DD system operates functionally in most respects like a conventional laser-based system but would not suffer from unwanted interference effects arising from the narrower laser source linewidth. The differences between OCT and DD occur in the noise fluctuation characteristics, which will be described below for the specific example of a single-spatial-mode receiver.

We describe one particular implementation of information storage, shown in Fig. 2. It resembles that of conventional compact disks and allows relatively straightforward analysis and comparison of the OCT and DD methods. Moreover, as discussed below, the resulting low optical reflectivity and large transmission of each data layer interface are well suited for disks having many layers. Binary signal levels are produced by the absence or presence of data pits or regions, approximately onequarter wavelength deep, at the interface of two layers having slightly different indices of refraction. We note that this technology is extendible to m-ary storage where the bits have m symbols representing ln2m bits by using modified pit depths. As shown in the cross section of the left-hand portion of Fig. 2, light reflected from the top and bottom surfaces of the pit will have relative phase shift R. With appropriate optical focus waist and pit size, the reflected beam can be greatly altered in the presence of a pit region. Actual disks may have not only circular data pits but also elongated depressions of varying length. For simplicity of analysis, we limit our model to circular pits, which should give good qualitative insight. Experimental results presented later will show data from actual disks.

In our analyses we will consider both the source and receiver to be near-dif- fraction-limited, so that (in the ideal case) light at the data layer is in a diffractionlimited focal spot, and the received signal can be found from the overlap of the reflected beam with the diffraction-limited single-receiver mode. For appropriate

Figure 2 Cross section and perspective view of data layer interface in one example of a multilayer optical disk storage medium. [Adapted from Ref. 11, Fig. 2.]

focus and pit parameters, the beam reflected from a pit can be made nearly spatially orthogonal to the input mode, giving a null in the detected signal when a pit is present. The right-hand portion of Fig. 2 illustrates this case, where the pit size and optical mode waist are such that the integrated optical intensity inside and outside the pit are equal. For simplicity, we assume that the diffraction-limited source and receiver modes are Gaussian beams The lighter shaded top of the

Gaussian intensity surface shows the region with -reflected phase shift. In this p

example the Gaussian mode waist w0 ¼ a 2=ðln 2Þ, where a is the pit radius. Also, in the interest of simplicity, we assume that depolarization effects are negligible. If the disk media significantly depolarize the reflected signal beam, then a polarization diversity receiver could be implemented for the OCT system. Recent work concerning issues of vector diffraction and polarization effects in optical disks is discussed in Refs. 19 and 20.

Because we expect some degree of beam degradation in using many data layers, we first analyze how a Gaussian beam propagates and find the statistics of the received signal under various conditions. This analysis will find the degradation in the received beam quality caused by scattering of light from the intermediate data layers as the signal beam propagates through them to the desired data layer and then reflects back. Then we perform a similar analysis of how spurious cross-talk signals reflected from other data layers interfere with the signal from the desired layer. Our results will show that such interlayer cross-talk plays a dominant role in limiting the receiver eye opening or bit error rate. These two analyses are important factors in determining overall system performance. For practical systems, it is important that the beam quality not be degraded (or the received signal level significantly attenuated) as deeper layers are addressed. In addition to this condition, it is necessary that interlayer cross-talk be low so that reliable bit decisions can be made. Our results will show that OCT is well suited to the requirements imposed by optical disks with many layers.

14.3PROPAGATION ANALYSIS

The goal of propagation analysis is to obtain as quantitative a model as possible while making it both analytically and numerically tractable. The propagation of a focused beam through multiple data layers and its reflection back through the same layers are simplified as much as possible while retaining the essence of the physical problem. For forward propagation, each data layer interface is idealized as a zerothickness phase mask, because the quarter-wave thickness of the pits is assumed to be a very small fraction of the separation between different data interfaces and a negligible distance in affecting propagation. To isolate the effects of beam distortion, we do not include the weak Fresnel reflectivity of the interface, which could easily be added as a multiplicative factor. The pit depth is t, so the relative phase difference of beams propagating through pit and planar region is

where is the mean free-space wavelength of the source, and n1 and n2 are the refractive indices of the adjacent layer media. Because we have chosen the reflective phase shift R to be , the pit depth is

is the interface’s power reflection coefficient (Fresnel reflectivity). Propagation through a pit region is approximated by multiplying the complex optical field in that region by expðj Þ. We will use a paraxial approximation for the field propagation, so no angular dependence of the phase factor will be included. For simplicity, we will also use a scalar field approximation that neglects depolarization effects.

Another assumption that one might question is the ability of a pit with fixed depth to provide a phase shift or reflective null for a broadband source. A simple physical argument shows that this is not a significant problem. Consider a shortpulse coherent source having bandwidth equivalent to a cw incoherent source. The portions of the pulse reflected from the top and bottom of the pit will suffer a relative time delay given by =2c. For a Gaussian temporal pulse, the full width at halfmaximum (FWHM) duration is 0:4413 2=c , so the fractional offset between these portions is 1:133 =. Most practical sources will have fractional bandwidths less than 5%, so the reduction in reflective phase nulling due to bandwidth spread should be negligible. This argument can be quantified and demonstrated by performing the appropriate integrations in the frequency domain.

14.3.1 Analytical Formulation

In the analytical formulation of beam propagation through multiple data layers we try to find an expression for the field transmitted to and reflected from the desired data layer, which is then detected by a single-spatial-mode receiver. This simplifies the problem from one requiring a complete field analysis to an evaluation of the coupling, or overlap, of the receiver field and the receiver spatial mode. Because the fields will be randomly affected by the phase mask patterns of intermediate data layers, we will try to find statistical means and deviations of the received signal levels.

After propagating through each data layer interface, the projection of the transmitted beam onto the ideal receiver Gaussian beam is given by the amplitude

coupling coefficient

ð

where the field EðrÞ is the complex normalized Gaussian field at the interface and ZðrÞ is the multiplicative phase function of the data pattern, which is assumed to have values 1 (in regions outside the pits) or expðj Þ (inside the pit regions). Each data layer is described by a grid of square cells, with a circular data pit present or absent (each with probability 1/2) at the center of each cell. The ratio of the circular pit area, C, to the square cell area, A, is . Figure 3 shows a schematic drawing of