Optical disk readout: a model for coherent scanning

Alan B. Marchant

The design and evaluation of optical recording systems, media, and codes require both qualitative and quan-titative understanding of the readout process. Scalar diffraction theory permits a simple formulation of thereadout process, which provides a qualitative insight and also permits rapid, detailed, numerical solutionsto a wide range of problems. Several examples demonstrate the application of the model to Laser Write andRead (LWR) optical recording media.

1. Introduction

Information stored in an optical recording mediumis read out by scanning the recording surface with adiffraction-limited focused spot of laser illumination.The information is stored in the form of reflectance (ortransmittance) marks of regular shape arranged intracks on the recording surface. In general the marksor pits show both amplitude and phase differences withrespect to the surrounding unmarked surface. Theinformation is usually coded in the lengths and spacingsof the pits, so the goal of the readout system is to locatepit edges by detecting intensity changes in the far fieldof the scanning spot.

Because of the coherent illumination and the smallsize of the focused spot, we must consider diffractioneffects in modeling readout. Scalar diffraction theoryis an acceptable approximation to the readout physicsfor many optical recording media. This paper describesa formulation of scalar optics which is particularlyadapted to readout problems and which includesangle-of-incidence variations of reflectance. The modelleads to a qualitative picture of the readout process andfacilitates rapid numerical simulations of detailedproblems.

The mathematics behind the readout model will begiven as well as some specific applications. Examplesof individual pit scans, tracking response, and spatialfrequency response will be presented. The optical re-cording medium used in these examples is Kodak's ex-perimental Laser Write and Read material (LWR), athin, selectively absorptive, polymeric layer on a re-flective substrate.

The author is with Eastman Kodak Company, Research Labora-tories, Rochester, New York 14650.

Received 11 January 1982.0003-6935/82/112085-04$01.00/0.© 1982 Optical Society of America.

II. Theory

Pit lengths, pit widths, and the focused spot areusually not much larger than A, the readout wavelength.Therefore, diffraction effects must be included in anytreatment of the readout problem. A completely rig-orous solution would be based on vector diffractiontheory, which takes polarization effects into account.However, the model described here is derived fromscalar diffraction theory, an approximation which is farmore tractable than vector diffraction.

There are several reasons for believing that scalardiffraction is an adequate approximation for thisreadout problem. A beam with a Gaussian intensityprofile passed through a perfect lens forms an optimumfocus (maximum central intensity) when the lens ap-erture truncates the beam at its exp(-2.5) intensityradius. Under the scalar approximation the optimumfocus profile differs from the true (vector theory) profileby <10% for the moderate lens numerical apertures,N.A. <0.65, expected in readout systems.' Edge-dragging of light polarized parallel to the edge of aconductor can make small shallow structures appearsmaller than scalar diffraction would predict.2 Butscalar calculations involving plane waves and focusedspots diffracted from 1-D reflective gratings indicatethat for groove depths <X/8 and periods >2A, errors of<25% can be expected from a scalar calculation.3 Mostoptically recorded pits will satisfy these constraints.More important, many media such as the LWR illus-trated in the examples below do not require deformationof a conductive layer and thus avoid edge-dragging ef-fects.

The basic elements of a readout system are di-agrammed in Fig. 1. A laser beam is directed throughan objective lens and focused at or near the surface tobe scanned. The illumination is characterized by Ei,the amplitude and relative phase of the optical field ateach point on the pupil sphere. For a Gaussian-profilelaser beam truncated at its exp(-ca) intensity radius bya lens of numerical aperture N.A., we have

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PUPIL RECORDED PUPILOBJECTIVE SPHERE SURFACE SPHERE OBJECTIVELENS / NS

LASER -- -j5E- DETECTOR

EIN r EOUT

Fig. 1. Optical path of an optical disk readout system. In a reflectivesystem the path is folded through the planar recording surface.

E VT exp(-a02 /20m2) exp(i4obj) 0 < Dm (1)

Here IO denotes the maximum intensity at the pupilsphere, 0 denotes angular position on the pupil sphere,and m sin-' N.A. describes the marginal ray. 0 mayalso be interpreted as the angle of incidence at the focalpoint of light from a given point on the lens. The phasefunction kobj can be used to describe slight defocusand/or aberration of the objective lens. For example,if the objective is a small distance outside its paraxialfocus and has third-order spherical aberration with amarginal phase shift of sm, then

OIob(O) = 2r(1 - coso)6/X + sin40 sn/N.A.4. (2)

Figure 2 summarizes the relevant optical structure ofthe recording medium. We consider it to be a planarreflective surface with a background reflectance rO; thisis the complex reflectance, related to the scalar landreflectivity by r - exp(i 0)l. On this surface arevarious shapes (P1,P2, ... ) with various reflectances(Rp,,Rp2, .. ) and phases (P 1,0p 2, .. .) representingindividual pits, rims, periodic structures, etc. We de-note the deviations of these areas from the backgroundreflectance as rn -\IR~ exp(ikn) - r0 ,n > 0. In gen-eral, all these reflectances are functions of 0; however,consistency with the scalar approximation forces us toignore possible polarization dependences. The angulardependences are not large for thin bilayer media, butfor trilayer or other thick structures they may be im-portant. The following results may all be applied totransmissive readout systems simply by inserting theanalogous complex transmittances in place of all re-flectances. The coordinate origin for descriptions ofthe shapes Pn(x,y,t) is the optical axis. The markschange their locations as the surface scans beneath theobjective with a velocity v, P = Pn(x - vt,y). Thefunctions Pnare defined as unity inside the marks andzero outside.

After interacting with the recording surface some ofthe light is recollected by an objective lens. Consistentwith previous applications of scalar diffraction to thereadout problem, 4 5 we express the complex field dis-tribution at the pupil sphere as

E0 ut(pq) = E frEin(p',q')rn(p'q')

X IPn(p - p',q - q')dp'dq',

IPn fJ Pn(x,y) exp(i27r(xp + yq)/X)dxdy. (4)

In Eq. (3) r is removed from the Fourier transformbecause the spatial dependence of reflectance is con-tained solely in the shape functions. Expressed inwords, the contribution to the far field from each shapeis the convolution of the incident beam (times its re-flectance) with the Fourier transform of the shape.This is identical to the transform of the product of thepoint spread function and the reflectance pattern. Inparticular, the n= 0 contribution from the unmarkedsurface is simply

L ~~~~E~uto(0) = Ei.(O) r(0)[Po(x,y) - l].

The light recollected by the objective is directed toa detector or detector array. The field at the detectorEdet is obtained by multiplying Eout by exp(i)Obj andthen appropriately scaling the distribution to accountfor relay optics and defocus. Finally, the detectorcurrent is

I= I Eded -Dda, (5)

where D is the detector response (positive or negative)at each point on the detector area A.

Equations (3) and (5) comprise a simple numericalmethod for simulating detector response as the re-cording surface is scanned. Most cases of interest canbe modeled by using shapes Pn, which are single or pe-riodic arrays of rectangles. More complex marks suchas a pit with a significant rim can be modeled as super-positions of rectangles. In such cases the definitionsof r should be modified appropriately. When themodel shapes are chosen in this way, P = P n(x) -Pyn (y). The transform 5IPn become simple analyticfunctions separable in p and q. Thus, for scanning inthe x direction the calculation of the response of onepoint on the detector at a given time simply involves a1-D convolution for each of the several shapes of theparticular model. The nth contribution to Eout is

Eoutn = Qn (p',q) Pxn (p -p')dp',

where the values of

Qn(p',q) S- f Ein(P,q-)rn(P ,q)5Pn(q-q')dq'

(6)

(7)

do not change during the scan. Px and ?Py are sim-ple 1-D Fourier transforms analogous to Eq. (4). In

(3)

where p and q are Cartesian coordinates on the pupilsphere, sin2O = p 2 + q2 , and Pn is the Fourier trans-form of the nth shape function:

Fig. 2. Model of an optical disk being scanned by the readout system.Marks are represented by planar areas of differing complex

reflectivity.

2086 APPLIED OPTICS / Vol. 21, No. 11 / 1 June 1982

2 -

C

ID

- e

-i

Pit position, /im5

Fig. 3. Response of a central-aperture detector as the readout systemscans a rimmed pit.

fact, Q, remains constant even when the in-track lengthscales are varied as in an MTF calculation.

When the recorded surface reflectance is strictlyperiodic in the in-track (x) direction, readout calcula-tions become particularly simple. In this case eachgPX,,, which is the transform of a square wave, becomesa sum of delta functions in the pupil coordinate p, andcomputation of Eout(pq) becomes a simple sum. Forwide periodic tracks (Pyn- 1) the far field is just a su-perposition of the incident field Ein displaced by thevarious diffraction angles of the 1-D gratings Pn, andmultiplied by rn (0) and the Fourier coefficients of Px..For shapes which are not wide in the y direction theimages of the entrance aperture are distorted by con-volution with ?IPy,, as shown in Eq. (7). If the elementsof the grating P,, scan past the optical axis at a rate w,,the corresponding orders in the far field are constant intime except that they rotate in phase as exp(i27rmwt),where m is the number of the diffraction order (0,+1,... ). The values of En,out need only be computed forone scan position in order to reconstruct the entire de-tector response as a function of time using these phasefactors. The spectrum of the resulting detector re-sponse [Eq. (5)] is a set of delta functions, correspondingto beating between pairs of orders when miwi 4mimj.

This description of the readout theory for periodicstructures is similar to approaches employed by oth-ers.45 It also provides a rigorous backing for the"semiquantitative" readout theory of Korpel,6 whoprovided simple approximations for the field distribu-tion in the diffraction orders; it extends the calculationalapproach to aperiodic structures and permits modelingin situations where reflectance is dependent on inci-dence angle. Several examples of readout of periodicas well as aperiodic structures are included below.

Ill. Applications

In Figs. 3 and 4 we apply the time-dependent modelof Eqs. (3)-(7) to compute the detector response to anisolated pit in an LWR (Kodak's Laser Write and Readbilayer material7 ) medium. The pit is modeled as a

single rectangle 0.8 Am wide and 1.0 Am long passingdirectly under the optical axis. A 0.2-Am wide pit rimis modeled by a 1.2 X 1.4 -Mm rectangle centered on thepit. The land reflectance is RI = 0.85, the pit reflec-tance is Rp = 0.81, Up = 1260, the rim reflectance is Rrim= 0.90, and Grim = -15°. These values are applicableto normal incidence on 70-nm deep pits and 40-nm thickrims in a 110-nm thick LWR layer. We have ignoredincidence angle dependence of reflectance in these ex-amples. The model readout beam, with X = 633 nm,has a Gaussian profile truncated at the exp(-2) inten-sity point by a square aperture of N.A. = 0.6. The de-tector is modeled by discrete points whose polarities andpositions in the (collimated) exit beam are shown in theupper right of the figures. The horizontal axis of thegraphs locates the pit center relative to the optical axis.Dashed lines indicate the model pit and rim shapes.The detector current is normalized with respect to theoptical power incident on the detector when a feature-less unrecorded surface is scanned.

Several of the approximations in these two examples(e.g., the square aperture) were introduced to make theproduct Ein r, [and thus Q, (p,q)] separable in p andq and further simplify the calculation.

Figure 3 shows the response of a central-aperturedetector which collects all the light diffracted back intothe objective aperture. The current is reduced when-ever part of the pit impinges on the focused spot. Fig-ure 4 shows the response of a split-aperture detectorwhich bisects the far field in the in-track direction anddifferences the signals from the two halves. Note thatthis detector's response is essentially a derivative signalidentifying the leading and trailing edges of the pit withshort pulses of opposite polarity. Although the pres-ence of significant rims may be expected to distort thereadout waveforms for many materials, neither Fig. 3nor Fig. 4 shows significant distortions which could beidentified with rims in LWR when compared to calcu-lations which neglect the rims entirely. These com-puted waveforms are virtually identical to actual signalsobtained in the readout of an LWR optical disk.

cID

0

a)IDID

-I L

-3Pit position, lm

Fig. 4. Response of a split-aperture detector as the readout systemscans a rimmed pit.

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...................

.5

0

-.5

Tracking, surn

Fig. 5. DC response of a cross-track split detector to tracking vari-ations for tracks of width W = 0.6 and 1.0 ,um. This system may be

used to drive a tracking servo.

Z

I

0'-a

IDID

ID

0

0

0 X / Pattern Period

Fig. 6. Signal response of a split-aperture detector as a function ofpit-pit spacing and defocus . Defocus is a serious problem for 6 >

1 Asm.

Table 1. Optical Model of Nominal LWR Recording Media

sin0 Rland I1and/r Rpit Itpit/r

0.0 0.846 0 0.812 1.2820.1 0.845 -0.002 0.812 1.2790.2 0.843 -0.007 0.813 1.2700.3 0.841 -0.017 0.814 1.2540.4 0.837 -0.031 0.816 1.2310.5 0.832 -0.049 0.819 1.2000.6 0.826 -0.073 0.823 1.161

Figures 5 and 6 present detailed calculations oftracking and focus effects on the readout of periodictracks of pits in an LWR medium. The tracks arecomposed of 70-nm deep rectangular pits spaced witha 50% duty cycle in a 110-nm thick LWR layer with arefractive index of 1.8 at X = 633 nm. The substrate ismodeled as aluminum, n = 1.5 + 7.3i, with a 5-nm thickoxide layer, n = 1.7. Table I lists the rim and land re-flectance values calculated for this model for a range of

incidence angles encountered with a 0.6 N.A. objective.The incident beam is truncated by a circular objectiveat its exp(-2) intensity radius.

Figure 5 shows the time-averaged response of atracking detector 8 to tracking errors for 0.6- and 1.4-,4mwide tracks. The detector again covers the entire re-troreflected beam (as truncated by the objective) anddifferences the photocurrents from the cross-trackhalf-areas as illustrated in the upper right corner of thefigure. For these tracking calculations the pit spacingis 1.9 /im. At this spacing the third-order contributionsto the in-track diffraction are almost entirely blockedfrom the retroreflected beam by the objective aperture.The second-order contributions are eliminated by thesymmetry of the 50% duty-cycle track. Therefore, onlythe 0, +1, and -1 in-track diffraction orders have beenincluded in the calculations of Fig. 5.

Qualitatively, Fig. 5 shows that a tracking system willhave somewhat reduced gain for wider tracks, but theresponse remains linear as long as the optical axis fallswithin the track, so such a system will permit precisetracking for a wide range of track widths.

Figure 6 demonstrates how the detector response overa range of pit spacings (the MTF) varies with defocus5. The system model is the same as for the previouscalculation, except that the split-aperture detector nowdivides the retroreflected beam in the in-track direction.The model assumes that defocus introduces a negligiblechange in the size of the spot at the detector. Theamplitude of the fundamental component of the de-tector current (modulation at the frequency: scanningvelocity/pit spacing) is plotted. This part of the re-sponse is composed only of interference between the 0,1and 0,-1 pairs of in-track diffraction orders, becausethe higher even orders are eliminated by symmetry.

Figure 6 demonstrates that for a 0.6 N.A. objectivea focal range of ±1 ,m is available, but a focus error of2 m severely degrades the response. The low valuesof modulation for large pits and pit spacings do notmean that the response is qualitatively poor; the leadingand trailing edges of long pits are identified by largepulses of opposite polarity (as suggested by Fig. 4), andthe signal returns to zero over the long land and pitareas.

We have shown how rigorous scalar diffraction theoryapplied to coherent optical scanning can be formulatedin a form analogous to the qualitative theory of Korpel,6

permitting rapid numerical solution of detailed prob-lems. The computational approaches outlined havegreatly facilitated realistic modeling of the readout ofoptical recording media.

References1. F. F. Geyer, private communication.2. J. G. Dil and B. A. J. Jacobs, J. Opt. Soc. Am. 69, 950 (1979).3. P. Sheng, RCA Rev. 39, 512 (1978).4. A. H. Firester et al., RCA Rev. 39, 392 (1978).5. H. H. Hopkins, J. Opt. Soc. Am. 69, 4 (1979).6. A. Korpel, Appl. Opt. 17, 2037 (1978).7. D. G. Howe and J. J. Wrobel, J. Vac. Sci. Technol. 18, 92 (1981).8. G. W. Hrbek, J. SMPTE 83, 580 (1974).

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