Electromagnetic Theory of Iris DetectionI. Kohlberg1 H. Szu2

1 Kohlberg Associates, Reston, VA 20190e-mail: ira.kohlberg@gmail.com. 2 Human Signatures Exploitation Branch, U.S. Army NVESDFort Belvoir, VA 22060

Abstract – Iris recognition is increasingly important, especially in critical areas such as airports and places of border control. For these locations, the targets are inherently non-cooperative, and it is then necessary to detect at ranges well beyond the nose-on range for cooperative targets. In this paper, we reexamine some of the basic electromagnetic issues of using LED or laser sources in relation to their range limitations.

1 INTRODUCTION

Identifying individuals by their irises is a powerful method of recognition and is in use today at several airports in the Middle East and other places. The current method is based on Sir John’s Daugman’sinnovative algorithm [1], which uses an incoherent light source for wavelengths in the near infrared. This light illuminates the willing target’s iris, and the backscattered radiation provides the unique signature after Gabor wavelets are used to render the back-scattered signal in suitable edge detection form for signal processing. Physical singularities, which are the discontinuities slopes on the independent 3-D iris curtain folds within more than 249 iris creases at 200or so radial directions at arbitrary distances from the eye’s center, make individual unique recognitionpossible. These discontinuities are due to person-unique shrinkage balance of the radial muscles against the sphincter muscle, causing 3-D material bulging at the micron wavelength probing scale. Variability of electromagnetic scattering from these discontinuities has so far been sufficient for matching at close range.

There is, however, a precipitous drop-off in matching as the distance between source and iris and/or between detector and iris increases. There is a collective effect. If the optical system cannot resolve the backscatter features in a particular single radial furrow, it will not be able to resolve any of them. In this exploratory paper, we set up the methodology for determining the range limitations of iris recognition of an optical sys-tem using an incoherent source such as a Light Emit-ting Diode (LED) and a partial coherence model laser source. Solving the wave optics and geometric optics equations [2] for a realistic iris model using a laser source is the critical next step in determining range limitations for iris recognition. We will not elucidate

Daugman’s iris imaging effort, except we wish to estimate the degrees-of-freedom (DOF) based on fun-damental scattering theories.

2 ELECTROMAGNETIC STRUCTURE OF THE IRIS

Loose iris skins have to be flattened out along the radial direction when closing the iris but protruded outward in the angular direction when the sphincter muscle shrinks the iris pupil to as small as 0.14 mmfrom a wide-open, relaxed position at 1.2 mm. There are 249 DOF at a close-up imaging, with a bright illumination producing a semi-closed iris curtain. Itseems to be sufficient (at 3.2 bits/mm2 discriminating entropy) to produce errors of less than 1 in 200 billion when doing cross comparisons among irises at ranges up to 10 m and for enrolled populations up to billions. The measurable protrusion locations seem to be fixed for a specific person under different pupil sizes. We have conjectured that there is a double layer of inner iris, one of which has a fixed 249 keyhole template that allows loose skins to protrude and leak through at these fixed 249 holes. This is our keys-locks model to explain a static protrusion nature despite the dynamic iris curtain. The sphincter muscle maintains a circular symmetry, with discontinuous slopes due to angular folds and radial wrinkles whose locations are unique features due to the chaotic morphogenesis of the growth of iris. The human iris is capable of expanding circularly factor 8 from 0.25 mm to 1.2 mm diameter with a time constant of between 0.25 and 1.0 sec.

3 ELECTROMAGNETIC EXCITATIONS

Figure 1 shows our model, which is not a scale repre-sentation. 0R is the vector connecting the center of the iris’ surface to the point source radiator,

2/120

200 )( YXR is the distance, and 00 / RR is

the unit vector in the backscatter direction. 0Y is com-parable but smaller than 0Z . The iris thickness, ,represents a complex biological structure, which, in the future, needs to be modeled to address the backscatter process adequately. We assume an iris radius a of

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about 0.5 cm, and ranges for either radiation or detection are over 5 m; thus, 4

0 10)/( Ra . If the radiating source is an isotropic radiator with total power 0P , the intensity at 0R is 0

20 )4/1( PRS , and

total power is SaPI20 .

a

Oz

x

y

r

Z0

R0Y0

Rmin

Radiating Source/Detector

Figure 1: Iris electromagnetic excitation.

When an LED is used, the waves travel from the source to the iris centered within the solid angle

20

2 / Ra about the direction . The radiated electric field produced by the source is an infinite set of random, uncorrelated contributions produced by atomic and molecular interactions. At distances in the far field of the source, 0min R , and meas-ured along the direction, the electric field is given

byn

sns tEtE ),(),( , where ),( tEsn are the

aforementioned random contributions from the sourceand min is the minimum distance from the source at which the far-field approximation becomes valid.

The incident field strikes the iris surface at angles within . If ' is a ray direction within and

snE ' is the wave’s electric field, the following condi-tions are satisfied at the iris’ surface: (1) the far-field condition, 0''snE , and (2) incoherence condition,

2)()( snnmmsns EtEtE .The icon denotes an

atomic/molecular time average. This time constant is substantially shorter than all other times considered.The incident electric field at the iris’ surface is

nsninc tEtE )(')( 0,0, (1)

As indicated, the incident electromagnetic field is actually an ensemble of fields that satisfy the far-field and incoherence conditions. Specifying the iris geo-metry, material constants, location, and shape of the singularities determines the electromagnetic field within the iris. We write

)exp()(ˆ),( tjrEtrEsn (2)

The singularities provide strong components of the backscatter that are attributable to the local electric field at their location. These singularity backscatter signals can be expressed in terms of current density,

),(ˆ rJ , contained within a local volume, V ;249...3,2,1 . The vector potential in the far field

produced by the singularity is given by

dVR

jkRrJA

)exp(),(

4(3)

where R is the scalar distance between the field point and location of the scattering singularity. Using the theory of dyadic Green’s function [3], we show that

0,'ˆ),(),( snn

ErDrJ (4)

In the weak field model, the response of the singularity is relatively insensitive to the polarization (in contrast

to the case for metallic-type singularities). ),(rDis the dyadic determined from the solution of Maxwell’s equations within the iris structure. Thecalculation of ),(rJ is substantially more difficult than it appears. Even though the solid angle is small and we can make the case that all rays from the source to the iris go along the direction , the polarization goes over 2 radians in the plane where the condition 0''snE is satisfied. The singularity backscatter signal is a weighted average over polarizations.

We are interested in the electric fields at the detector whose surface is transverse to . The detector’s area is DA and is sufficient to receive the entire backscat-tered signal from the iris. The total far-field vector potential and electric field are

AA , AjE (5)

Let r be the location of a point on DA (which is assumed circular with radius, 0Rd ). Its distance

from the center of the iris surface is rRR 0 and

the distance to the singularity is 2)( rRR :

)(0 rrRR (6)

Since 40 10)/( Ra and 0Rd , we get

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QR

jkRA

0

0

4)exp( (7)

dVrrjkrJQ ))(exp(),( (8)

TQR

jkRjE

0

0

4)exp(

)( (9)

QQT (10)

The differences between the set Q is what makes iris recognition possible. If the detector is located at 0Rand is able to measure the maximum value of the electric field, we can determine the fundamental limits of performance for this simple illustrative case. The maximum values of Q and TQ are

dVrJQ ),( (11)

249

1QQQT (12)

There will be a maximum absolute value of Q in the set of 249N singularities, which we define as

}max{max QG (13)

249

1maxNGQ (14)

The maximum value of the electric field is

0

max

max 4 RNG

E (15)

The foregoing set of equations provides the maximum electric field observable. If there were no limits on our ability to measure electric fields precisely, it would be possible to associate a peak electric field with a partic-ular target iris for our ideal model. There would bewould be no limit on the number of enrollees.

Now let equal the inherent (irreducible) uncertainty in our ability to measure the magnitude of the electric field. The best that can be done is to divide

maxE into

equal segment of range . This gives the maximum number of distinguishable segments, DN , which is, in fact, the maximum number recognizable entities:

0

max

max 4 RNG

NE D (16)

0

max

4 RNG

N D (17)

DNNG

R maxmaxmin, 4

(18)

The foregoing analysis has established a theoretical limit to iris detection when partial coherence is absent.

To better understand the dependence of recognition on range, we examine the formalism developed by Daug-man in terms of the Gabor wavelet, Gaussian Window Fourier transform, which in Taylor expansion is kept at the long wavelength limit the first and the second derivatives of Gaussian, or the even or the odd Mexican hat wavelets [4]. This is where the first derivative (odd Mexican hat) and the second derivative curvature (even Mexican hat) come from. The basic EM wave information resides in the Q functions defined by Eq. (8). The incident power density at anypoint on the detector is

)*20

12)4(

22*}){,( TQTQ

RsZsZ

EErrS

(19)

In its present form, }){,( rrS is not very useful for recognition and matching. The purpose of signal processing is to construct a functional }){,( rrS that

renders the information contained in Q accessible.When a coherent illumination is used at the micron short wave infrared (SWIR), it is relative saver than the UV light at 0.2 m. In fact, one shall automaticallyadjust the intensity by the distance after detection of the human face by the color hue as already adopted in a system on chip (SOC) in every Japanese made camera, which can detect all faces in 0.04 sec in parallel. Furthermore, it applies those detected faces to decide an automatic focus on the smiling one, and warning, if any, the eye-closed one. We will begin with this preprocessing to shine the coherent SWIR upon the eyes.

The coherent illumination will provide the partial coherent ensemble average in the backscattering forming the interference pattern from both sides of the iris wedge. This coherent feature information has 2Ndegrees of freedom, where N is about 249 depending on the range and lens resolution as the discernable N. Comparison will be discussed in theory, but the proof is finally rested at the easting. Lacking the experi-mental verification as yet, we believe that this coherent illumination imaging stands a better chance ofidentifying people by face and ocular features and

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identifying the iris at a distance than the traditional methodology.

4 PRECIPITOUS DROP-OFF IN MATCHING WITH RANGE

There is an important collective property that accounts for the precipitous degradation of matching perform-ance with respect to the standoff distance. The folds form discontinuities for optical scattering. The folds are visible from close range, with about 1.44 o per fold, affording up to 249 discontinuities over 360o

(249 DOF × 1.44o = 360o). This means that if a given optical imaging system can resolve a given iris fold, then the system tends to be able to resolve almost all iris folds within the 249 pie-shaped areas due to the circular symmetry of the iris field. On the other hand, if the optical system cannot resolve a given fold, it will most likely be unable to resolve many of the remaining folds, again due to the iris’ circular symmetry. Thus, if any of the 249 singularities should suffer the loss of imaging resolution due to distance, they would all tend to do so collectively, and the performance will drop suddenly due to circular symmetry. Then, instead of the expected gentle degradation with distance due to the inverse square law for imaging, performance drops precipitously. This is the reason that understanding and modeling the 3-D electromagnetic wave response of the iris is necessary.

5 MODELS USING NONLINEAR DETECTORS

The current density is iris excess material in a semi-closed pupil having a 3-D dielectric fold bulging out-ward, which will be modeled within one wavelength by two layers of inhomogeneities in partial coherence. Figure 2 shows the relevant diagram.

Figure 2: Scattering geometry – one incident plan wavewill be scattered back in multiple rays, and we are only interested in the returns within one wavelength.

Gabor asked how to keep the phase information by means of the square law film or sensor array. He did it by using a reference plane wave . Coherent imaging of 3-D iris will generate an iris hologram.

Write to film: ;

Read by the plane wave :

(ghost iris to be blocked)

In principle, this 3-D image could extend the range for iris recognition.

6 CONCLUSION

In this paper, we have examined the issues involved in extending the range for iris recognition, accounting for the unique physical, biological, and electromagnetic properties of the iris. A more complete wave optic model of coherent and incoherent interactions could perhaps lead to improved recognition at greater ranges.

Acknowledgement

We wish to thank the Army Science Board (ASB) for bringing us together and U.S. NVESD for granting us the time for the analysis during the U.S. Army Military Sensing Symposia MSS conference.

References

[1] John Daugman, “Results from 200 billion iris cross-comparisons,” Technical Report UCAM-CL-TR-635, University of Cambridge Computer Laboratory, June 2005.

[2] R.G. Foster, I. Provencio, D. Hudson, S. Fiske, W.De Grip, and M. Menaker, “Circadian photo-reception in the retinally degenerate mouse (rd/rd),” J Comp Physiol [A], 1991 Jul, 169 (1):39–50. Abstract inhttp://www.ncbi.nlm.nih.gov/pubmed/1941717.

[3] C. T. Tai, “Dyadic Green’s Functions in Electro-magnetic Theory,” Intext Educational Publishers, 1971.

[4] H. Szu, C. Hsu, L.D. Sa, and W. Li, “Hermitian Hat Wavelet Design for Singularity-Detection in the Paraguay River Level Data Analyses,” Proceedings of SPIE Wavelet Applications IV,Vol. 3078, pp. 96–115, 1997.

z

E1E2E

z z2

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