Extended depth-of-field iris recognition system for a workstation environment

Ramkumar Narayanswamya*, Paulo E. X. Silveiraa, Harsha Settyb, V. Paul Paucab, and Joe van der Grachtc

a CDM Optics, Inc; b Wake Forest University; c HoloSpex, Inc;

ABSTRACT Iris recognition imaging is attracting considerable interest as a viable alternative for personal identification and verification in many defense and security applications. However current iris recognition systems suffer from limited depth of field, which makes usage of these systems more difficult by an untrained user. Traditionally, the depth of field is increased by reducing the imaging system aperture, which adversely impacts the light capturing power and thus the system signal-to-noise ratio (SNR). In this paper we discuss a computational imaging system, referred to as Wavefront Coded® imaging, for increasing the depth of field without sacrificing the SNR or the resolution of the imaging system. This system employs a especially designed Wavefront Coded lens customized for iris recognition. We present experimental results that show the benefits of this technology for biometric identification. Keywords: Iris recognition, imaging, depth-of-field, optics, computational imaging, biometric

1. INTRODUCTION In many applications, such as airport security, physical access control, computer security, financial transactions, and health-care documents, personal identification is typically confirmed with the use of ID cards or passwords. However, these forms of identification are in themselves not secure. ID cards and passwords can be stolen or counterfeited. As a result, any action or application that is contingent on establishing identity can be compromised. Systems based on the use of biometrics verify identity on the basis of innate metrics, such as facial features, finger prints or iris patterns, making the process more robust and substantially difficult to tamper [1]. In particular, identity verification using a person’s iris is attracting considerable interest. The human iris as a biometric has several attractive features: the iris texture is highly unique; it is generally stable over the lifetime of an individual and the image of the eye/iris can be captured from a distance using standard camera systems. The iris is the annular area between the pupil and the white sclera in the eye. The iris has a rich texture of interlacing features that provide a signature that is unique to each subject. In fact, the operating probability of false identification by the Daugman algorithm can be as high as 1 in 1010 [2-4]. Compared to finger printing, hand shape, facial features, or voice, the iris is generally considered more stable and reliable for identification.

24”24”

Figure 1: Iris Biometric Recognition System. Increasing the depth of field of this system improves ease-of-use and facilitates the adoption of the technology.

* corresponding author: ramkumarn@cdm-optics.com

Appeared in: Proceedings of the SPIE Biometric Technology for Human Identification II, Vol. 5779, pp. 41-50, Orlando, FL, 2005.

In one particular application, iris recognition is used instead of passwords for controlling the access and monitoring the use of computer systems. Figure 1 illustrates an instance of this application where a computer user is situated 2 feet (61 cm) from an iris recognition camera and is expected to authenticate his/her identity on a periodic basis. Currently existing commercially available iris recognition systems for this application are difficult to use. The subject must be carefully positioned so that the correct eye is within the field of view, in focus, and is held stationary to avoid motion blur. This narrow field of view and a shallow depth of field mandate considerable user cooperation and training. Ideal iris imaging systems should have a large field of view and a large depth of field, allowing users to be identified without requiring their active cooperation. The system should capture adequate signal to facilitate good discrimination and operate with both stationary and moving objects. This need for a high SNR at the detector and minimum motion blur (short exposures) calls for a relatively fast optical systems (low F-number), which inherently leads to a shallow depth of field in traditional optical systems. In this paper we present a fast (low F-number) iris imaging system with an extended depth of field, a solution that cannot be delivered with traditional optical designs. Our imaging system uses asymmetric-aspheric optics and complementary signal processing. This technology referred to as Wavefront Coded imaging is an example of the emergent field of computational imaging [5-6]. The use of Wavefront Coded imaging for biometric iris recognition has been previously proposed [7-9]. This paper presents what is, to the best of our knowledge, the best performing Wavefront Coded system available to date specifically designed for iris biometric recognition.

Figure 2: The diffraction limited optical resolution of the imaging system bears an inverse relationship with the F-number. This effect is typically not noticed, since digital imaging systems are usually limited by the detector resolution rather than the optical resolution.

2. TRADE-OFF IN TRADITIONAL IMAGING SYSTEMS Some of the main parameters that specify an imaging system are its resolution, depth of field (DOF), field of view and exposure period per image-frame. The resolution is defined as the maximum spatial frequency that can be resolved in the image at a predetermined contrast. For example, the resolution specification can be 50 line-pairs/mm at 10% contrast. The field of view determines the spatial extent of the scene acquired by the sensor. Depth of field determines how far a planar object can move away from the best focus position and still be imaged without focus errors. The exposure period is defined as the detector integration time while acquiring an image frame, and it is mainly determined by the scene illumination and how fast the scene is changing or the object is moving. These parameters are however not always complementary. In this Section we show that to increase the DOF in traditional imaging systems one must trade off the DOF for optical resolution and light gathering capacity, leading to a loss of contrast and SNR.

2.1. Diffraction limited resolution The resolution of the optics is related to the aperture diameter and, for objects sufficiently distant from the imaging system, it can be approximated by

f

D

F !!" =#

/#.

10

, (1)

where 0

! is the cut-off spatial frequency (specified in cycles/length),! is the wavelength of light being used, D is the

diameter of the entrance pupil, f is the effective focal length and F/# is the F-number, given by the effective focal length of the imaging system divided by its entrance pupil diameter. As the imaging system’s entrance pupil diameter, D, is reduced (larger F-number), the optical resolution of the system drops as 1/F#, as shown in Figure 2. This effect is typically overlooked, since digital camera systems tend to sample the image at a spatial frequency lower than the optical resolution. Even in this regime, where the resolution is determined by the sensor and the not the optics, reducing the aperture size leads to a drop in contrast at all spatial frequencies, especially at the high spatial frequencies, leading to an overall loss in SNR.

Figure 3: The DOF of traditional imaging systems grows linearly with F-number from F/1 to F/32. For example, moving from F/4 to F/8 doubles the depth of field. The depth of field is higher for objects located further away from the lens. The plot shows the depth of field for objects located at 500, 600 and 700 mm from the lens. The focal length of the lens is 50mm and the sensor pixel pitch is approximately 5 microns.

2.2. Depth of Field The limiting resolution of the sensor is given by

pvs2

1= , (2)

where νs is the cut-off spatial frequency and p is the pixel pitch. The system is referred to as an “under-sampled” system when νs < vo. The depth of field in an under-sampled system is mainly determined by the diameter of the tolerable blur (pixel size). In this case, the DOF is linear with F-number, as shown in Figure 3. Increasing the F-number further leads to an over-sampled system, where the sensor cut-off frequency is greater than the highest frequency in the image-plane. For such an over-sampled system, diffraction and aberration effects determine the DOF, which starts bearing a non-linear relationship with F-number.

Figure 4: Light gathering capacity of the lens drops quadratically with increasing F-number.

2.3. Light gathering capacity The F-number of the lens also determines its light gathering capability. A lens with large entrance pupils relative to its focal length (small F-number) captures more light from the object compared to a lens with a smaller entrance pupil and the same focal length (larger F-number). Each increase in the F-number, (usually rated in multiples of the square root of two, i.e., F/1, F/1.4, F/2, F/2.8, etc) reduces the light gathering capacity by 50%. Figure 4 illustrates this point by plotting the optical power incident on a single pixel of a hypothetical imaging system as a function of the F-number. The drop in signal leads to a drop in the overall operating SNR.

2.4. Trade-off discussion The depth of field of an imaging system increases linearly with increasing F-number. However optical resolution drops as 1/F# and the light capturing capacity drops as the square of 1/F#. In this paradigm, doubling the depth of field by going up two F-stops implies reducing the light captured to 25% of the original amount of light, while suffering loss of contrast at the higher spatial frequencies. The reduced SNR will lead to poor detection and, most likely, to a larger fraction of false positive and/or false negative identifications. Increasing the integration time to compensate for the loss of signal can result in motion blur.

3. WAVEFRONT CODED IMAGING SYSTEM Wavefront Coded imaging, is a new paradigm in imaging that provides us with imaging systems that operate with large apertures (low F-numbers) but with the DOF of a reduced aperture system. Wavefront coded imaging uses non-conventional aspherical optics to form point spread functions which do not vary significantly over an extended imaging volume compared to traditional optics. Alternatively stated, the Wavefront Coded systems operate by coding the wavefront such that the modulation transfer function (MTF) of the system does not lose modulation at higher spatial frequencies with increasing defocus error. Defocus is commonly measured in terms of waves of defocus, and typically a quarter wave of defocus is considered substantial in an optical design. Our iris imaging system has more than fifteen waves of defocus over the intended imaging volume.

Figure 5: Experimentally measured modulation transfer function of a traditional imaging system in the presence of defocus error. Notice that the MTF drops rapidly with increasing defocus at the higher spatial frequencies. This plot graphs the MTF for defocus error associated with object distances of 20”, 23”, 24.5” and 28”. The lens focal length is 50mm, operated at f/3.5 with a 5 micron pixel sensor, and the nominal object distance is 24.5”. The nulls present in the defocused MTFs lead to an irreversible loss of information. Aliasing leads to measured MTF values at high spatial frequencies that are higher than in reality.

3.1. Modulation transfer functions of a traditional and of a Wavefront Coded imaging systems. Figure 5 shows the experimentally-determined MTF of our iris recognition system without Wavefront Coded optics for various object positions. For the purpose of this discussion, we refer to our iris recognition system without Wavefront Coded optics as the traditional imaging system. The various curves correspond to the system MTFs for different distances from the object to the imaging system. The lens is a 50-mm focal length Cosmicar lens operated at F/3.5, and the detector used has a pixel pitch p = 5 µm. The lens is adjusted to provide us with in-focus images at an object distance of 24.5”. The corresponding MTF shows good modulation across all spatial frequencies. As the object moves away from the best focus position, the system suffers from defocus error. This error manifests in the MTF as a dramatic drop in the modulation at the higher spatial frequencies. Once this modulation drops below the noise floor all information in those spatial frequencies is irremediably lost. Notice that a displacement of just 1.5” from the best focus position introduces nulls in the MTF. The spatial frequency suffers a phase reversal every time the modulation goes through a null. Automated detection systems are often sensitive to such contrast reversal, and these phenomena can limit the system performance even before the overall loss in modulation would. Figure 6 plots the MTF of the Wavefront Coded version of the same imaging set up. The MTF is plotted for 20”, 23” , 24.5” and 28” object distances. Notice that the Wavefront Coded system maintains the modulation substantially higher than the traditional MTF with defocus. The MTF is also free of nulls. Since the modulation is maintained above the noise floor and free of nulls (zeros), the information from the object is preserved in spite of the large defocus error. Wavefront Coded images can be processed to boost the spatial frequency to the desired levels to form crisp high-contrast images or to suit the requirement of an automated detection algorithm. The processing is typically linear and achieved by convolving the image with a filter, as depicted in Figure 7.

Figure 6: Experimentally measured modulation transfer of the custom designed Wavefront Coded imaging system. Notice that the modulation levels are higher than those of the defocused traditional system, but lower than those of the best focus traditional system. Also notice that that the MTFs do not have any nulls.

Custom optical element for iris recognition

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Wavefront Coded Processing

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Custom optical element for iris recognition

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Figure 7: Schematic diagram of the Wavefront Coded imaging system for iris recognition. The optical system differs from a traditional imaging system in that it is fitted with a custom optical element, and the acquired image is post-processed as part of the detection process.

3.2. Description of a Wavefront Coded imaging system. Wavefront coded imaging systems typically consist of a digital detector and a conventional optical system retrofitted with a Wavefront Coded optical element (see Fig. 7). One side of the optical element usually has a non-spherical, circularly asymmetric surface and the other side typically has a flat surface. The optical system is focused at the nominal object distance and images of the object are recorded exactly as in a traditional system. In the processing step the recorded images are convolved with a filter to arrive at the “decoded” image, fit for use in the application of choice. Examination of a recorded image prior to processing renders a blurred version of the scene. But the blur is nearly uniform across the image and does not vary significantly as a function of field or object distances within certain specifications. This blurred image

can be thought of as an image optimized for “information capture” rather than for human visualization. For better processing performance, different filters can be applied to different object ranges. In the case of iris recognition, the radius of the iris (which is quite invariant across the human population) can be used to estimate the object distance. In our system best results were achieved when seven ranges were used.

4. WAVEFRONT CODED IMAGING APPLIED TO IRIS RECOGNITION A Wavefront Coded element was custom designed for biometric iris recognition using the same conventional optical system described in Section 3.1. The recognition algorithm was included in the optimization loop, resulting in a Wavefront Coded optical element specifically optimized for iris recognition. The design process is described in more detail by Narayanswamy et al [9]. The optical transmission of the Wavefront Coded element is defined by a high-order separable function of the form P(x,y) = exp{-j[f(x) + g(y)]}, where f(x) and g(y) are high-order polynomials. One of the key steps in the design of the Wavefront Coded iris recognition system is translating the iris recognition algorithm’s requirement in terms of parameters relevant to optical and imaging systems design. In our system, this requirement was partially met by optimizing the Wavefront Coded element with an iris recognition algorithm inside the optimization loop [9]. This is particularly important in order to take into account the non-linear steps required for feature extraction and identification. Nevertheless, correct iris identification requires the acquisition of the iris texture over a band of spatial frequencies without distortion and at a sufficiently high SNR. A detailed analysis of the algorithm helped us identify the spatial frequency bands of interest, and during the optimization of the Wavefront Coded optical element it was also required that the resulting system maintained adequate modulation within these bands over the entire imaging range.

Figure 8: Estimated SNR at the highest spatial frequency of interest as the object distance is varied from 17.5” to 30”. The variation of spatial frequency with magnification is taken into account, so that the SNRs are plotted at a constant spatial frequency in the object plane.

Figure 8 plots the estimated system SNR at the highest spatial frequency of interest as the object moves through the imaging volume and undergoes different amounts of defocus error. Note that the magnification of the imaging system is inversely proportional to the object distance, resulting in a variation of the highest spatial frequency of interest in the image plane. We take this effect into account by tracking higher spatial frequencies in the image plane as the object moves farther away. The plot shows that Wavefront Coded imaging (solid line) maintains the modulation sufficiently high to deliver a minimum of 15 dB SNR. The corresponding curve for the traditional system (dashed line) drops below 15 dB for a displacement of 1.5” from the best focus position. The iris recognition algorithm can be characterized in terms of the minimum SNR needed at various spatial frequency bands of interest. Subsequently, the depth of field of the system can be estimated by examining the SNR of the various frequency bands of interest.

Figure 9: Comparison between images of eyes captured with a traditional imaging system (left) and a Wavefront Coded imaging system (right) at object distances of 20”, 24” and 28”. Both systems use a 50mm lens operating at F/3.5. The lens is focused at an object distance of 24” and not refocused as the object is moved away from the best focus position.

Figure 9 shows a comparison of the performance of both the traditional and Wavefront Coded systems by using iris images acquired by each system at object distances of 20”, 24” and 28” when the each of the imaging systems are focused at an object distance of 24”. The Wavefront Coded imaging system is fitted with a custom asymmetric aspherical optical element, as shown in Figure 7, and the acquired images have been filtered as part of the processing step. Notice that the Wavefront Coded images show fine detail such as eye-lashes and skin texture in all three distances, whereas the traditional images appear very blurred when out of focus. Iris images often present specular reflections due to the reflection of the illuminating light sources by the cornea. In the traditional images, the specular reflections are circular while in the Wavefront Coded images they posses a peculiar shape. This is a characteristic of Wavefront Coded systems, whose point-spread functions are often non-circular and take on a variety of shapes due to the asymmetry of the pupil function. Also note that the specular reflections have been partially removed from the Wavefront Coded images as part of the iris recognition processing. Figure 10 compares the iris identification Hamming distances (HD) as the user moves from a distance of 18” to 30” at 0.5” increments. The HD is a measurement of the fractional difference between bits in two given binary iris codes [1]. A lower HD indicates a good match, whereas a HD higher than 0.3 indicates a mismatch. The HDs are plotted for an “authentic” or valid user. An “imposter” or a non-user would have HDs consistently around 0.45. Ten images are captured at each object position and the HDs are calculated for each of the ten images. Then, the average of the ten HDs are calculated and represented by a diamond-shape in Fig. 10. A threshold value of 0.2 provides us with accurate iris recognition from 23” to 25.5” for the traditional imaging system, whereas in the Wavefront Coded system we have accurate iris recognition from 20.5” to 28.5”, which is an increase in the depth of field by a factor of 3.

5. CONCLUSION Iris biometric systems are increasingly being used for access control of computer systems. Current iris recognition systems are difficult to use due to their limited depth of field and field of view. Wavefront Coded imaging can be used to increase the depth of field by mitigating defocus error. Field of view is increased by using sensors that cover a greater area on the focal plane. Wavefront Coded imaging can mitigate the field-dependent aberrations present when operating at large angles. In this paper we have presented a custom Wavefront Coded optical element for the iris recognition application and experimentally demonstrated the positive impact it has on the application by extending the depth of field by three times without requiring a reduction in the entrance pupil diameter of the imaging system. Traditionally, increasing the depth of field by a factor of 3, requires moving from an F-number of 3.5 to an F-number of 10. However, the light captured at F/10 drops to 12.5% of the light captured at F/3.5. Since eye-safety is a significant concern in this application, it may be impossible to increase the light power by a factor of 8 and maintain the same SNR as that achieved at F/3.5. Should increasing the illumination be possible, the application still may not attain the depth of field since diffraction effects at F/10 will lead to loss in contrast and poor SNR at the higher spatial frequencies.

(a) Traditional System (b) Wavefront Coded System.

Figure 10: Comparison between iris Hamming distances (HD) as the user moves from an object distance of 18" to 30" away from the imaging system. Ten images are captured at each position. The corresponding HDs are shown as dots and the averages of the ten HDs at each position are shown as diamonds. Setting a threshold of 0.2 provides a 2.5” depth of field for the traditional imaging system (a). The Wavefront Coded system (b) is able to maintain the HD below 0.2 for a distance of 8”.

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