INTRODUCTION

The scope of potential use of identification systems widens, including restricted area or confidential data access , credit card use etc. Only in 1993 banks lost more than three billions dollars due to credit cards forgery and misuse [1].

"No two fingerprints from different fingers have ever been found identical ..." [2].

That is why the fingerprint structure is successfully used in criminology [3] and is one of the properties that can be used for the person verification purpose [3]. Any fingerprint can be easily scanned and the verification process which goes along with it and lasts within pushing of a button seems natural and ergonomic. So far , optical sensors for the recognition of fingerprints, palm of the hand and the structure of eye blood vessels have been utilized and all of them have some disadvantages.

The authors have proposed and have been developing ultrasonic method of fingertip papillary lines representation acquisition [4]. We have stated that ultrasound is highly sensitive and brings out high contrast at the subsurface structure of the finger . One may expect that due to the uniqueness of the skin structure and its specific physical properties, the preparation of an artificial finger would be very complicated .

At the early stage of the research we concentrated on the far field diffractive representation (or Fourier transform) of the fingerprint structure. Now we are able to measure pulse response representation of the finger-tip and perform reconstruction of papillary lines from the set of measured data. Some techniques of reconstruction quality improvements and results achieved are presented below.

DETECTION AND RECONSTRUCTION METHODS

In all of our setups finger-tip is applied to a window of ultrasonic head. The head contains one , two or a ringshaped matrix of electro-acoustic transducers (Figure 1a). Ultrasonic method of acquiring fingerprint representation is based on sending acoustic signals towards the finger and detecting the echo.

Localization of the sender T 'and receiver T allows us to detect first diffractive order of the fingerprint structure:

 -ultrasound wave length ( 0.25 mm in water by 6 MHz),

 - papillary line distance ( 0.3 - 0.9 mm for most fingers) .

what makes °.

Figure 1a. Schema of                              Figure 1b. Project geometry
the data acquisition head                

Reflected pulse model

To get the data needed for the reconstruction of the finger-tip structure we apply the pulse method. The sender generates short acoustic pulses and the receiver , moving around a circle , detects the responses sampled then by a 50 MHz scope board. For 3D object observed by a flat receiver, tilted by angle Q, space variables p, z and time t are related by the time of flight relation:

, (2)
c - sound velocity

(The same relation holds for spherical cross-sections of the object and properly located point transducers.)

By the fixed angle Q, we can then measure time in millimeters and use the space variable p paralely with t . For 2-D flat object g(x,y), the receiver rotated by the angle f observes the scaled projection

(3)

In real case we have to take into account the shape of voltage spike  , used to drive the transducer , and time depending transfer functions of the sender and receiver ,. The echo e(t) is then described by the multiple convolution

 (4)

where  represents the pulse response of the setup and  set of projections of the object scaled to the time domain..An example of the echo of a finger tip structure is presented in the Figure 2.

Figure 2. Visual presentation of measured
echo matrix e(t,f) of a fingerprint.

Point Spread Distribution of reconstruction

There exist well known methods of reconstruction of the 2D function g'(x,y) from the set of projections r(p,f). Back projection algorithm which we use is linear and stationary , which means that we can analyze the quality of reconstruction using 2D point spread distribution (PSD). The projection of a point d(x0,y0) gives a trace in a form of a sinusoidal line, therefore during the reconstruction we find the value for every point by integration along such lines.

(5)

z - defocusing parameter, - echo scaled to the space domein,

For a point object we get the 2D PSD function of the setup (including reconstruction algorithm). Due to the rotational symmetry of the PSD , it is enough to calculate and show its crooss- section. The shape of PSD depends on the defocusing z, and thus we get 3D PSD. Now we can consider transversal and axial resolution of reconstruction in Reileigh's sense (a distance from the maximum to the first zero of PSD in p and z direction).

There are three examples of pulse responses in Figure 3. We have analyzed narrow band transducer, transducer with short pulse response and a signal after deconvolution.

Figure 3 shows that even using transducers of several periods per one pulse response we are able to

Figure 3a. good quality

obtain narrow central maximum of PSD, due to the suppression of side loops by the reconstruction

integral (5). The disadvantage of such transducer is that we can get also a false reconstruction for another defocusing parameter (Figure 3 (a)).

Deconvolution dramatically improves the pulse response of the setup, or the amplitude and phase of of the signal spectrum specially at the higher frequencies (Figure3(c)).

Figure 3b. poor quality

Figure 3. Examples of pulse responses h(p), its fourier transforms H(v) and cross-sections of 2D PSD

depending on defocussing parameter z0, for electronic setup and transducers of:

good quality - (a), poor quality - (b), poor quality transducer after convolution - (c)

Figure 3c. poor quality transducer after convolution

ENHANCEMENTS OF THE RECONSTRUCTION

Due to the limited quality of transducers , electronic noises and interference with signals from deeper layers , we have to use some enhancement techniques to obtain satisfactorily reconstructed image. The first of them is deconvolution of the echo. Also three methods of 2D image processing are used by us: smoothing , directional filtering in spectral domain and binearization.

     
Figure 4a.                  Figure 4b.            Figure 4c.             Figure 4d.               Figure 4e.

   
  Figure 4f.             Figure 4g.                  Figure 4h.            Figure 4i.

Figure 4.

(a) - optical picture of a fingerprint,
(b) - optical picture after binearization,
(c) - reconstructed and enhanced acoustic picture of the same finger,
(d) - acoustic fingerprint reconstruction,
(e) - acoustic fingerprint reconstruction after directional filtering,
(f) - acoustic fingerprint reconstruction after deconvolution and directional filtering,
(g) - another acoustic fingerprint reconstruction after deconvolution and directional filtering,
(h) - binearization of (g),
(i) - 2D Fourier spectrum of (g),

We see suppresion of the noises after directional filtering (Figure 4e), and appearance of fine detals after deconvolution (Figure 4f).

CONCLUSIONS

Measurements and reconstructions of finger-tips show that acoustic field diffraction occurs mainly on fingerprint lines. Quality of the reconstructed images depends on the bandwidth of the transducer , but may be improved by some signal and image enhancement methods. Reconstructed images are so similar in form to the optical ones that one can use the same classification and recognition methods. The advantage of the ultrasonic method is the uniqueness of the acoustic properties of the finger-tip , which means that preparing its dummy should be very difficult.

Presented setup may by also used for measuring of other objects and be treated as synthetic aperture microscope of .14mm resolution.

REFERENCES

[1]. Kriminalität , "Mafia nera" , Der Spiegel, No.11, p. 81, März 1994.
[2]. A.A. Moenssnens, "Fingerprint Techniques " , Chilton Company (1971)
[3]. Cz. Grzeszyk , "Daktyloskopia ", PWN, Warszawa, 1994,(in polish)
[4]. R.H. Andersen, P. Jürgensen , "Fingerprint Verification - For use in Identity Verification Systems", Aalborg University , (1993)
[5]. W. Bicz, M. Pluta, "Ultrasonic sensor for fingerprints recognition ", COE '94 Warszawa , Poland, (to be published by SPIE Vol 2634 / p. 104).

Legends

*
Research - Production Enterprise OPTEL Ltd. ul. Otwarta 10a, 50-212 Wrocław

**
Institute of Physics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland