Optical imaging system

Optical imaging system between an object plane (2.2) of a total reflexion prism (2) and an image plane, mainly for a fingerprint reading apparatus, that comprises an optics (3) for imaging the object plane to the image plane, and an electronic image detector (4) in the image plane. The optics defines an optical axis (3.0) and input and output pupils, respectively. The total reflexion prism (2) is arranged in front of the input pupil of the optics (3). The prism has a first surface receiving light for illuminating the object plane through the interior of the prism and a further surface through which light reflected from the object plane passes towards the optics. The object plane closes an angle with the optical axis, which is preferably between 45.degree. and 65.degree. if the refraction index of the prism is between 1.5 and 1.85. The object plane (2.2) of the total reflexion prism (2) is offset relative to the optical axis (3.0) in normal direction and the image detector (4) is also offset in normal direction relative to the optical axis (3.0) to an extent which corresponds to the location of the image of said object plane.

The invention relates to an optical imaging system for imaging an object, 
mainly for a fingerprint reading apparatus, which comprises a total 
reflection prism with a total reflection surface that constitutes an 
object plane for receiving the object, the total reflection prism has a 
first transmitting surface for receiving light to illuminate the object 
when placed on the object plane through the interior of the prism, and a 
second transmitting surface for transmitting the light reflected from the 
total reflection surface; optical means with an optical axis and an input 
and output pupil, the input pupil receives the reflected light transmitted 
through the second transmitting surface and the optical means forms the 
image of the object plane in an image plane which is perpendicular to the 
optical axis; and an electronic image detector means located in the image 
plane. 
Such a fingerprint identifying optical system is described in U.S. Pat. No. 
5,187,748. In this patent a semi-transparent mirror is placed in slant 
position in the path between the total reflexion prism and the optics, the 
mirror divides the light coming from the prism, therefore the image will 
pass not only to the image detector but it will also enable direct 
observation. The total reflexion prism is arranged in the optical axis and 
its object plane is in a slant position relative to that axis. This slant 
position of the object plane is characteristic to all systems using a 
total reflexion prism. 
In EP 0 585 141 A2 the image of a finger is provided by using a total 
reflection prism, an imaging optics and a CCD camera. The object plane is 
placed on the optical axis of the imaging optics and the consequence of 
this arrangement is that the image is distorted just as in case of the 
previously cited publication. 
When a slant object plane is imaged to an image plane extending normal to 
the optical axis, owing to the path difference between the rays arriving 
from opposing edges of the object, distortions and an unacceptable 
decrease in image resolution will take place that can be compensated only 
by use of a sophisticated lens system and simultaneously by selecting a 
large object-to-optics distance. The large distance increases the size of 
the device and renders the handling more difficult or even excludes some 
applications, where the size is critical. The complexity of the lens 
system is a factor that increases costs. 
A partial compensation for the path difference can be learned from EP 0 361 
987 A1, wherein in the light path between the total reflexion prism and 
the optics a further prism and between the optics and the image detector a 
pin hole was inserted. Although by this solution the picture distortion 
was decreased below 5%, owing to the increased number of optical elements 
and to the presence of the pin hole a decreased sensitivity was obtained, 
i.e. a very high illumination is required for obtaining an image of 
acceptable brightness. 
The object of the invention is to provide an optical imaging system of the 
kind defined hereinabove which, in spite of the slant object plane 
relative to the optical axis, can produce images with acceptable 
distortion and good resolution and has sufficient sensitivity, furthermore 
which has a geometrical length substantially smaller compared to known 
systems. The reduced dimensions are crucial for constructing a compact 
fingerprint reading apparatus. 
According to the invention it has been recognized that the above problems 
can be decreased if the total reflexion prism is offset relative to the 
optical axis in normal direction so that the center of the object plane 
will not lie on the optical axis any more. From this offset arrangement it 
follows that the image detector i.e. a CCD matrix detector should also be 
placed in a position offset from the optical axis. This position 
corresponds to the one when the object plane is imaged in the image plane. 
The offset arrangement enables an easier dimensioning of the optics, the 
geometric distortion due to the geometrical differences in the path length 
decreases to an acceptable level, and the image can be of high resolution 
even if the object-to-optics distance is reduced. 
The conditions for total reflexion are given if the object plane closes and 
angle between 45.degree. and 65.degree. with the optical axis and if the 
refraction index of the total reflexion prism is between 1.5 and 1.85. 
In a preferable embodiment the second surface of the total reflexion prism 
is a curved surface which images the object plane into a further curved 
surface falling in the interior of the prism, and the average angle 
between this further curved surface and the optical axis is higher than 
the angle between the object plane and the optical axis. 
The curved surface is preferably spherical and the center of the radius of 
its curvature falls on the optical axis in the close region of the input 
pupil of the optics. With such a design the effective path difference of 
the image forming main rays will be smaller than 4%. 
For minimizing distortions and the point spread function the relative 
aperture of the optics is between f/6 and f/3.5 and the Petzval-sum of the 
optics is between -0.1 and 0.3. 
Distortions can be decreased to acceptable levels even if using an optics 
with three or four simple lenses, wherein optimum values can be determined 
for the radii of curvature, refraction indices, thicknesses and spacings 
of the lenses. 
The light intensity of the optical imaging system according to the 
invention is high, thus it has a sufficient sensitivity, its volume is 
small, and owing to the small number of optical elements used the 
manufacturing costs are also small. The electronic image processing 
enables the correction of the remaining slight distortion by using 
appropriate correction software in the system coupled to the CCD matrix 
detector. 
The extent of "trapezoid" distortion depends on the angle between the 
object plane and the optical axis, and it lies between 4% and 8%. Also the 
extent of the point-spread function lies between 10-35 .mu.m thus 
providing excellently sharp images.

In the fingerprint imaging optical system shown in FIG. 1 a prism 2 has a 
total reflection object plane 2.2 which closes an angle of 
.delta.=45.degree. with the optical axis 3.0 of optics 3. The illumination 
of the total reflection object plane 2.2 occurs through lower surface 2.1 
of the prism 2 by means of a light source 1 of nearly collimated 
monochromatic rays. The fingerprint will be formed in a field of the 
object plane 2.2 being 25 mm.times.25 mm and illustrated by points 2.2.1, 
2.2.2, 2.2,3. The object field of the above size is arranged in an offset 
position relative to the optical axis 3.0. The image of the fingerprint 
will be formed by a spherical surface 2.3 of the prism towards the optics 
3 which has a relative aperture of f/6, and the refraction index of the 
material of the prism is n.apprxeq.1.5. In this embodiment the radius of 
curvature of the spherical surface 2.3 is R=75 mm. The spherical surface 
2.3 of the prism 2 performs the function of a correction prism by creating 
the image of the fingerprint with points 2.2.1, 2.2.2, 2.2.3 in a virtual 
surface 2.4 with corresponding points 2.2.1', 2.2.2', 2.2.3'. The average 
angle between the surface 2.4 and the optical axis 3.0 is larger than the 
angle of the object plane 2.2. The existence of the spherical surface 2.3 
makes it possible that the difference in the path length of main rays P1, 
P2, P3 starting from extreme points 2.2.1, 2.2.2, 2.2.3 of the fingerprint 
will be less than 4%. 
The image of the fingerprint created by the spherical surface 2.3 on the 
surface 2.4 will substantially coincide with the Petzval-field of the 
optics 3. In that case the Petzval-sum of the optics 3 will be P=-0.1. The 
quasi-symmetric optics 3 which consists of four lenses i.e. collecting 
lens 3.1, diffraction lens 3.2, diffraction lens 3.3 and collecting lens 
3.4 together with a Petzval-sum of -0.1, will provide a good quality image 
in the image plane of the optics 3 which is normal to the optical axis and 
where an image detector 4 can be arranged also in offset position relative 
to the optical axis 3.0. The image detector 4 is preferably a CCD detector 
of sufficient resolution. The "trapezoid" distortion for the central point 
2.2.2 of the object field of the fingerprint with a size of 25 mm.times.25 
mm at the object plane 2.2 will be about 8% in case if the angle of 
inclination of the object plane is 45.degree.. 
FIG. 2 shows a further embodiment of the imaging system according to the 
invention wherein the angle between the total reflection object surface 
2.2 of the prism 2 with the optical axis 3.0 is .delta.=6520 . The 
illumination of the prism 2 occurs in the same way as in case of the 
previous embodiment. The field for the fingerprint has a size of 25 
mm.times.25 mm on the total reflection object plane 2.2 of the prism 2, 
which is again in offset position relative to the optical axis 3.0 of the 
optics 3. The prism 2 has a refraction index n.apprxeq.1.8, and the image 
of the fingerprint will pass through the spherical surface 2.3 of the 
prism 2 towards the optics 3. The central point of the curvature of the 
spherical surface 2.3 falls on the optical axis 3.0 in the close vicinity 
of the input pupil of the optics 3, and the radius of its curvature is 
R=76.43 mm. The function of this spherical surface 2.3 is the same as in 
the first embodiment. With the arrangement of FIG. 2 the difference 
between the effective optical path lengths of the main rays starting from 
the central point of the field of the fingerprint till the image plane 
will be less than 2%, and this is largely due to the presence of the 
spherical surface 2.3. 
The image of the fingerprint as formed on the virtual surface 2.4 makes it 
possible that the Petzval-sum of the optics 3 be as high as P=0.3. The 
optics 3 will consist in this embodiment of only three lenses i.e. of 
collecting lens 3.5, diffraction lens 3.6 and collecting lens 3.7. The 
optics 3 provides a high quality image in the image plane normal to the 
optical axis 3.0 where the image detector 4 is arranged. The "trapezoid" 
distortion relative to the central point 2.2.2 of the field of the 
fingerprint at the object plane 2.2 will be .+-.4%. The extent of the 
point-spread function lies between 10-35 .mu.m being sufficient to reach 
very good image resolution. 
The embodiments shown in FIGS. 1 and 2 correspond to the two extreme values 
of the practically realizable range. Between these extreme values several 
other intermediate embodiments can be realized which can all be 
characterized by the following properties: 
1) The prism 2 as an object plane being offset from the optical axis 3.0 of 
the optics 3 and the closest surface of the prism 2 to the optics 3 is the 
spherical surface 2.3 and the central point of curvature of this surface 
falls on the optical axis 3.0 at the proximity of the input pupil of the 
optics 3. 
2) As a function of the angle of inclination between the total reflection 
object plane 2.2 and the optical axis 3.0, the values of the refraction 
index n, the difference dP in the effective optical path length of the 
main rays P1, P2, P3, the Petzval-sum P, the number of lenses and the 
relative aperture f/NO of the optics 3 as well as the amount of 
"trapezoid" distortion T are given in Table 1 below. 
TABLE 1 
______________________________________ 
Number of 
.delta. 
n P f.sub./NO 
P lenses T 
______________________________________ 
45.degree. 
1,50 4% f.sub./6 
-0,1 4 .+-.8% 
. . . . . . . 
. . . . . . . 
. . . . . . . 
65.degree. 
1,85 2% f.sub./3,5 
0,3 3 .+-.4% 
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To obtain a good quality image certain relationships between the focal 
distances f.sub.i of the lenses constituting the optics 3 and the 
resulting focal distance f' of the optics 3 should be kept. In case of the 
embodiment with four lenses this relationship is: 
##EQU1## 
In case of the second embodiment with three lenses, the function is as 
follows: 
##EQU2## 
In preferable embodiments of the optics 3 for four and three lenses, 
respectively, the actual parameters of the optics are given in tables 2 
and 3. Table 2 refers to the first embodiment with four lenses and Table 3 
to the second embodiment with three lenses. In the tables Ri designates 
the radius of curvature of the ith surface, wherein the number is positive 
in case of a convex surface and negative if the surface is concave. The 
serial number i increases from the light source towards the image plane. 
The lens li designates the ith lens, di designates the thickness the ith 
lens li along the optical axis, ni designates the refraction index of the 
ith lens li, eij designates the spacing along the optical axis between the 
lenses li and lj. 
TABLE 2 
______________________________________ 
radius of thickness refraction 
curvature (mm) 
lens (mm) index 
______________________________________ 
R1 7,94 
11 d1 = 1,5 n1 = 1,76 
R2 -15,17 
e1,2 = 0,55 
R3 -8,71 
12 d2 = 0,8 n2 = 1,65 
R4 10,15 
e2,3 = 1,3 
R5 -11,43 
13 d3 = 0,6 n3 = 1,65 
R6 9,83 
e3,4 = 0,78 
R7 20,82 
14 d4 = 1,2 n4 = 1,76 
R8 -6,79 
______________________________________ 
TABLE 3 
______________________________________ 
radius of thickness refraction 
curvature (mm) 
lens (mm) index 
______________________________________ 
R1 8,31 
11 d1 = 1,78 n1 = 1,80 
R2 45,06 
e1,2 = 2,02 
R3 -14,17 
12 d2 = 0,71 n2 = 1,61 
R4 8,31 
e2,3 = 1,17 
R5 33,24 
13 d3 = 1,87 n3 = 1,82 
R6 -13,17 
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