We designed a new image scanner using the reflective optics of a compound eye system that can easily assemble plural imaging optical units (called imaging cells) and is compact with a large depth of field (DOF). Our image scanner is constructed from 32 reflective imaging cells, each of which takes an image of approximately a 10-mm field of view (FOV) that slightly overlap the adjacent imaging cells. The total image is rebuilt by combining the 32 images in post processing. We studied how to fold the optical path in the imaging cells and simplified the structure, resulting in the following three advances of our previous work: 1) greater compactness (50 × 31 mm2 in the cross section), 2) less variable optical characteristics among the imaging cells, and 3) easy assembly thanks to small number of optical components constructing the imaging cell.
© 2014 Optical Society of America
Image scanners take two-dimensional high resolution images by a linear image sensor when an object moves at a relatively constant speed, for example, observations from artificial satellites  or product inspection in factories. Image scanners are also useful to take precise images without distortion or magnification error, for example, the digitalization of heritage art works  and copying documents . Such a reduction type image scanner in which a monocular lens makes a reduced-size image of an object on one chip image sensor is usually used for such applications. Since the scanner needs a large object distance to take an image of a wide field of view (FOV) and needs a driving mechanism to scan the mirrors in order to keep the object distance, it occupies a large space in the copier, for example, 400 × 80 mm2 in the cross section.
Over three decades, compound eye optical systems have been researched to reduce optical size by dividing a large FOV into many small areas so that plural optical units (called imaging cells) take images of the separated areas. A wafer-level camera  and TOMBO  are compound eye optical systems that target thin optics. Brady et al. developed a gigapixel camera with super high resolution  using many cameras whose FOVs overlap each other. Anderson used two arrays of lenses to form an erect composite image  for a close-up imaging system. Although the above examples are area cameras, there are examples of image scanners. A contact image sensor based on a gradient index (GRIN) lens array , which can also be classified in a compound eye optical system, is widely used as a scanner in automated teller machines or the automatic document feeders of copiers. Other constitutions for contact image scanners use refractive lens arrays  or reflective concave mirror arrays . These scanners using compound eye systems have a DOF limit, typically under 1 mm, which is insufficient for flatbed scanners that must read the floating inner margins of a book. The limit is caused by combining images taken by non-telecentric imaging cells that change the magnification ratio with the object distance.
We previously developed image scanners with compact size and large DOFs by a new concept of compound eye optical systems that overcame the above difficulties [11,12]. The basic constitution is shown in Fig. 1. Imaging cells shown as cylinders in Fig. 1(a) are aligned in a zigzag alignment made of two lines of A and B. A large FOV of 312 mm along the X direction is divided into 32 areas, and each imaging cell takes an image of approximately 10-mm FOV for each divided area. The divided FOVs slightly overlap as shown in Fig. 1(b), and the 32 images are electrically combined in the signal processing. The optical axes are inclined in the Y direction as shown in Fig. 1(c) to read the same position in the Y direction. One of the features of our optics is the telecentricity in the object space that enables a large DOF in the compound eye optical systems. Since the magnification ratio is constant regardless of the object distance change, the images are easily combined without magnifying or shrinking the image size. The aperture size of the objective lens must be bigger than the FOV in telecentric optics as drawn in Fig. 1(b), and therefore it is impossible to arrange lenses in a row without a clearance gap of the FOV among adjacent imaging cells. That is the reason why we arranged the imaging cells in a zigzag alignment in two rows to keep the overlapping of the adjacent FOVs while avoiding the mechanical interference of the lenses.
Each imaging cell was constructed by reflective optics to reduce its size; however, in our previous model , the structure was complex, complicating assembly and producing large deviation of the optical characteristics. We are studying how to fold the ray path in reflective optics to simplify the structure for easy assembly and small deviation of the optical characteristics. Our manufactured prototype is as small as 50 × 31 mm2 in the cross section, which is smaller than the above example of the reduction type image scanner, and has an enough large 4-mm DOF for a flatbed scanner in a copier.
2. Optical design
Each imaging cell in Fig. 1 is constructed from two lenses (the first lens (L1, focal length f1) and the second lens (L2, focal length f2)) and an aperture stop placed at the back focal position of L1 to form telecentric optics in the object space as shown in Fig. 2(a). Figure 2(b) shows the ray path in the Y direction, where a is the distance among the object plane and L1, l is the distance among L1 and L2, and b is the distance among L2 and the image plane.
Aberrations in an imaging system can be easily corrected when rays are gradually deflected at plural surfaces. The easiest aberration correction is probably done when the maximum deflection angle of the marginal ray is minimum. When the deflection angles of the marginal ray at L1 and L2 are defined as φ1 and φ2, the above condition equals φ1 = φ2 under thin lens approximation.
Our previous models [11,12] were double-sided telecentric imaging systems with the same magnification ratio, so the focal lengths of L1 and L2 were identical. In this condition of f1 = f2, the condition of φ1 = φ2 is satisfied when a = f1 and b = f2 = f1, which means that the rays starting from a point on the object plane are collimated by L1. Figure 2(c) shows the folded path under this condition by replacing the two lenses by concave mirrors to reduce the path size. However, it is impossible to scan a document on the object plane because it is placed under L2. We inserted two flat mirrors in Fig. 2(c) to fold the ray path two more times as shown in Fig. 2(d) in the previous models.
Here we consider an imaging system with reduced magnification ratio of f1 > f2. Distance a satisfying φ1 = φ2 condition is expressed as
Figure 2(e) shows such an optical layout. If the object plane can be above L2 as shown in Fig. 2(f) after replacing the two lenses by two concave mirrors, distance a must become larger than (f1 + f2), resulting in the following condition:Eq. (2) and assuming f1 > 0 and f2 > 0. To release the strong restriction of f2 expressed in Eq. (3), a flat mirror, M1, is inserted between L1 and the aperture stop as shown in Fig. 2(g). The total height represented by distance a becomes smaller than in Fig. 2(f).
We specifically designed optics of an imaging cell based on the structure of Fig. 2(g). Since the target resolution is 600 dots per inch (dpi) and the resolution of the image sensor we chose is 1200 dpi, the magnification ratio is 0.5. A space is necessary over the imaging cell for an illumination unit and a top glass on which manuscripts are put. Therefore, distance from the object plane to M1 (c as shown in Fig. 2(g)) must be large (c = 23 mm). If we suppose the system is double-sided telecentric with the magnification ratio of 0.5, f2 equals to 0.5f1. The aberration correction is the easiest when distance a satisfies the condition of a = 1.5f1 according to Eq. (2). However, distance c cannot be as long as 23 mm in this condition. Therefore, the condition of telecentricity in the image space is released, forming one-sided telecentric in the object space.
Figure 3 shows the optical layout designed with a commercially available optical design software to reduce aberrations. Figure 3(a) is a perspective view in which four imaging cells are aligned in zigzag alignment, and Fig. 3(b) is the cross-sectional view. The total height is 31 mm including the illumination unit and the base plate, and the width is 50 mm including image sensors. In compound eye optical systems, it is important that optical characteristics of each imaging cell are uniform within the FOV because we easily recognize image characteristics that are shown repeatedly in the combined total image. Therefore, we applied free-form surfaces to L1 and L2 mirrors to suppress aberrations like distortion and to uniform values of modulation transfer function (MTF) within the FOV.
Figure 4 shows the simulation result of some optical characteristics. In Fig. 4(a), MTF is plotted as the function of the object height in the X direction, where graph (1) and (2) are calculated at the spatial frequency of 6 line-pairs/mm (lp/mm) in the X and Y directions, respectively, and graph (3) and (4) are that of 12 lp/mm corresponding to Nyquist spatial frequency of 600 dpi. Every graph is almost horizontal, which shows that image quality is even within the FOV. Figure 4(b) shows the image distortion against the object height in the X direction, that is to say how distorted the straight line object along the X axis is in the image. The vertical axis is the value of 2Yimg, where Yimg is the Y coordinate value of the arrived point of the chief ray on the image plane and Yimg is multiplied by the coefficient two to translate in the object space value. The distortion value is 1 μm at most, showing that the distortion is negligible for the pixel size of 42 μm of 600 dpi. Figure 4(c) shows MTF at 6 lp/mm against the defocus amount in the object space, calculated at two object heights, h = 0 and 5 mm, in the X and Y directions. The four graphs almost overlap each other, showing that the image quality is uniform even at defocused positions.
The structure in Fig. 3 has several merits in terms of manufacturing and reducing the assembly variation. Figure 5 shows the prototype in the assembly process. Since L1 and L2 mirrors belonging to the same imaging cell are closely placed on the same plane, they can be integrated in one piece by plastic molding. The 32 integrated L1 and L2 mirrors are lined up on one reference plane of a base plate as shown in Fig. 5(a), making the attitudes and the positions of the mirrors uniform. In the previous models [11,12] based on the model of Fig. 2(d), L1 and L2 are separated components and are glued on a holder placed on a base plate. Therefore, the attitude errors of L1 and L2 relative to the base plate are larger than the new model because assembly error and manufacturing error of the holder are added.
Since the 32 flat M1 mirrors are placed on the same plane, one big plane can cover all of them. Such a mirror is fabricated by aluminum evaporation coated on a glass substrate, and the coating has a slit window in the center that opens passages from the object to the L1 mirrors as shown in Fig. 5(b). The integration of the 32 M1 mirrors makes the directions of the optical axes of the 32 imaging cells uniform. The slit window between the coatings prevents the intrusion of dust into the imaging system. In the previous models, each imaging cell has two flat mirrors that are glued on the holder. Therefore, attitude errors of the two flat mirrors vary largely, causing large variability of optical characteristics among imaging cells.
Aperture stops are made on holders, which are placed behind the coating of the M1 mirror in Fig. 5(b). The holders also have roles to hold the image sensor substrates and prevent stray light between the imaging cells. Four neighboring holders are combined as one piece made by plastic molding. The structure is simple with a low number of components.
Figure 5(c) shows the finished prototype of our new image scanner after an illumination unit was placed on the imaging cells. It is compact; its width and height are 50 and 31 mm, respectively.
4. Experimental result
Figure 6 shows our experimental setup where a test chart is placed on a moving stage shown on the left and the prototype of our image scanner is facing downward in the center. The stage moves back and forth to the right and the image scanner reads the test chart’s image, which is a sterically-bulky object of accessories on a piece of rough cloth. The image information taken by the 32 image sensors is sent to a personal computer and the images are combined. The monitor on the right in Fig. 6 displays the processed image. Figure 7 shows the part of it that indicates a clear image from the top of the accessory to the cloth under it. Figure 8(b) is an image of a step-like object, which shows the images from the depth of the reference to 4.0 mm. Figure 8(a) is the cross section, and five pieces of the character charts are pasted on top of each step surface. 6-point characters are clearly imaged at all the depths.
Figure 9 compares the measured data and the designed value of MTF at 7.1 lp/mm through Z, which is the floating distance from a reference plane to the object. The test chart’s pattern is a Ronchi ruling, where black lines and spaces are equally spaced at 7.1 lp/mm, equivalent to 358 dpi, in the two orthogonal directions of X and Y. The images were taken at different distances of Z and contrast C is calculated by Eq. (4):Fig. 9, where the numerical aperture in the object space is NA = 0.021, and the calculated MTF data are shown in solid lines. Our prototype’s DOF exceeds 4.0 mm when we define DOF as a range exceeding 30% of MTF at 7.1 lp/mm.
Figure 10 shows the image rotation errors in each imaging cell: (a) this study’s new model and (b) the previous model . The image of a line along the X direction is slightly rotated by the assembly errors, especially the attitude errors of the L1 and L2 mirrors. The line image becomes polygonal if there is a large variability of the image rotation among the imaging cells. The variability of graph (a) is smaller than graph (b) because L1 and L2 are integrated in one piece and all 32 integrated L1 and L2 mirrors are mounted on one base plane. The maximum difference of the rotation angle between the adjacent imaging cells is under 0.2°, which is negligible for visual use in a document copier.
Table 1 compares our previous model  and this study. Size of this study’s model in the cross section is smaller than the previous one. Though DOF is larger than the previous model, it is only a matter of design parameter. DOF can be arbitrarily enlarged by reducing the diameter of the aperture stop, which is a trade-off with the required illumination intensity.
The number of components for the 32 imaging cells in this study is 41, including the 32 integrated concave mirrors (L1 and L2), the 8 integrated holders covering the four imaging cells and the one flat mirror covering all imaging cells. The number in the previous model is 160, consisting of 64 concave mirrors, 32 holders, and 64 flat mirrors. Smaller number of components leads to less variability of rotation angle among the imaging cells. This rotation angle variability is under 0.2° in this study, which is lower than the previous model as stated in the above section.
We studied how to fold the ray path in reflective optics by a compound eye system. Our manufactured image scanner is compact and has a large 4-mm DOF, which is suitable for a flatbed scanner in a copier. This new scanner is more practical than our previous model and is easy to assemble with less variability of optical characteristics among imaging cells because all of its concave mirrors are mounted on one base plane. Although our scanner was developed for copier use, the above characteristics are useful for other scanner applications, such as product inspection in factories or automated teller machines.
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