Patent Publication Number: US-7718940-B2

Title: Compound-eye imaging apparatus

Description:
TECHNICAL FIELD 
     The present invention relates to a compound-eye imaging apparatus that captures an image with a plurality of imaging optical lenses arranged substantially in the same plane. 
     BACKGROUND ART 
     Imaging apparatuses used in mobile equipment need to have both a high resolution and a small size. In many cases, the reduction in size is obstructed by the size and focal length of an imaging optical lens and the size of an imaging device. 
     In general, since the refractive index of a material varies depending on the wavelength of light, it is difficult to form an image of light from a subject including information of an entire wavelength range on an imaging plane using a single lens. Therefore, in an optical system of usual imaging apparatuses, a plurality of lenses are arranged along an optical axis direction so that images of red wavelength light, green wavelength light and blue wavelength light are formed on the same imaging plane. Accordingly, the optical system is elongated, resulting in a thicker imaging apparatus. 
     Therefore, as a technique effective for a reduction in size of imaging apparatuses, particularly for a reduction in thickness, a compound-eye imaging apparatus has been proposed in which a plurality of single lenses having a short focal length are arranged substantially in the same plane (see JP 2002-204462 A, for example). A compound-eye color imaging apparatus includes an optical system having a lens for blue wavelength light, a lens for green wavelength light and a lens for red wavelength light that are arranged on the same plane, and imaging devices respectively corresponding to the lenses. Since the wavelength range of light handled by each lens is limited, it becomes possible to form a subject image on the imaging device using the single lenses. Therefore, the thickness of the imaging apparatus can be reduced considerably. 
       FIG. 15  is a perspective view showing an exemplary compound-eye imaging apparatus. Numeral  900  denotes a lens array including three lenses  901   a ,  901   b  and  901   c  that are formed integrally. The lens  901   a  is for red wavelength light and forms a subject image in an imaging region  902   a . A red wavelength separation filter (color filter) is attached to pixels (photodetector portions) in the imaging region  902   a , and the imaging region  902   a  converts the formed red subject image into image information. Similarly, the lens  901   b  is for green wavelength light and forms a subject image in an imaging region  902   b . A green wavelength separation filter (color filter) is attached to pixels (photodetector portions) in the imaging region  902   b , and the imaging region  902   b  converts the formed green subject image into image information. Further, the lens  901   c  is for blue wavelength light and forms a subject image in an imaging region  902   c . A blue wavelength separation filter (color filter) is attached to pixels (photodetector portions) in the imaging region  902   c , and the imaging region  902   c  converts the formed blue subject image into image information. The pieces of image information outputted from the imaging regions  902   a ,  902   b  and  902   c  are superposed and synthesized, thereby obtaining color image information. 
     Although the compound-eye imaging apparatus described above can achieve a reduced thickness, it has a problem of a poorer resolution compared with a usual single-eye imaging apparatus. In the single-eye imaging apparatus, an imaging device having a large number of pixels (photodetector portions) arranged in an image forming plane converts incident light into image information. In order to take out color information at each position, the pixels respectively are provided with wavelength separation filters (color filters) in a Bayer arrangement. In other words, the wavelength separation filters transmitting green light are arranged in a checkered pattern so as to correspond to the arrangement of the large number of pixels arranged in a matrix, and the wavelength separation filters transmitting red light and those transmitting blue light are arranged alternately in the rest of the pixels. Each of the pixels only outputs the color information corresponding to the wavelength range of the light that is transmitted by the wavelength separation filter provided in that pixel and does not output color information corresponding to the wavelength range of the light that is not transmitted thereby. However, since the pieces of color information of three colors are known to be correlated in a local region of an image (see Hiroaki KOTERA and two others, “Representation of Full Color Image from a Single Color Image Using Color Correlation” Proceedings of 1988 Annual Conference of The Institute of Image Electronics Engineers of Japan 20, pp. 83-86 (1988), for example), the green color information can be estimated from the red or blue color information. Utilizing such characteristics, the missing color information is interpolated in the imaging device with the wavelength separation filters in the Bayer arrangement. Accordingly, it is possible to obtain a color image having a resolution corresponding to pixels as many as the total number of pixels. For example, in an imaging device with 1,000,000 pixels, 500,000 pixels detect green color information, 250,000 pixels detect blue color information, and 250,000 pixels detect red color information. However, by the above-described interpolation, it is possible to obtain color information having a resolution corresponding to 1,000,000 pixels for each of red, green and blue. 
     On the other hand, in the compound-eye imaging apparatus, since each of the imaging regions corresponding to the respective colors acquires any of red, green and blue color information, a color image corresponding to pixels as many as the pixels in that imaging region is achieved. For example, in the case where red color information, green color information and blue color information are acquired by three imaging regions each with 250,000 pixels, 750,000 pixels in total are needed, but the resolution of a color image obtained by superposition corresponds to 250,000 pixels. 
     As a method for improving the image resolution, there is a known technology called “pixel shifting” in which plural pieces of image information whose positional relationships between a subject image and pixels are shifted from each other are acquired by shifting the relative positional relationship between an optical system and an imaging device time-wise or by separating a light beam into plural beams using a prism and making them to enter plural imaging devices and then synthesized so as to achieve a high-resolution image (see JP 10(1998)-304235 A, for example). In this case, the optimal amount of shifting is determined by the direction of shifting and the number of pieces of image information to be acquired. For example, in the case of synthesizing two pieces of image information, when the relative positional relationship between the subject image and the pixels is shifted by an odd multiple of one-half the arrangement pitch of the pixels (in the following, referred to as the “pixel pitch”) between the two pieces of image information, it is possible to obtain the highest resolution image. This technology is applicable as long as it is possible to acquire plural pieces of image information whose relative positional relationships between the subject image formed by the lens and the pixels of the imaging device are shifted from each other, regardless of the method of shifting. In the present invention, the relative positional relationship between the subject image and the pixels of the imaging device that makes it possible to acquire the plural pieces of image information whose relative positional relationships between the subject image and the pixels of the imaging device are shifted from each other and to synthesize these plural pieces of image information so as to obtain a high-resolution image is referred to as a “shifted pixel arrangement.” 
     In the compound-eye imaging apparatus, a high-resolution image also can be obtained as long as the relative positional relationships between the subject image and the pixels are shifted between plural pieces of image information, in other words, the shifted pixel arrangement can be achieved. 
     For example, JP 2002-209226 A mentions that, in a compound-eye imaging apparatus using a plurality of lenses to form a plurality of subject images on a plurality of imaging regions, a high-resolution image is obtained by arranging the plurality of lenses and a plurality of imaging devices so that the individual subject images are formed so as to be shifted in a direction connecting optical axes of the lenses, thus achieving the shifted pixel arrangement. 
     Also, in the compound-eye imaging apparatus, it is possible to determine the distance to a subject using a parallax generated due to the difference between the optical axes of the plurality of lenses. 
     DISCLOSURE OF INVENTION 
     Problem to be Solved by the Invention 
     However, in order to obtain a high-resolution image by the pixel shifting technology, the relative positional relationship between the subject image and the pixels always has to be the shifted pixel arrangement.  FIG. 16A  is a side view showing the positional relationship between a plurality of lenses, a subject and subject images in a compound-eye imaging apparatus, and  FIG. 16B  is a plan view thereof.  FIG. 16A  shows the state as viewed along a direction perpendicular to a plane including the optical axes of the plurality of lenses, and  FIG. 16B  shows the state viewed along a direction parallel with the optical axes of the lenses. Numerals  200   a  and  200   b  denote the optical axes of lenses  201   a  and  201   b , and numeral  202   a  and  202   b  denote positions at which the optical axes cross an imaging region  203 . An image of a subject  204  located on the optical axis  200   a  is formed as subject images  205   a  and  205   b  by the lenses  201   a  and  201   b . In the compound-eye imaging apparatus, since the optical axes  200   a  and  200   b  of the lenses  201   a  and  201   b  are different, when the distances from the lenses  201   a  and  201   b  to the subject  204  vary, the position of the subject image  205   b  moves in the imaging region  203  along a straight line  206  connecting intersection points  202   a  and  202   b . This phenomenon is called “parallax.” When A indicates a subject distance (the distance from the lens  201   a  to the subject  204 ), d indicates the distance between the optical axes  200   a  and  200   b  and f indicates an imaging distance, an amount S that the subject image  205   b  is shifted from the intersection point  202   b  is expressed by the following formula. 
     
       
         
           
             
               
                 
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                       f 
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                       d 
                     
                     A 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
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                     1 
                   
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     In this way, the relative positional relationship between the subject image  205   b  and the pixels in the direction of the straight line  206  varies according to the subject distance A. Thus, when the shifting amount S of the subject image in the direction of the straight line  206  is set to a predetermined relationship with respect to the pixel pitch, the resolution varies depending on the subject distance A, causing a problem that it is not always possible to obtain a high-resolution image. 
     It is an object of the present invention to provide a compound-eye imaging apparatus that can always obtain a high-resolution image regardless of the subject distance. 
     Means for Solving Problem 
     A compound-eye imaging apparatus according to the present invention includes a plurality of imaging optical lenses arranged in substantially the same plane, and a plurality of imaging regions for converting into a plurality of pieces of image information a plurality of subject images that are formed respectively by the plurality of imaging optical lenses. Each of the plurality of imaging regions includes a large number of pixels that are arranged in a plane perpendicular to respective optical axes of the plurality of imaging optical lenses. 
     Then, when viewed along a direction parallel with the optical axes, at least one straight line connecting corresponding points in at least one pair of the subject images that are formed by at least one pair of the imaging optical lenses is inclined with respect to a direction in which the pixels are arranged. 
     Effects of the Invention 
     In accordance with the present invention, the shifted pixel arrangement can be achieved in a direction perpendicular to a direction in which the pixels are arranged. The subject distance has substantially no influence on the relationship of this shifted pixel arrangement. Therefore, it always is possible to obtain a high-resolution image regardless of the subject distance. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a perspective view showing a schematic configuration of a compound-eye imaging apparatus according to Embodiment 1 of the present invention. 
         FIG. 2  is a plan view showing a positional relationship between optical axes of lenses and pixels in imaging regions in the imaging apparatus according to Embodiment 1 of the present invention. 
         FIG. 3  is a plan view for describing image information synthesis in the imaging apparatus according to Embodiment 1 of the present invention. 
         FIG. 4  is a plan view showing the image information synthesis when an image of a distant subject is captured. 
         FIG. 5  is a plan view showing the image information synthesis when an image of a near subject is captured. 
         FIG. 6A  is a plan view showing an imaging apparatus according to Example 1 of the present invention. 
         FIG. 6B  is a sectional view thereof taken along a line  6 B- 6 B in  FIG. 6A . 
         FIG. 7A  is a plan view showing an arrangement of the lenses in the imaging apparatus according to Embodiment 1 of the present invention. 
         FIG. 7B  is a plan view showing an arrangement of lenses in an imaging apparatus according to Embodiment 2 of the present invention. 
         FIG. 8A  is a plan view showing an imaging apparatus according to Example 2 of the present invention. 
         FIG. 8B  is a sectional view thereof taken along a line  8 B- 8 B in  FIG. 8A . 
         FIG. 9A  is a plan view showing an arrangement of lenses constituting a lens array in the imaging apparatus according to Example 2 of the present invention. 
         FIG. 9B  is a plan view showing the arrangement of the lenses when the lens array has been rotated from the state shown in  FIG. 9A  in the imaging apparatus according to Example 2 of the present invention. 
         FIG. 10A  is a plan view showing an imaging apparatus according to Example 3 of the present invention. 
         FIG. 10B  is a sectional view thereof taken along a line  10 B- 10 B in  FIG. 10A . 
         FIG. 11A  is a plan view showing an imaging apparatus according to Example 4 of the present invention. 
         FIG. 11B  is a sectional view thereof taken along a line  11 B- 11 B in  FIG. 11A . 
         FIG. 12A  is a plan view showing an arrangement of a color filter provided on one imaging region in the imaging apparatus according to Example 4 of the present invention. 
         FIG. 12B  is a plan view showing an arrangement of a color filter provided on the other imaging region in the imaging apparatus according to Example 4 of the present invention. 
         FIG. 13A  is a plan view showing another arrangement of the color filters provided on one imaging region in the imaging apparatus according to Example 4 of the present invention. 
         FIG. 13B  is a plan view showing another arrangement of the color filters provided on the other imaging region in the imaging apparatus according to Example 4 of the present invention. 
         FIG. 14A  is a plan view showing yet another arrangement of the color filters provided on one imaging region in the imaging apparatus according to Example 4 of the present invention. 
         FIG. 14B  is a plan view showing yet another arrangement of the color filters provided on the other imaging region in the imaging apparatus according to Example 4 of the present invention. 
         FIG. 15  is a perspective view showing a schematic configuration of an example of a conventional compound-eye imaging apparatus. 
         FIG. 16A  is a side view showing a positional relationship among a plurality of lenses, a subject and subject images in a compound-eye imaging apparatus. 
         FIG. 16B  is a plan view showing a positional relationship between optical axes of the plurality of lenses and the subject images in the compound-eye imaging apparatus. 
     
    
    
     DESCRIPTION OF THE INVENTION 
     In the present invention, the “direction in which the pixels are arranged” is determined as follows. A plurality of parallel first straight lines and a plurality of parallel second straight lines that are included in a plane in which a large number of pixels are arranged are assumed. The inclination of the plurality of first straight lines and that of the plurality of second straight lines are set so that the large number of pixels all are arranged at a plurality of intersection points at which these plurality of first straight lines and these plurality of second straight lines cross. Each of a first direction and a second direction that are respectively parallel with the plurality of first straight lines and the plurality of second straight lines set as above is referred to as the “direction in which the pixels are arranged.” 
     Further, in the present invention, the “direction in which the pixels are arranged,” on which attention is focused when considering the relationship with the straight line connecting a pair of optical axes of a pair of the imaging optical lenses, refers to a direction that forms a smaller angle (smaller than 90°) with the straight line connecting the pair of optical axes among the first direction and the second direction described above. 
     Moreover, in the present invention, the straight line being “inclined” with respect to the direction in which the pixels are arranged means that the straight line and the direction in which the pixels are arranged are not parallel with each other but cross at an angle other than 90°. 
     In the present invention, since a pair of the subject images that are formed by a pair of the imaging optical lenses are formed in the relationship of the shifted pixel arrangement in a direction perpendicular to the direction in which the pixels are arranged, the shifted pixel arrangement always can be achieved regardless of the distance to the subject. In other words, when viewed along the direction parallel with the optical axes of the lenses, by adjusting the angle θ that the straight line connecting the pair of optical axes of the pair of imaging optical lenses forms with the direction in which the pixels are arranged, the shifted pixel arrangement is achieved in a direction (in the following, referred to as a “pixel shifting direction”) at right angles with the direction, in which the pixels are arranged, forming the angle θ with this straight line connecting the pair of optical axes. 
     In the case where the plurality of pieces of image information obtained from the plurality of imaging regions are synthesized, an image with the highest resolution is obtained when
 
(2 n− 1)× p/ 2= d ×sin θ
 
is satisfied, where d indicates the distance between optical axes of a pair of imaging optical lenses, p indicates an arrangement pitch of the pixels along a direction perpendicular to the direction in which the pixels are arranged and n indicates a positive integer.
 
     In practice, due to manufacturing variations, it is difficult to manufacture an imaging apparatus that satisfies this equation completely. When this equation is satisfied substantially, the effect of pixel shifting is achieved. In other words, when the inequality
 
(2 n− 1)× p/ 2 −p/ 4 &lt;d ×sin θ&lt;(2 n− 1)× p/ 2 +p/ 4
 
is satisfied, it is possible to obtain a high-resolution image by pixel shifting.
 
     Also, even with manufacturing variations, the shifted pixel arrangement can be achieved easily and reliably by adjusting the angle θ. Thus, the manufacturing is easy, leading to improved yield at the time of mass production. 
     In the present invention, by focusing attention on the fact that the parallax component in the pixel shifting direction is extremely small, the effect of pixel shifting is achieved regardless of the subject distance. However, it is difficult to bring the parallax component in the pixel shifting direction to zero. As described above, the parallax increases sharply as the subject distance decreases. Also, the parallax component in the pixel shifting direction increases in keeping with the angle θ (namely, n). Thus, it is preferable that n satisfies
 
 n&lt;A min/(4× f ).
 
     Here, Amin indicates a distance to the nearest subject whose image is to be captured (the minimum value of the subject distance A), and f indicates an imaging distance. When n satisfies the above-noted relationship, the angle θ is extremely small, so that a direction along which the subject image moves according to the variation in the subject distance (in other words, a direction of the straight line connecting the pair of optical axes) and the direction in which the pixels are arranged can be considered as substantially the same. Then, it becomes possible substantially to ignore the parallax component in the pixel shifting direction. Thus, the shifted pixel arrangement in the pixel shifting direction always can be achieved regardless of the subject distance. 
     Since the refractive index of a lens material and the efficiency of a diffraction grating depend on wavelengths, the lens characteristics improve by limiting the wavelengths. Accordingly, in the present invention, it is preferable that a filter transmitting light at a predetermined wavelength is provided on each optical path of the plurality of imaging optical lenses. This limits the wavelengths of the subject images to be formed on the imaging regions, thereby achieving clear images. The pre-synthesis images subjected to the pixel shifting are clear, so that a synthesized high-resolution image also becomes clear. 
     Further, filters transmitting light in the same wavelength range may be provided on individual optical paths of the plurality of imaging optical lenses. Thus, using a plurality of clear images in the same wavelength range, the subject distance can be determined by the parallax. As described above, the parallax caused by the difference in subject distance occurs in the direction of the straight line connecting the optical axes of the pair of lenses. In response to this, in the present invention, the shifted pixel arrangement is set in the direction perpendicular to the straight line connecting the optical axes of the pair of lenses. In this way, since the direction in which the parallax occurs and the direction of the shifted pixel arrangement are different in the present invention, variations in the subject distance (namely, the parallax) have substantially no influence on the shifted pixel arrangement. Thus, the accuracy of determining the subject distance does not vary substantially regardless of the subject distance, thus making it possible both to determine the subject distance and to raise the image resolution. 
     In order to achieve the shifted pixel arrangement in the present invention, the amount of pixel shifting, namely, the value of “d×sin θ” has to be set appropriately. For this purpose, it is appropriate to make fine adjustment to the angle θ while maintaining the distance d between the optical axes to be constant. Thus, it is preferable that the plurality of imaging optical lenses is an integrally-formed lens array. In this way, by making an adjustment so as to rotate slightly the entire lens array with respect to the plurality of imaging regions within a plane parallel with photodetector surfaces of the plurality of imaging regions instead of adjusting individual lenses, it is possible to achieve the shifted pixel arrangement in the present invention. Thus, the shifted pixel arrangement can be achieved easily without the need for assembling or forming a lens array at a high accuracy. 
     It is preferable that the imaging apparatus according to the present invention further includes a mechanism of rotating the plurality of imaging optical lenses and the plurality of imaging regions relative to each other in the plane perpendicular to the optical axes of the plurality of imaging optical lenses. 
     By providing such a rotating mechanism, it becomes possible to adjust the pixel shifting amount, namely, the angle θ easily and accurately in a manufacturing process. Incidentally, the adjustment of the angle θ is carried out in the manufacturing process, and the rotating mechanism already is fixed in a final product. 
     It is preferable that the imaging apparatus according to the present invention further includes a mechanism of adjusting a distance between the plurality of imaging optical lenses and the plurality of imaging regions. 
     This makes it possible to arrange the imaging regions reliably in imaging planes of the respective lenses, thereby achieving a plurality of pieces of clearer image information. Accordingly, by synthesizing these plurality of pieces of image information, a higher-resolution image can be obtained. 
     In the imaging apparatus according to the present invention, it is preferable that the number of the imaging optical lenses is at least three. In this case, it is preferable that, when viewed along the direction parallel with the optical axes, a first straight line and a second straight line respectively connecting the optical axes of two pairs of the imaging optical lenses form substantially a right angle and that
 
(2 n− 1)× p 1/2 −p 1/4 &lt;d 1×sin θ1&lt;(2 n− 1)× p 1/2 +p 1/4 and
 
(2 m− 1)× p 2/2 −p 2/4 &lt;d 2×sin θ2&lt;(2 m− 1)× p 2/2+ p 2/4
 
are satisfied, where, when viewed along the direction parallel with the optical axes, θ1 indicates an angle that the first straight line forms with a first arrangement direction of the pixels, θ2 indicates an angle that the second straight line forms with a second arrangement direction of the pixels, d1 indicates a distance between the optical axes of a pair of the imaging optical lenses arranged along the first straight line, d2 indicates a distance between the optical axes of a pair of the imaging optical lenses arranged along the second straight line, p1 indicates an arrangement pitch of the pixels along a direction perpendicular to the first arrangement direction, p2 indicates an arrangement pitch of the pixels along a direction perpendicular to the second arrangement direction, and m and n indicate positive integers.
 
     Here, in the case where the pixels are arranged along two directions, a direction that forms a smaller angle (smaller than 90°) with the first straight line among the two arrangement directions is defined as the “first arrangement direction,” and a direction that forms a smaller angle (smaller than 90°) with the second straight line is defined as the “second arrangement direction.” 
     In this way, the shifted pixel arrangement can be achieved in a plurality of directions, thereby improving the resolution in these plurality of directions. Also, since at least three lenses are provided, pieces of image information of red, green and blue are obtained through the respective lenses and synthesized, thereby obtaining a color image. In the above description, the arrangement pitches p1 and p2 of the pixels may be the same, which achieves a similar effect. 
     In the above description, it is preferable that the distance d1 between the optical axes and the distance d2 between the optical axes are different. 
     In order to improve the resolution in a plurality of directions, the amounts of pixel shifting in the respective directions, namely, d1×sin θ1 and d2×sin θ2 need to be adjusted. However, when using a lens array in which a plurality of lenses are integrally-formed, it is not possible to adjust the positions of the individual lenses independently. Also, the positions of the lenses might include forming errors. If d1≠d2, the amount of pixel shifting in the respective directions when the lens array is rotated with respect to the imaging regions is adjusted in a wider range. Consequently, even when the lens array involves forming errors, it is possible to optimize the amount of pixel shifting in a plurality of directions, thus improving the resolution in the plurality of directions. 
     Alternatively, the arrangement pitch p1 and the arrangement pitch p2 may be different. In this case, even when the lens array involves forming errors, it also is possible to optimize the amount of pixel shifting in a plurality of directions, thus improving the resolution in the plurality of directions. 
     In the imaging apparatus according to the present invention, it is preferable that the number of the imaging optical lenses is four and the number of the imaging regions is four. In this case, when viewed along the direction parallel with the optical axes, optical axes of the four imaging optical lenses preferably are arranged at vertices of a substantial rectangle. Also, it is preferable that a filter transmitting light in a blue wavelength range is provided on an optical path of light entering one of the four imaging regions, a filter transmitting light in a red wavelength range is provided on an optical path of light entering one of the remaining three imaging regions, and a filter transmitting light in a green wavelength range is provided on an optical path of light entering the remaining two imaging regions. 
     This makes it possible to calculate a parallax amount using the two pieces of green image information containing much brightness information. By calculating the parallax amount using light in the same wavelength range, the accuracy of the parallax amount improves. Using this parallax amount, parallax amounts of red image information and blue image information can be calculated, respectively. Thus, it is possible to obtain a color image whose resolution is raised in the two directions. Also, the subject distance may be calculated using this parallax amount. In that case, the accuracy of the subject distance improves. 
     It is preferable that the four imaging regions are formed on a common single imaging device, and the substantial rectangle and a shape of an effective pixel region of the imaging device are substantially similar. This makes it possible to utilize the pixels in the imaging device effectively without any waste. 
     The following is a detailed description of embodiments of the present invention, with reference to the accompanying drawings. 
     Embodiment 1 
     A compound-eye imaging apparatus according to the present embodiment improves vertical and horizontal spatial sampling characteristics compared with a conventional compound-eye imaging apparatus. 
       FIG. 1  is a perspective view showing an example of the compound-eye imaging apparatus according to Embodiment 1. Numeral  300  denotes a lens array formed of a transparent resin and including three lenses  301   a ,  301   b  and  301   c  that are integrally-formed. Optical axes  300   a ,  300   b  and  300   c  of the three lenses  301   a ,  301   b  and  301   c  are parallel with each other. The three lenses  301   a ,  301   b  and  301   c  are arranged in substantially the same plane so that, when viewed along a direction parallel with these optical axes, a first straight line  211  connecting the optical axes  300   a  and  300   b  and a second straight line  212  connecting the optical axes  300   b  and  300   c  form a right angle. The lenses  301   a ,  301   b  and  301   c  form subject images on imaging regions  302   a ,  302   b  and  302   c , respectively. The imaging regions  302   a ,  302   b  and  302   c  respectively have a large number of pixels (photodetector portions) arranged in a plane orthogonal to the optical axes  300   a ,  300   b  and  300   c , and each of the pixels converts incident light into electric signals. In this way, the imaging regions  302   a ,  302   b  and  302   c  convert the subject images respectively formed thereon into pieces of image information and output them. The imaging regions  302   a ,  302   b  and  302   c  are formed by dividing an effective pixel region of a common single imaging device. Thus, the pieces of image information from the imaging regions  302   a ,  302   b  and  302   c  are obtained by extracting pixel signals corresponding to the respective imaging regions from the signals outputted from this single imaging device. 
     In order to achieve a high-resolution image, the three lenses  301   a ,  301   b  and  301   c  and the imaging regions  302   a ,  302   b  and  302   c  are arranged so that a shifted pixel arrangement in a direction perpendicular to each of directions in which the pixels are arranged is achieved between the subject images formed respectively by the lenses  301   a ,  301   b  and  301   c  and the pixels in the imaging regions  302   a ,  302   b  and  302   c . This will be described in the following. 
       FIG. 2  is a plan view showing the positional relationship between the optical axes of the lenses and the pixels in the imaging regions, taken along a direction parallel with the optical axes. 
     Numerals  100   a ,  100   b  and  100   c  denote pixels arranged in the imaging regions  302   a ,  302   b  and  302   c . Since the imaging regions  302   a ,  302   b  and  302   c  are formed by dividing the effective pixel region of the single imaging device as described above, an arrangement direction and a pixel pitch of the pixels  100   a ,  100   b  and  100   c  in the respective imaging regions  302   a ,  302   b  and  302   c  are the same among the imaging regions  302   a ,  302   b  and  302   c . In  FIG. 2 , pixels outside the imaging regions  302   a ,  302   b  and  302   c  are omitted. As shown in the figure, the pixels  100   a ,  100   b  and  100   c  are arranged in a matrix along vertical and horizontal directions. A direction parallel with the vertical arrangement direction (a first arrangement direction) is given by a Y axis, and a direction parallel with the horizontal arrangement direction (a second arrangement direction) is given by an X axis. Then, a direction parallel with the optical axes  300   a ,  300   b  and  300   c  is given by a Z axis. The X axis, the Y axis and the Z axis cross at right angles to each other. 
     Numeral  101   a ,  101   b  and  101   c  denote intersection points of the optical axes  300   a ,  300   b  and  300   c  of the lenses  301   a ,  301   b  and  301   c  and the imaging regions  302   a ,  302   b  and  302   c , respectively. 
     The angle that the first straight line  211  connecting the intersection points  101   b  and  101   a  forms with the first arrangement direction of the pixels (the Y axis) is given by θ(θ≦90°). Assuming that the three lenses  301   a ,  301   b  and  301   c  are integrally-formed in the lens array  300  without any errors, the angle that the second straight line  212  connecting the intersection points  101   b  and  101   c  forms with the second arrangement direction of the pixels (the X axis) also is θ. 
     When d indicates the distance between the intersection points  101   b  and  101   a  (namely, the distance between the optical axes  300   b  and  300   a ), the intersection point  101   a  is shifted from the intersection point  101   b  by d×sin θ in the X-axis direction. If this amount of shifting is an odd multiple of one-half a pixel pitch p1 in the X-axis direction of the imaging device, the image information converted by the imaging region  302   a  serves as information of portions  102   b  between the pixels in the X-axis direction of the image information converted by the imaging region  302   b.    
     Numerals  103   a ,  103   b  and  103   c  denote subject images of a subject located on the optical axis  300   b  that are formed by the lenses  301   a ,  301   b  and  301   c . The positions of the subject images  103   a ,  103   b  and  103   c  vary according to the positions of the optical axes  300   a ,  300   b  and  300   c  of the lenses and the subject distance (the subject distance A in  FIG. 16A ). Thus, due to parallax, the subject image  103   a  formed by the lens  301   a  is formed at a position shifted from the intersection point  101   a  to a side away from the intersection point  101   b  along the direction of the first straight line  211  connecting the intersection points  101   b  and  101   a . Since the first straight line  211  is not parallel with the Y axis, the position at which the subject image  103   a  is formed varies in the X-axis direction and the Y-axis direction according to the subject distance. In the present embodiment, the distance d between the optical axes is sufficiently larger than the pixel pitches p1 and p2 along the X-axis direction and the Y-axis direction. Therefore, as long as the angle θ is sufficiently small, the amount that the variation in the subject distance causes the position at which the subject image  103   a  is formed to vary along the X-axis direction is so small that it can be ignored. Accordingly, by utilizing the shifting of the subject image  103   a  with respect to the subject image  103   b  along the X-axis direction, it always is possible to achieve the shifted pixel arrangement in the X-axis direction regardless of the subject distance, thereby achieving a higher resolution in the X-axis direction. 
     Furthermore, in order to achieve the shifted pixel arrangement also in the Y-axis direction, it is appropriate that d2=(p1/p2)×d be satisfied, where p2 indicates a pixel pitch in the Y-axis direction and d2 indicates the distance between the intersection points  101   b  and  101   c  (namely, the distance between the optical axes  300   b  and  300   c ). This allows the relationship similar to that in the above-described shifted pixel arrangement in the X-axis direction between the imaging regions  302   b  and  302   a  to be established in the Y-axis direction between the imaging regions  302   b  and  302   c . Thus, a higher resolution can be achieved in the X-axis direction and the Y-axis direction regardless of the subject distance. 
     Although  FIG. 2  has illustrated an example in which the lens array  300  is rotated clockwise by the angle θ with respect to the imaging device around the optical axis  300   b , this is intended to facilitate understanding. The present invention is not limited to this. What is important is to set the angle θ so that the above-described shifted pixel arrangement is achieved in the X-axis direction and the Y-axis direction. The position of an axis of rotation and the relative rotational direction may be different from the above. 
     Variations in the temperature of an image capturing environment cause the lens array  300  to expand (or contract) thermally. When the temperature rises from room temperature, the lens array  300  expands substantially isotropically, so that the distances d and d2 between the optical axes  300   a ,  300   b  and  300   c  of the lenses increase. However, since the above-described angle θ remains unchanged and is sufficiently small, the relationship of the shifted pixel arrangement described above is maintained. Thus, the shifted pixel arrangement in the imaging apparatus according to the present invention is impervious to the variations in the distances d and d2 between the optical axes of the lenses caused by the temperature variation of the surrounding environment. 
     The imaging regions  302   a ,  302   b  and  302   c  convert the subject images respectively formed therein into pieces of image information. After the resultant three pieces of image information are subjected to parallax correction, they are synthesized so as to obtain a single piece of image information. This computation processing will be described in the following. 
     First, a parallax amount deriving means  303  calculates a parallax amount between the pieces of image information (the shifting amount S in  FIG. 16A ) for the parallax correction. 
     The parallax amount can be calculated if the subject distance is known. However, the introduction of a new sensor for measuring the subject distance makes it difficult to reduce the size of the apparatus. Accordingly, in the present embodiment, two pieces of image information are compared directly, and the shifting amount between them is determined, thereby obtaining the parallax amount. The pieces of image information are compared by calculating the correlation between them. The image information is expressed as a group of pieces of brightness information distributed in a matrix along the X-axis direction and the Y-axis direction, and the brightness of a pixel, which is the k-th pixel in the X-axis direction and the l-th pixel in the Y-axis direction, is given by I(k, l). Since the pixels are finite, k and l are integers. Assuming the brightness of a pixel in one piece of the image information to be referred to (in the following, referred to as the “reference image information”) of the two pieces of image information that are to be compared as I1(k, l) and the brightness of a pixel in the piece of the image information to be compared (in the following, referred to as the “compared image information”) as I2(k+m, l+n), the correlation R(m, n) between the reference image information and a piece of image information obtained by shifting the compared image information by m pixels along the X-axis direction and n pixels along the Y-axis direction is calculated by the formula below. 
     
       
         
           
             
               
                 
                   
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     When the reference image information and the piece of image information obtained by shifting the compared image information by m pixels along the X-axis direction and n pixels along the Y-axis direction are similar, the correlation R(m, n) becomes close to 1. Conversely, when they are different, the correlation R(m, n) becomes small. While changing m and n sequentially, R(m, n) is calculated. When R(m, n) becomes closest to 1, m and n indicate the parallax amount (shifting amount) between the reference image information and the compared image information. It should be noted that m and n are not limited to integers. For example, in the reference image information and the compared image information, if the brightness at a position between pixels is calculated by interpolation based on the brightnesses of the surrounding pixels, the parallax amount at the decimal level can be calculated with a high resolving power. As the interpolation method of the pixels, known various methods such as bi-linear interpolation, bi-cubic interpolation and cubic convolution interpolation can be employed. For example, in the case of employing the bi-linear interpolation, the brightness I(u, v) at a position where X=u and Y=v between the pixels can be calculated by the formula below. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     Next, an image synthesizing means  304  synthesizes the two pieces of image information. Prior to the synthesis, one piece of image information is moved by the parallax amount obtained above in the X-axis direction and the Y-axis direction between the two pieces of image information (parallax correction). 
       FIG. 3  is a plan view showing the imaging regions  302   b  and  302   a  and the subject images  103   b  and  103   a  formed therein in a state achieved by moving the imaging regions  302   b  and  302   a  in the X-axis direction so that the intersection points  101   b  and  101   a  are aligned in a single straight line parallel with the Y axis. 
     As described in  FIGS. 16A and 16B , the shifting amount S of the subject image due to parallax is inversely proportional to the subject distance A, and it can be ignored if the subject distance A is sufficiently large. In this case, as shown in  FIG. 3 , an image of the subject on the optical axis  300   b  is formed as the subject image  103   b  on the imaging region  302   b  and formed at a position indicated by a solid line  400  on the imaging region  302   a . In other words, the relative positional relationship of the subject image  103   b  with respect to the intersection point  101   b  in the imaging region  302   b  and that of the position  400  at which the subject image is formed with respect to the intersection point  101   a  in the imaging region  302   a  are substantially the same. In this case, as shown in  FIG. 4 , the image information obtained from the imaging region  302   b  and that obtained from the imaging region  302   a  are superposed so that the intersection points  101   b  and  101   a  match. This allows the subject image  103   b  on the imaging region  302   b  and the subject image  103   a  on the imaging region  302   a  to be superposed with substantially no displacement. At this time, the pixels  100   b  in the imaging region  302   b  and the pixels  100   a  in the imaging region  302   a  are shifted from each other by an odd multiple of one-half the pixel pitch p1 along the X-axis direction. Thus, the resolution of the synthesized image in the X-axis direction improves. 
     When the subject distance is small, as shown in  FIG. 3 , an image of the subject on the optical axis  300   b  is formed as the subject image  103   b  on the imaging region  302   b  and formed at a position indicated by a broken line  402  on the imaging region  302   a . In other words, the relative positional relationship of the subject image  103   b  with respect to the intersection point  101   b  in the imaging region  302   b  and that of the position  402  at which the subject image is formed with respect to the intersection point  101   a  in the imaging region  302   a  are different. As described with reference to  FIG. 2 , the subject image  103   a  is formed at a position shifted from the intersection point  101   a  to a side away from the intersection point  101   b  along the direction of the first straight line  211  connecting the intersection points  101   b  and  101   a . Here, the shifting of the position  402  at which the subject image  103   a  is formed when the subject distance is small from the position  400  at which the subject image  103   a  is formed when the subject distance is large (the parallax) is expressed by a vector  405 . In this case, as shown in  FIG. 5 , the intersection point  101   a  is moved relative to the intersection point  101   b  by an inverse vector  406  of this vector  405 , thereby superposing the image information obtained from the imaging region  302   b  and that obtained from the imaging region  302   a . This allows the subject image  103   b  on the imaging region  302   b  and the subject image  103   a  on the imaging region  302   a  to be superposed with substantially no displacement. At this time, the pixels  100   b  in the imaging region  302   b  and the pixels  100   a  in the imaging region  302   a  also are shifted from each other by an odd multiple of one-half the pixel pitch p1 along the X-axis direction. Thus, the resolution of the synthesized image in the X-axis direction improves. 
     As described above, by performing the synthesis after the parallax correction, it is possible to obtain an image with improved resolution in the X-axis direction regardless of the subject distance. Incidentally, the pixel positions in the Y-axis direction sometimes might not match depending on the parallax amount. In such cases, the pixel positions can be corrected to an appropriate position by interpolation such as linear interpolation. 
     The parallax correction and the synthesis similar to the above are conducted on the image information obtained from the imaging region  302   b  and that obtained from the imaging region  302   c . This makes it possible to obtain an image with improved resolution in the Y-axis direction regardless of the subject distance. 
     As described above, by synthesizing the image information obtained from the imaging region  302   b  with the image information obtained from the imaging region  302   a  and the image information obtained from the imaging region  302   c , an image whose resolution is raised in the X-axis direction and the Y-axis direction can be obtained. 
     In the present invention, the pixel pitch p1 in the X-axis direction and the pixel pitch p2 in the Y-axis direction may be the same or different. For example, it is possible to combine a plurality of imaging devices to form a single imaging region or to use separate imaging devices for individual imaging regions. In any case, it is possible to obtain a high-resolution image regardless of the subject distance by performing the pixel shifting in the direction perpendicular to the direction in which the pixels are arranged and further to adjust the amount of pixel shifting by relative rotation between the plurality of imaging regions and the lens array. 
     Example 1 
     The following is a description of an example corresponding to Embodiment 1. 
       FIG. 6A  is a plan view showing an imaging apparatus according to Example 1 viewed along a direction parallel with optical axes, and  FIG. 6B  is a sectional view thereof taken along a line  6 B- 6 B in  FIG. 6A . Numeral  700  denotes a lens array having three lenses that are integrally-formed using an acrylic resin. As shown in  FIG. 6A , the three lenses were arranged so that their optical axes were located at three vertices of a square whose one side d was 2 mm long. All of the lenses were designed so that their optical characteristics were optimal with respect to green wavelength light. In the Z-axis direction, the distance from the lens center to the image forming plane was 2.5 mm. The lens array  700  was held by a cylindrical barrel  701 . A surface of the barrel  701  facing the subject was provided with three apertures  702  corresponding to the positions of the lenses. A portion of a base  703  to be fitted with the barrel  701  was provided with a circular recess (a groove). The barrel  701  was rotated along this recess around a center axis of the barrel  701  relative to the base  703 , thereby making an adjustment so that the above-described shifted pixel arrangement was achieved between the subject images respectively formed by the three lenses and the pixels in an imaging device  704 . 
     The imaging device  704  was fixed onto the base  703 . The imaging device  704  was a 2,000-pixel (in the X-axis direction)×2,000-pixel (in the Y-axis direction) CCD whose pixel pitches p1 and p2 in the X-axis direction and the Y-axis direction were both 2 μm. In an effective pixel region of this imaging device  704 , three 800-pixel (in the X-axis direction)×600-pixel (in the Y-axis direction) regions in which the three lenses respectively form subject images were used as imaging regions. Since the distance between the optical axes of the lenses was 2 mm and the pixel pitches p1 and p2 were 2 μm, the angle θ that the straight line connecting the optical axes of a pair of the lenses forms with the direction in which the pixels are arranged when viewed along a direction parallel with the optical axes (see  FIG. 2 ) was set to 5×10 −4  rad. In this way, it was possible to achieve the shifted pixel arrangement between all of the three subject images respectively formed by the three lenses and all of the pixels in the three imaging regions corresponding to these subject images. 
     In order to take out green image information alone, a color filter  705  transmitting light in a green wavelength range was provided on the subject-side surface of the imaging device  704 . A spacer  706  was interposed between the barrel  701  and the base  703 , thus achieving accurate positioning between the image forming planes of the lenses and a photodetector surface of the imaging device  704 . 
     Using the imaging apparatus produced as above, the limiting resolution was evaluated with a resolution chart placed at a subject distance of 1 m. The limiting resolution of a 800-pixel (in the X-axis direction)×600-pixel (in the Y-axis direction) image captured by only one lens was 550 TV lines in both of the X-axis direction and the Y-axis direction. On the other hand, the limiting resolution of the image obtained by synthesizing the three pieces of image information obtained from the three imaging regions by the method according to the present invention was 1,000 TV lines in both of the X-axis direction and the Y-axis direction, which was about 1.8 times higher than the above. When the limiting resolution was evaluated while varying the subject distance from 10 cm to 3 m, the limiting resolution in the case of synthesizing the three pieces of image information was 1.5 to 1.8 times as high as that in the case of capturing with only one lens at every distance. 
     Further, the relationship between the pixel shifting amount d×sin θ (see  FIG. 2 ) and the limiting resolution was examined while varying the above-described angle θ. When d×sin θ was in the range of 0.5×p1±0.25×p1,the limiting resolution improved in the X-axis direction. When d×sin θ was in the range of 0.5×p2±0.25×p2, the limiting resolution improved in the Y-axis direction. In particular, when d×sin θ was in the ranges of 0.5×p1±0.1×p1 and 0.5×p2±0.1×p2, the resolution improved stably. 
     Moreover, the produced imaging apparatus was placed in a thermostat, and the characteristics thereof were determined with varying temperature. The limiting resolution in the case of synthesizing the three pieces of image information was at least 1.5 times as high as that in the case of capturing with only one lens from −10° C. to 40° C., thus confirming that the present invention was effective for the temperature variation. 
     Embodiment 2 
     Embodiment 1 has described the imaging apparatus using the lens array  300  including the three lenses  301   a ,  301   b  and  303   c  that are integrally-formed without any error in their relative positional relationship. However, if any forming error occurs in the relative positional relationship between a plurality of the lenses in an actual production of the lens array, it is difficult to correct. Thus, the lens array has to be formed at an accuracy finer than the pixel pitch in the imaging region, requiring a very high forming accuracy, so that a low-cost mass-production might become difficult. 
     On the other hand, it indeed is possible to prepare plural lenses separately and assemble these plural lenses while making a fine adjustment to the positional relationship with the corresponding plural imaging regions so that a desired shifted pixel arrangement is achieved, but this involves many adjusting processes and is not suitable for mass-production. 
     Embodiment 2 provides an imaging apparatus obtained by adding a function of compensating for a forming error of the lens array to the imaging apparatus of Embodiment 1. 
       FIG. 7A  is a plan view showing an arrangement of the lenses in the imaging apparatus according to Embodiment 1. For simplicity of description, the description will be directed to the case where the distance between the optical axes of the lens  301   b  and the lens  301   a  and that between the optical axes of the lens  301   b  and the lens  301   c  are both d and the pixel pitches p1 and p2 in the X-axis direction and the Y-axis direction in the imaging region are both p. Accordingly, when the lens array is rotated by the angle θ, the amount that the optical axis of the lens  301   a  is shifted with respect to the optical axis of the lens  301   b  in the X-axis direction and the amount that the optical axis of the lens  301   c  is shifted with respect to the optical axis of the lens  301   b  in the Y-axis direction are both d×sin θ. 
     However, if the first straight line  211  connecting the optical axes of the lenses  301   b  and  301   a  and the second straight line  212  connecting the optical axes of the lenses  301   b  and  301   c  do not form an exact right angle due to forming errors, the above-noted two shifting amounts are not both d×sin θ. Accordingly, it sometimes is difficult to achieve both of the shifted pixel arrangement between two subject images formed respectively by the lenses  301   b  and  301   a  and the shifted pixel arrangement between two subject images formed respectively by the lenses  301   b  and  301   c . In such cases, no matter how the angle θ is varied, an image whose resolution is raised in both of the X-axis direction and the Y-axis direction cannot be obtained. 
       FIG. 7B  is a plan view showing an arrangement of the lenses in the imaging apparatus according to Embodiment 2. Similarly to  FIG. 7A , the description will be directed to the case where the pixel pitches p1 and p2 in the X-axis direction and the Y-axis direction in the imaging region are both p. In Embodiment 2, the distance between the optical axes of the lens  301   b  and the lens  301   a  is d1, and that between the optical axes of the lens  301   b  and the lens  301   c  is d2(d2≠d1). Accordingly, when the lens array is rotated by the angle θ, the amount that the optical axis of the lens  301   a  is shifted with respect to the optical axis of the lens  301   b  in the X-axis direction (namely, the pixel shifting amount in the X-axis direction) is d1×sin θ, and the amount that the optical axis of the lens  301   c  is shifted with respect to the optical axis of the lens  301   b  in the Y-axis direction (namely, the pixel shifting amount in the Y-axis direction) is d2×sin θ. Since the pixel shifting amounts in the X-axis direction and the Y-axis direction are different as described above, they can be adjusted so as to be in the respective ranges of 0.5×p1±0.1×p1 and 0.5×p2±0.1×p2 at the same time, which achieve particularly high limiting resolution as described in Example 1, more easily even when the forming error of the lens array occurs. In other words, even when a production error occurs, it is possible to produce an imaging apparatus whose resolution can be raised easily and reliably in both of the X-axis direction and the Y-axis direction by adjusting the angle θ, so that the production becomes easier, leading to improved yield. 
     Unlike  FIG. 7B , it also may be possible to make the distances d1 and d2 between the optical axes of the lenses equal to each other (d1=d2=d) and the pixel pitch p1 in the X-axis direction and the pixel pitch p2 in the Y-axis direction in the imaging region different from each other (p1≠p2). In this case, when a rotation angle for allowing the amount that the optical axis of the lens  301   a  is shifted with respect to the optical axis of the lens  301   b  in the X-axis direction (namely, the pixel shifting amount in the X-axis direction) to match one pixel pitch p1 in the X-axis direction is given by θ (namely, d×sin θ=p1), the amount that the optical axis of the lens  301   c  is shifted with respect to the optical axis of the lens  301   b  in the Y-axis direction (namely, the pixel shifting amount in the Y-axis direction) is d×sin θ, which does not match one pixel pitch p2 in the Y-axis direction. In other words, similarly to  FIG. 7B , the ratio of the pixel shifting amount to the pixel pitch can be made different between the X-axis direction and the Y-axis direction. Accordingly, the pixel shifting amounts in the respective directions can be adjusted so as to be in the respective ranges of 0.5×p1±0.1×p1 and 0.5×p2±0.1×p2 at the same time, which achieve high limiting resolution, more easily even when the forming error of the lens array occurs. 
     Example 2 
     The following is a description of an example corresponding to Embodiment 2. 
       FIG. 8A  is a plan view showing an imaging apparatus according to Example 2 viewed along a direction parallel with optical axes, and  FIG. 8B  is a sectional view thereof taken along a line  8 B- 8 B in  FIG. 8A . 
     Example 2 is different from Example 1 ( FIGS. 6A and 6B ) in the following points. The lens array  700  was constituted by four lenses that were integrally-formed. As shown in  FIG. 8A , the four lenses were arranged so that their optical axes were located at individual vertices of a rectangle whose shorter sides (with a length d1=1.5 mm) were substantially parallel with the Y axis and longer sides (with a length d2=2 mm) were substantially parallel with the X axis. No color filter was provided on the imaging device  704 . Instead, color filters  800   a ,  800   b ,  800   c  and  800   d  were provided in four apertures  702  in the barrel  701  that corresponded to the four lenses. The diagonally-opposed color filters  800   b  and  800   d  transmitted light in a green wavelength range, the color filter  800   a  transmitted light in a red wavelength range, and the color filter  800   c  transmitted light in a blue wavelength range. Each of the lenses was designed so that its optical characteristics were optimal with respect to light at wavelengths of the light transmitted by the corresponding color filter. In an effective pixel region of the imaging device  704 , four 800-pixel (in the X-axis direction)×600-pixel (in the Y-axis direction) regions in which the four lenses respectively formed subject images were used as imaging regions. In this manner, the imaging apparatus for synthesizing a color image was produced. Other than the above, the configuration was the same as that in  FIGS. 6A and 6B . The same elements are assigned the same reference numerals, and the detailed description thereof will be omitted. 
     Two pieces of image information obtained from the two imaging regions corresponding to the two diagonally-opposed color filters  800   b  and  800   d  for transmitting light in the green wavelength range were compared, thereby calculating the parallax amount accurately. An X-axis component of this parallax amount indicated the parallax amount of blue image information obtained from the imaging region corresponding to the color filter  800   c , and a Y-axis component thereof indicated the parallax amount of red image information obtained from the imaging region corresponding to the color filter  800   a.    
     As described earlier, the pieces of image information of red (R), green (G) and blue (B) colors are known to be correlated in the local region of an image. In an imaging apparatus using an imaging device in which the color filters of three colors are in the Bayer arrangement, it is known that, utilizing such characteristics, information of the other two colors in a pixel having a filter of one color is estimated from color information of this pixel, thereby interpolating color information. In the present example, since the red image information and the blue image information were shifted from the two pieces of green image information by an amount substantially corresponding to an odd multiple of one-half the pixel pitch, the above-mentioned interpolation of the color information was applicable. In this way, the individual pieces of color information were superposed (synthesized) after achieving higher resolution, thereby obtaining a high-resolution color image. 
       FIG. 9A  shows an arrangement of the lenses in the lens array  700 . In  FIG. 9A , only three lenses (indicated by numerals  401   a ,  401   b  and  401   c , respectively) corresponding to the color filters  800   a ,  800   b  and  800   c  of the four lenses are illustrated. Positions of the optical axes of these three lenses were measured accurately. In the case where the pixel pitches p1 and p2 in the X-axis direction and the Y-axis direction were both p (p1=p2=p=2 μm), the amount that the optical axis of the lens  401   a  was shifted with respect to the optical axis of the lens  401   b  in the X-axis direction was 0.4×p (=0.8 μm), with a straight line  212  connecting the optical axes of the lenses  401   b  and  401   c  being set to parallel with the X axis. When the lens array  700  was rotated clockwise with respect to the imaging device  704  by 7.5×10 −4  rad from this state, the amount that the optical axis of the lens  401   c  was shifted with respect to the optical axis of the lens  401   b  in the Y-axis direction was 1.5×p (=3.0 μm) and the amount that the optical axis of the lens  401   a  was shifted with respect to the optical axis of the lens  401   b  in the X-axis direction was 1.525×p (=3.05 μm) as shown in  FIG. 9B . In other words, it was possible to set both of the shifting amounts to substantially an odd multiple of one-half the pixel pitch. 
     When the positions of the optical axes of the lenses in 100 lens arrays were measured, there were variations within the range of +2 μm from the designed positions. These lens arrays were each mounted in an imaging apparatus, and the angle of rotation of the lens array with respect to the imaging device was adjusted. The limiting resolution was evaluated similarly to Example 1. The limiting resolution of a 800-pixel (in the X-axis direction)×600-pixel (in the Y-axis direction) image captured by only one lens was 550 TV lines in both of the X-axis direction and the Y-axis direction. On the other hand, the limiting resolution of the color image obtained by synthesizing the four pieces of image information obtained from the four imaging regions always was 800 to 900 TV lines in both of the X-axis direction and the Y-axis direction in all the cases of using these lens arrays. 
     It should be noted that the arrangement of the color filters is not limited to the above-described example. For instance, numerals  800   a  and  800   c  may denote color filters transmitting light in the green wavelength range, numeral  800   b  may denote a color filter transmitting light in the red wavelength range, and numeral  800   d  may denote a color filter transmitting light in the blue wavelength range. 
     Comparative Example 1 
     In Comparative Example 1, the optical axes of the four lenses in Example 2 described above were arranged so as to be located substantially at individual vertices of a square whose one side d was 2 mm long. Other than the above, the configuration of the imaging apparatus and the processing of the image information were the same as those in Example 2. 
     As shown in  FIG. 9A , in the case where the pixel pitches p1 and p2 in the X-axis direction and the Y-axis direction were both p (p1=p2=p=2 μm), the amount that the optical axis of the lens  401   a  was shifted with respect to the optical axis of the lens  401   b  in the X-axis direction was 0.4×p (=0.8 μm), with the straight line  212  connecting the optical axes of the lenses  401   b  and  401   c  being set to parallel with the X axis. In this case, no matter how the lens array  700  was rotated with respect to the imaging device  704 , it was not possible to adjust both of the amount that the optical axis of the lens  401   a  was shifted with respect to the optical axis of the lens  401   b  in the X-axis direction and the amount that the optical axis of the lens  401   c  was shifted with respect to the optical axis of the lens  401   b  in the Y-axis direction to be within the range of 0.5×p+0.2×p at the same time. 
     The limiting resolution was evaluated similarly to Example 2. The limiting resolution of a color image obtained by synthesizing four pieces of image information obtained from the four imaging regions often varied between the X-axis direction and the Y-axis direction. For example, when the angle of rotation of the lens array  700  with respect to the imaging device  704  was at a certain value, the limiting resolution was 900 TV lines in the X-axis direction and 600 TV lines in the Y-axis direction, indicating that the resolution was not raised in the Y-axis direction. 
     This results for the following reason. In Comparative Example 1, since the distances d1 and d2 between the optical axes of the lenses were equal to each other, no matter how the lens array  700  was rotated with respect to the imaging device  704 , the amount that the optical axis of the lens  401   a  was shifted with respect to the optical axis of the lens  401   b  in the X-axis direction and the amount that the optical axis of the lens  401   c  was shifted with respect to the optical axis of the lens  401   b  in the Y-axis direction remained the same. Consequently, it sometimes was impossible to set both of these shifting amounts to substantially odd multiple of one-half the pixel pitch depending on the forming error of the lens array. 
     Embodiment 3 
     The present embodiment provides an imaging apparatus achieving both of the determination of a subject distance and the higher image resolution. 
     As described referring to  FIG. 16A , in the compound-eye imaging apparatus, the parallax due to the difference in subject distance is generated in the direction of a straight line connecting the optical axes of a pair of lenses. In contrast, in the present invention, with the shifted pixel arrangement in the direction perpendicular to the straight line connecting the optical axes of the pair of lenses, a higher image resolution is achieved. As described above, in the present invention, since the direction in which the parallax is generated and the direction of the shifted pixel arrangement are different, it is possible to achieve both of the determination of the subject distance (namely, the parallax amount) and the higher image resolution. 
     In the present embodiment, the parallax amount is determined by dividing an image to be referred to (a reference image) into a plurality of blocks and examining with which portion of an image to be compared (a compared image) each of the blocks correlates to the highest degree, similarly to Embodiment 1. The shifted pixel arrangement of the present invention causes the compared image to move with respect to the reference image in a direction perpendicular to the straight line connecting the optical axes of a pair of the lenses. Accordingly, if an image is searched for along the straight line connecting the optical axes of the pair of lenses similarly to the method of determining the distance in a usual compound-eye imaging apparatus, the correlation is poor, so that it becomes readily difficult to detect the parallax highly accurately. On the other hand, if an image is searched for along a straight line shifted by the amount of pixel shifting due to the shifted pixel arrangement in a direction perpendicular to the straight line connecting the optical axes of the pair of lenses, the influence of the shifted pixel arrangement of the present invention is corrected, thereby making it possible to improve an accuracy for detecting the parallax amount. Thus, under the shifted pixel arrangement of the present invention, the subject distance can be determined highly accurately. 
     Example 3 
     The following is a description of an example corresponding to Embodiment 3. Example 3 achieves both of the determination of a subject distance and the capturing of a high-resolution image. 
       FIG. 10A  is a plan view showing an imaging apparatus according to Example 3 viewed along a direction parallel with optical axes, and  FIG. 10B  is a sectional view thereof taken along a line  10 B- 10 B in  FIG. 10A . A lens array  1000  having a pair of lenses  1000   a  and  1000   b  was integrally-formed. The distance between optical axes of the pair of lenses  1000   a  and  1000   b  was set to 3 mm. The lens array  1000  was held by a tube-like barrel  1001 . A surface of the barrel  1001  facing the subject was provided with two apertures  1002  corresponding to the positions of the pair of lenses  1000   a  and  1000   b . As shown in  FIG. 10A , the shape of a plan view of an outer peripheral surface of the barrel  1001  viewed along a direction parallel with the optical axes was a deformed rectangle whose longer sides corresponded to a pair of straight lines  1001   a  and shorter sides corresponded to a pair of circular arcs  1001   b  connecting both ends of the pair of straight lines  1001   a . A portion of a base  1003  to be fitted with the barrel  1001  was provided with a recess (a groove) with curved surfaces  1003   b  having the same curvature as the pair of circular arcs  1001   b . The barrel  1001  was rotated along this recess around a center axis of the barrel  1001  relative to the base  1003 , thereby making an adjustment so that the shifted pixel arrangement was achieved between a pair of subject images respectively formed by the pair of lenses  1000   a  and  1000   b  and the pixels in an imaging device  1004 . 
     The imaging device  1004  was fixed onto the base  1003 . The imaging device  1004  was a CCD whose pixel pitches p1 and p2 in the X-axis direction and the Y-axis direction were both 2.2 μm. A spacer  1006  was interposed between the barrel  1001  and the base  1003 , thus achieving accurate positioning between the image forming planes of the lenses and a photodetector surface of the imaging device  1004 . 
     The parallax due to the difference in subject distance is generated in a direction of the straight line connecting the optical axes of the pair of lenses  1000   a  and  1000   b , namely, the X-axis direction. Thus, the angle θ that the straight line connecting the optical axes of the pair of lenses  1000   a  and  1000   b  formed with one of the directions in which the pixels were arranged was set to 3.6×10 −4  rad. This achieved the shifted pixel arrangement in the Y-axis direction with a pixel shifting amount of about 1.1 μm. 
     No color information is needed for determining the distance. Thus, the pair of apertures  1002  in the barrel  1001  were provided respectively with wavelength selection filters  1005  transmitting light in a green wavelength range. Two images formed by the pair of lenses  1000   a  and  1000   b  were compared, thereby determining the subject distance. 
     From the pair of images formed respectively by the pair of lenses  1000   a  and  1000   b  on the imaging device  1004 , the parallax amount was determined as follows. That is, first, a whole of the image formed by the lens  1000   b  (the compared image) was moved by image transformation along the Y-axis direction by an amount corresponding to one-half the pixel pitch. Then, in the compared image, a position of a portion corresponding to a block in the image formed by the lens  1000   a  (the reference image) was searched for. The amount that this block in the reference image was shifted with respect to the position of the portion in the compared image corresponding to this block in the X-axis direction (namely, the parallax amount) was determined, thereby determining the subject distance. 
     An imaging apparatus according to Comparative Example 2, which was the same as that according to Example 3 except that the shifted pixel arrangement in the Y-axis direction was not carried out, was produced. When the imaging apparatus according to Example 3 and that according to Comparative Example 2 were compared in terms of the determination accuracy of the subject distance, they were not different significantly. On the other hand, when they were compared in terms of the limiting resolution of the synthesized image, the apparatus according to Example 3 achieved an image with a resolution 1.5 times as high as that of the apparatus according to Comparative Example 2. 
     In Example 3 described above, the filter transmitting light in the green wavelength range was used as the pair of wavelength selection filters  1005 . However, this merely is an example, and the present invention is not limited thereto. As long as a filter selectively transmitting light in a specific wavelength range is used, the effect similar to the above can be obtained. For example, when filters transmitting infrared light are used as the pair of wavelength selection filters  1005 , it is possible to achieve an imaging apparatus capable of determining the subject distance and capturing a high-resolution image even in the nighttime. 
     Example 4 
     The following is a description of another example corresponding to Embodiment 3. Example 4 achieves both of the determination of a subject distance and the capturing of a high-resolution image. 
       FIG. 11A  is a plan view showing an imaging apparatus according to Example 4 viewed along a direction parallel with optical axes, and  FIG. 11B  is a sectional view thereof taken along a line  11 B- 11 B in  FIG. 11A . A lens array  1100  having a pair of lenses  1100   a  and  1100   b  with a diameter of 2.1 mm was integrally-formed. The distance between optical axes of the pair of lenses  1100   a  and  1100   b  was set to 3 mm. The lens array  1100  was held by a tube-like barrel  1101 . A surface of the barrel  1101  facing the subject was provided with two apertures  1102  corresponding to the positions of the pair of lenses  1100   a  and  1100   b . As shown in  FIG. 11A , the shape of a plan view of an outer peripheral surface of the barrel  1101  viewed along a direction parallel with the optical axes was a deformed rectangle whose longer sides corresponded to a pair of straight lines  1101   a  and shorter sides corresponded to a pair of circular arcs  1101   b  connecting both ends of the pair of straight lines  1101   a . A portion of a base  1103  to be fitted with the barrel  1101  was provided with a recess (a groove) with curved surfaces  1103   b  having the same curvature as the pair of circular arcs  1101   b . The barrel  1101  was rotated along this recess around a center axis of the barrel  1101  relative to the base  1103 , thereby making an adjustment so that the shifted pixel arrangement was achieved between a pair of subject images respectively formed by the pair of lenses  1100   a  and  1100   b  and the pixels in an imaging device  1104 . 
     The imaging device  1104  was fixed onto the base  1103 . The imaging device  1104  was a CCD whose pixel pitches p1 and p2 in the X-axis direction and the Y-axis direction were both 2.2 μm. A spacer  1106  was interposed between the barrel  1101  and the base  1103 , thus achieving accurate positioning between the image forming planes of the lenses and a photodetector surface of the imaging device  1104 . 
     The parallax due to the difference in subject distance is generated in a direction of the straight line connecting the optical axes of the pair of lenses  1100   a  and  1100   b , namely, the X-axis direction. Thus, the angle θ that the straight line connecting the optical axes of the pair of lenses  1100   a  and  1100   b  formed with one of the directions in which the pixels were arranged was set to 3.6×10 −4  rad. This achieved the shifted pixel arrangement in the Y-axis direction with a pixel shifting amount of about 1.1 μm. 
     A lens including a refractor lens whose surface was provided with a diffraction grating, and a layer that was applied onto the diffraction grating and made of a material whose refractive index was different from a material of the refractor lens (in the following, referred to as the “refractive diffractive lens with an applied layer”) was used as the lenses  1100   a  and  1100   b . This made it possible to form a subject image by visible light on a photodetector surface of the imaging device  1104  with a little aberration, despite the fact that the lens was a single lens having a relatively small aperture. 
     A color filter  1105  was formed on the imaging device  1104 .  FIG. 12A  shows an arrangement of the color filter on pixels in an imaging region corresponding to the lens  1100   a , and  FIG. 12B  shows an arrangement of the color filter on pixels in an imaging region corresponding to the lens  1100   b . As shown in  FIGS. 12A and 12B , in Example 4, a color filter in which filters each transmitting any of red (R), green (G) and blue (B) colors were arranged in the Bayer arrangement in such a manner as to correspond to the pixel arrangement was used as the color filter  1105 . 
     Each of the pixels in the imaging device  1104  can obtain only information of any one of red, green and blue. However, as described earlier, the pieces of image information of red, green and blue colors are known to be correlated in the local region of an image. In an imaging apparatus using an imaging device in which the color filters of three colors are in the Bayer arrangement, it is known that, utilizing such characteristics, information of the other two colors in a pixel having a filter of one color is estimated from color information of this pixel, thereby interpolating color information. By this known technique, pieces of color information of red, green and blue were obtained in the individual pixels. Accordingly, it was possible to achieve the shifted pixel arrangement for each color of red, green and blue. After a high-resolution image was obtained by synthesizing pieces of single color image information obtained from two imaging regions for each color of red, green and blue, a red high-resolution image, a green high-resolution image and a blue high-resolution image were synthesized further, thus obtaining a high-resolution color image. 
     On the other hand, a subject distance was determined from the single color image information obtained from the two imaging regions, similarly to Example 3. 
     In this manner, Example 4 achieved both of the capturing of a high-resolution color image and the determination of a subject distance. 
     Unlike Example 4 described above, it also may be possible to synthesize pieces of image information of the other colors with reference to the image information of green without interpolating color information and then interpolate color information in each of the pixels. In the case of interpolating the color information after the synthesis in this way, this interpolation can be performed using color information at a position closer to the pixel. 
     The color arrangement in the color filter  1105  provided on the imaging device  1104  is not limited to the Bayer arrangement shown in  FIGS. 12A and 12B . As long as pieces of image information of three primary colors can be obtained, it is possible to capture a color image. 
     For example, it also may be possible to provide the imaging region corresponding to the lens  1100   a  with a color filter of the Bayer arrangement as shown in  FIG. 13A  and provide the imaging region corresponding to the lens  1100   b  with only filters transmitting green light as shown in  FIG. 13B . This makes it possible to obtain more information of green to which a human eye is most sensitive, so that a high-resolution image can be obtained. In this case, it is preferable to use the above-mentioned refractive diffractive lens with an applied layer as the lens  1100   a.    
     Alternatively, it also may be possible to provide the imaging region corresponding to the lens  1100   a  with a color filter in which filters transmitting green light and filters transmitting red light are arranged in a checkered pattern so as to correspond to the pixel arrangement as shown in  FIG. 14A  and provide the imaging region corresponding to the lens  1100   b  with a color filter in which filters transmitting green light and filters transmitting blue light are arranged in a checkered pattern so as to correspond to the pixel arrangement as shown in  FIG. 14B . One imaging region receives light of two colors at wavelengths close to each other as described above, whereby it becomes easier to correct aberrations caused by the difference in refractive index due to the difference in wavelength compared with the case of receiving light of three primary colors of red, green and blue, so that the single lens can be designed more easily. 
     The invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The embodiments disclosed in this application are to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, all changes that come within the meaning and range of equivalency of the claims are intended to be embraced therein. 
     INDUSTRIAL APPLICABILITY 
     Although the imaging apparatus according to the present invention can be utilized in any fields without particular limitation, it preferably is used, in particular, for a camera or the like to be mounted in mobile equipment because it can capture a high-resolution image despite its small thickness and size. Further, since the imaging apparatus according to the present invention can determine the distance to a subject, it also can be utilized for an input apparatus used in the fields of monitoring of vehicle surroundings, security, motion capture, endoscopes, etc.