Patent Publication Number: US-9888177-B2

Title: Imaging device and electronic device

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a continuation of International Patent Application No. PCT/JP2014/075801, having an international filing date of Sep. 29, 2014, which designated the United States, the entirety of which is incorporated herein by reference. Japanese Patent Application No. 2013-210714 filed on Oct. 8, 2013 is also incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     The present invention relates to an imaging device, an electronic device, and the like. 
     Technology that is referred to as depth-from-defocus (DFD) is known that acquires a plurality of images that are identical in scene, but differ in focal distance (or in-focus object plane position (that represents the position of the object in an in-focus state)) using a camera, and measures the distance by utilizing the fact that the spread parameter (that represents the correlation between the images as to the amount of defocus) and the object distance have a one-to-one relationship. 
     JP-A-4-343312 discloses a method that acquires a plurality of images that differ in focal distance by driving the imaging lens in the direction along the optical axis. JP-A-5-30409 discloses a method that divides the incident light using a half mirror or a prism, and simultaneously captures a plurality of images that differ in focus state using a plurality of image sensors placed at positions that differ in optical path length. 
     It is ideal that the images subjected to DFD only differ in the amount of defocus. If the images subjected to DFD also differ in a factor other than the amount of defocus, the spread parameter may include an error, and the ranging accuracy may deteriorate due to the absence of correct object distance information. 
     SUMMARY 
     According to one aspect of the invention, an imaging device comprising: 
     a first image sensor that is placed to intersect an optical axis of an imaging lens, and captures a first image; 
     a second image sensor that is placed to intersect the optical axis of the imaging lens so as to be situated at a given distance from the first image sensor, and receives light that has passed through the first image sensor to capture a second image; and 
     a processor comprising hardware, 
     wherein the processor is configured to implement: 
     a brightness correction process that amplifies a pixel value of the second image captured by the second image sensor using a gain that has been set based on a light transmittance of a light-receiving section of the first image sensor; and 
     an object distance calculation process that performs a depth-from-defocus (DFD) process based on a pixel value of the first image and the pixel value of the second image subjected to the brightness correction process to calculate an object distance, and 
     the processor is configured to implement the brightness correction process that causes brightness of the second image to be substantially identical to that of the first image. 
     According to another aspect of the invention, an electronic device includes the imaging device. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a basic configuration example of an imaging device according to several embodiments of the invention. 
         FIG. 2  illustrates a detailed configuration example of an imaging device according to several embodiments of the invention. 
         FIGS. 3A and 3B  illustrate an example of the structure of an image sensor (first embodiment). 
         FIG. 4  is a flowchart illustrating a process (first embodiment). 
         FIG. 5  illustrates a detailed configuration example of a direct image sensor. 
         FIG. 6  is a view illustrating the transmittance of a first image sensor with respect to incident light. 
         FIG. 7  is a view illustrating a state in which a first image sensor functions as a diffraction grating. 
         FIG. 8  is a view illustrating wave-front propagation. 
         FIGS. 9A to 9D  illustrate a specific example of a diffraction pattern. 
         FIG. 10  is a flowchart illustrating a DFD process. 
         FIGS. 11A and 11B  illustrate an example of the relationship between a spread parameter and an object distance. 
         FIG. 12  illustrates another configuration example of an imaging device according to several embodiments of the invention. 
         FIG. 13  illustrates a configuration example of a Bayer-array image sensor. 
         FIG. 14  illustrates an example of the structure of an image sensor (second embodiment). 
         FIG. 15  is another view illustrating a state in which a first image sensor functions as a diffraction grating. 
         FIGS. 16A and 16B  illustrate an example of the pixel positional relationship between a first image sensor and a second image sensor. 
         FIG. 17  illustrates a configuration example when a microlens is provided to a first image sensor. 
         FIG. 18  illustrates a configuration example of a back-illuminated image sensor. 
         FIGS. 19A to 19C  illustrate an example of a specific device to which a method according to several embodiments of the invention may be applied. 
         FIG. 20  illustrates another configuration example of an imaging device according to several embodiments of the invention. 
         FIG. 21  illustrates another configuration example of an imaging device according to several embodiments of the invention. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     According to one embodiment of the invention, an imaging device comprising: 
     a first image sensor that is placed to intersect an optical axis of an imaging lens, and captures a first image; 
     a second image sensor that is placed to intersect the optical axis of the imaging lens so as to be situated at a given distance from the first image sensor, and receives light that has passed through the first image sensor to capture a second image; and 
     a processor comprising hardware, 
     wherein the processor is configured to implement: 
     a brightness correction process that amplifies a pixel value of the second image captured by the second image sensor using a gain that has been set based on a light transmittance of a light-receiving section of the first image sensor; and 
     an object distance calculation process that performs a depth-from-defocus (DFD) process based on a pixel value of the first image and the pixel value of the second image subjected to the brightness correction process to calculate an object distance, and 
     the processor is configured to implement the brightness correction process that causes brightness of the second image to be substantially identical to that of the first image. 
     In the imaging device, the processor may be configured to further implement a noise reduction process that causes an SN ratio of the second image subjected to the brightness correction process to be substantially identical to that of the first image. 
     In the imaging device, the first image sensor may be a direct image sensor that sequentially separates RGB colors in a direction along the optical axis of the imaging lens. 
     In the imaging device, the first image sensor may be an image sensor that includes given color filters that are placed in a mosaic-like pattern on a pixel basis. 
     In the imaging device, the first image sensor may be a back-illuminated image sensor in which a transfer electrode is provided on a side of a semiconductor substrate opposite to an illumination side. 
     In the imaging device, the processor may be configured to further implement a diffraction correction process that performs a process that corrects defocus caused by diffraction due to the first image sensor on the second image captured by the second image sensor. 
     In the imaging device, the second image sensor may be placed at a given distance L that satisfies L&gt;F×r from the first image sensor in a direction along the optical axis of the imaging lens, F being an F-number determined by a lens system that includes the imaging lens, and r is a size of a permissible circle of confusion. 
     The imaging device may further include a microlens that is provided to the first image sensor on a pixel basis, and used to focus light. 
     In the imaging device, the processor may be configured to further implement a pixel binning process, the pixel binning process being performed on at least one of the first image and the second image so that a number of pixels of the first image corresponds to a number of pixels of the second image. 
     In the imaging device, the processor may be configured to further implement a pixel sampling process, the pixel sampling process being performed on at least one of the first image and the second image so that a number of pixels of the first image corresponds to a number of pixels of the second image. 
     In the imaging device, the second image sensor may be an image sensor that has a number of pixels that corresponds to a number of pixels of the first image sensor that are used to generate an R signal among RGB signals. 
     Another embodiment of the invention relates to an electronic device that includes the imaging device. 
     1. Method 
     As described above, it is ideal that the images subjected to DFD only differ in the amount of defocus. According to the method disclosed in JP-A-4-343312, however, the imaging lens is driven each time an image is captured. Since a shake or the movement of the object may occur when the imaging lens is driven, a difference in object position or a motion blur may occur between the images. Therefore, the ranging accuracy may deteriorate (i.e., an error may occur). 
     According to the method disclosed in JP-A-5-30409, since images are simultaneously captured using two image sensors placed at positions that differ in optical path length, it is possible to suppress or reduce the effects of a shake or a motion blur due to a difference in image acquisition timing. According to the method disclosed in JP-A-5-30409, however, it is necessary to provide a half mirror or a prism beam splitter that divides the optical path of the incident light, and a mirror that changes the optical path length. It is necessary to provide a space for guiding the divided light to each image sensor, and a space for providing two image sensors. Therefore, the structure of the imaging device becomes complex, and in increase in cost and size may increase. 
     In order to solve the above problems, several embodiments of the invention propose a method that places two image sensors side by side in the direction along the optical axis of an imaging lens in view of the fact that light having a relatively long wavelength (i.e., light having a wavelength that corresponds to an R signal (among R, G, and B signals) in a narrow sense) is not completely absorbed by an image sensor, but partially passes therethrough. 
     According to several embodiments of the invention, an imaging device includes a first image sensor  101  that is placed to intersect the optical axis of an imaging lens  100 , a second image sensor  102  that is placed to intersect the optical axis of the imaging lens  100  so as to be situated at a given distance from the first image sensor  101 , and receives light that has passed through the first image sensor  101 , and an object distance calculation section  115  that performs a depth-from-defocus (DFD) process based on a pixel value of a first image captured by the first image sensor  101  and a pixel value of a second image captured by the second image sensor  102  to calculate the object distance (see  FIG. 1 ). 
     Note that the term “DFD” refers to a method that calculates the distance to the object (object distance) based on the relationship between a plurality of images as to the amount of defocus (see above), and the term “DFD process” refers to a process that calculates the object distance using DFD. 
     The spectral transmittance of the image sensor is determined taking account of the design of the image sensor. As described later with reference to  FIG. 6 , light having a relatively long wavelength is not completely absorbed by a given image sensor, but partially passes through the image sensor. In the example illustrated in  FIG. 6 , light that corresponds to the B signal among the RGB signals and has a short wavelength and light that corresponds to the G signal among the RGB signals has a short wavelength (A 3  and A 4 ) are almost completely (completely in a narrow sense) absorbed by the image sensor (i.e., do not pass through the image sensor), but light (A 5 ) that corresponds to the R signal and has a wavelength longer than that of the light that corresponds to the B signal and the light that corresponds to the G signal partially passes through the image sensor. Specifically, the part of the light that corresponds to the R signal that is indicated by A 1  in  FIG. 6  is absorbed by the image sensor, and the part of the light that corresponds to the R signal that is indicated by A 2  in  FIG. 6  passes through the image sensor. 
     Specifically, when the first image sensor  101  and the second image sensor  102  are arranged side by side so as to intersect the optical axis of the imaging lens  100  (see  FIG. 1 ), light that has passed through the first image sensor  101  is received by the second image sensor  102  (i.e., a situation in which light is completely absorbed by the first image sensor  101 , and does not reach the second image sensor  102  does not occur). Therefore, since it is possible allow the first image sensor  101  and the second image sensor  102  to receive light that corresponds to an identical object without providing a half mirror or the like for separating light, the configuration of the imaging device can be simplified. Since the second image sensor  102  is placed at a given distance from the first image sensor  101  in the direction along the optical axis of the imaging lens  100 , a difference in optical path length necessarily occurs when the configuration illustrated in  FIG. 1  is used, and it is unnecessary to provide a lens or the like for producing a difference in optical path length. 
     In this case, the first image sensor  101  can acquire the R signal, the G signal, and the B signal, and the second image sensor  102  can acquire the R signal. Therefore, the image that has been acquired by the first image sensor  101  and corresponds to the R signal (hereinafter may be referred to as “R image”) and the image that has been acquired by the second image sensor  102  and corresponds to the R signal are images obtained by capturing an identical object at an identical timing, and are suitable for the DFD process. Therefore, it is possible to suppress or reduce the occurrence of a motion blur and the like, and implement the DFD process with high accuracy by utilizing the method according to several embodiments of the invention illustrated in  FIG. 1 . Specifically, it is unnecessary to use all of the B signal, the G signal, and the R signal acquired by the first image sensor  101  for the DFD process, and it suffices to use only the signal (i.e., R signal) that corresponds to the signal acquired by the second image sensor  102  for the DFD process. Therefore, the pixel value of the first image mentioned above corresponds to the pixel value of the R image acquired by the first image sensor  101 . 
     When using the method according to several embodiments of the invention, it is necessary for the first image sensor  101  to allow light within a wavelength band that can be received by the second image sensor  102  while maintaining the intensity of the light to a certain extent. It was found that most of the image sensors widely used for a digital still camera and the like allow part of light having a wavelength that corresponds to the R signal to pass through, and various image sensors can be widely used as the first image sensor  101 . 
     Note that the quantity (intensity) of light that is received by the second image sensor  102  can be increased, and the intensity of the signal used to form the second image can be increased by increasing the intensity of light that passes through the first image sensor  101 . Therefore, it is considered that the accuracy of the comparison process (i.e., amount-of-defocus comparison process) performed on the first image and the second image can be improved, and the accuracy of the DFD process can also be improved. In view of the above point, an image sensor having a specific structure may be used as the first image sensor  101 . 
     For example, the first image sensor may be a back-illuminated image sensor in which a transfer electrode is provided on a side of a semiconductor substrate opposite to the illumination side. 
     A known image sensor (front-illuminated image sensor) has a configuration in which a transistor and a wiring layer used to input and output a voltage are formed on the side on which light is incident. Therefore, the incidence of light on a light-receiving device (e.g., photodiode) is hindered due to the wires, and deterioration in image and the like occur. On the other hand, the back-illuminated image sensor is configured so that light is applied from the back side of a silicon substrate (see  FIG. 18 ). Therefore, the photodiode can efficiently receive the incident light without being affected by the wires and the like, and the sensitivity characteristics can be improved, for example. 
     Several embodiments of the invention also focus on the fact that the back-illuminated image sensor has a reduced thickness in addition to the fact that the back-illuminated image sensor can generate a high-quality image. When producing the back-illuminated image sensor, a support substrate is bonded to the surface of a silicon wafer, and the silicon wafer is ground. The back-illuminated image sensor can thus be produced to have a thickness smaller than that of a front-illuminated image sensor and the like. It is possible to suppress or reduce the scattering of light within the image sensor, and increase the intensity of transmitted light by reducing the thickness of the image sensor. Specifically, it is possible to increase the intensity of transmitted light, and increase the quantity (intensity) of light that is received by the second image sensor  102  by utilizing the back-illuminated image sensor as the first image sensor  101 . It is thus possible to improve the accuracy of the DFD process, for example. 
     First to third embodiments of the invention are described below. The first embodiment illustrates an example in which a direct image sensor is used as the first image sensor  101 . In this case, the intensity of light that is absorbed by the first image sensor  101  differs from the intensity of light that is absorbed by the second image sensor  102 . The first embodiment also illustrates a brightness correction process for obtaining two images having an substantially identical brightness. Since the first image sensor  101  functions as a diffraction grating, defocus that differs from defocus due to the difference in in-focus state also occurs in the second image. The first embodiment also illustrates the details of a process that compensates for the effects of diffraction. 
     The second embodiment illustrates an example in which a Bayer-type image sensor that is widely used is used as the first image sensor  101 . The second embodiment also illustrates a modification in which a microlens is provided to the image sensor on a pixel basis. Note that the microlens need not necessarily be used for a Bayer-type image sensor. The microlens may also be used in connection with the first embodiment. The third embodiment illustrates an example in which a noise reduction process is additionally performed. 
     2. First Embodiment 
     The first embodiment is described below. As illustrated in  FIG. 2 , an imaging device according to the first embodiment includes an imaging lens  100 , a first image sensor  101 , a second image sensor  102 , an A/D conversion section  103 , a first buffer  104 , a second buffer  105 , a full-color processing section  106 , an image output section  107 , a brightness correction processing section  108  (gain processing section), a diffraction correction processing section  109 , a spread parameter calculation section  110 , an LUT reference section  111 , a distance output section  112 , an imaging section control section  113 , and a capture parameter control section  114 . Note that the configuration of the imaging device is not limited to the configuration illustrated in  FIG. 2 . Various modifications may be made, such as omitting some of the elements illustrated in  FIG. 2 , or adding other elements. Various modifications may also be made in connection with  FIG. 12  and the like. 
     The process performed by each block illustrated in  FIG. 2  is described below referring to the flow of the process illustrated in  FIG. 4 . The first image sensor  101  and the second image sensor  102  must be provided so that a recognizable difference in amount of defocus occurs between the first image sensor  101  and the second image sensor  102  in order to implement DFD. The distance L 1  between the image sensors is determined to satisfy the following expression (1) (S 301 ).
 
 L 1&gt;2 Fr   (1)
 
     Note that F in the expression (1) is the F-number of the imaging lens  100 , and r in the expression (1) is the diameter of the permissible circle of confusion. In the first embodiment, the permissible circle of confusion corresponds to the size of one pixel. Therefore, when the pixel pitch is set to d 1  (see  FIG. 7 ), the diameter r of the permissible circle of confusion is d 1  (r=d 1 ). The right side of the expression (1) represents the depth of focus φ illustrated in  FIG. 3B . The distance L 1  is set to satisfy the expression (1) so that a situation in which both the first image sensor  101  and the second image sensor  102  lie within the depth of focus does not occur. It is considered that an in-focus image is obtained within the range of the depth of focus φ even when the incident light does not optically converge at one point. Specifically, when both the first image sensor  101  and the second image sensor  102  lie within the depth of focus φ, a difference in the amount of defocus does not occur between the first image sensor  101  and the second image sensor  102 , and it is difficult to appropriately implement DFD. The expression (1) represents the condition that is set from the above point of view. Specifically, at least a difference in the amount of defocus occurs between the image sensors by providing the image sensors to be situated away from each other by the distance L 1 . 
     The distance L 1  increases as the F-number increases (see the expression (1)). In the first embodiment, the imaging section control section  113  illustrated in  FIG. 2  drives the image sensor each time the capture parameter control section  114  illustrated in  FIG. 2  has set the F-number to adjust the distance L 1  (S 302 ). The positions of the image sensors may be fixed using the distance L 1  that satisfies the expression (1) when the maximum F-number that can be set in advance is used. 
     The light that has passed through the imaging lens  100  is captured using the first image sensor  101  and the second image sensor  102  that differ in the optical path length from the object (S 303 ). 
     The first image sensor  101  and the second image sensor  102  are placed in layers in the direction along the optical axis, and the second image sensor  102  captures the light that has passed through the first image sensor  101 . In the first embodiment, an image sensor that can record RGB (3 ch) information on a pixel basis (see  FIG. 3A ) is used as the first image sensor  101 . Silicon layers  201 ,  202 , and  203  are formed in the image sensor, and the incident light is subjected to color separation in the depth direction by utilizing the characteristics in which light having a longer wavelength reaches a deeper part of the silicon layer. 
     The layer  201  absorbs light ( 207 ) within a wavelength band that corresponds to Bch, light ( 208 ) within a wavelength band that corresponds to Gch, and light ( 209 ) within a wavelength band that corresponds to Rch included in the incident light. The light within a wavelength band that corresponds to Bch does not reach the layer  202 , and the layer  202  absorbs the light ( 208 ) within a wavelength band that corresponds to Gch, and the light ( 209 ) within a wavelength band that corresponds to Rch. The deepest layer  203  absorbs the light ( 209 ) within a wavelength band that corresponds to Rch. The charge acquired by each layer is transmitted to a substrate-wiring layer  204 . 
     When the charge acquired by each layer is respectively referred to as I 201 , I 202 , and I 203 , the Bch signal can be calculated by removing the G component and the R component from the charge I 201  using the charge I 202 . Likewise, the Gch signal can be calculated by removing the R component from the charge I 202  using the charge I 203 . The Rch signal can be acquired from the charge I 203 . In the first embodiment, the full-color processing section  106  performs a process (full-color process) that calculates the RGB signals using the charges I 201  to I 203  (S 304 ). 
     Light  210  that has passed through the layer  203  reaches a photodiode  205  of the second image sensor  102  that is situated at the distance L 1  from the layer  203 , and is converted into charge. 
     Note that the first image sensor  101  may have a cross-sectional structure as illustrated in  FIG. 5 . In the illustrated in  FIG. 5 , an npn junction layer is formed on a p-type silicon substrate. A signal charge that corresponds to blue light, green light, and red light is generated in the np junction layer formed on the surface of the substrate, and a signal (I 201 ) that includes a B signal, a G signal, and an R signal is output based on the signal charge. Likewise, a signal charge that corresponds to green light and red light is generated in the intermediate pn junction layer, and a signal (I 202 ) that includes a G signal and an R signal is output based on the signal charge. A signal charge that corresponds to red light is generated in the deepest np junction layer, and a signal (I 203 ) that includes an R signal is output based on the signal charge. The electrode and the wiring structure are illustrated in  FIG. 3A  and the like in a simplified manner, and a charge is generated at the junction between the n-type layer and the p-type layer as illustrated in  FIG. 5 . 
     Two images respectively acquired by the first image sensor  101  and the second image sensor  102  that differ in the amount of defocus are subjected to an A/D conversion process, and stored in the first buffer  104  and the second buffer  105 , respectively. Specifically, a first image captured by the first image sensor  101  is stored in the first buffer  104 , and a second image captured by the second image sensor  102  is stored in the second buffer  105 . 
     In order to calculate the spread parameter (that represents the correlation in the amount of defocus) using the Rch information stored in the first buffer  104  and the image information stored in the second buffer  105 , a given correction process is performed on the image information stored in the second buffer  105 . The image information stored in the second buffer  105  represents the light that has passed through the first image sensor  101 . Therefore, the images differ in brightness based on the spectral transmittance (i.e., the spectral transmittance of the layers  201  to  203  illustrated in  FIG. 3A  in a narrow sense) of the first image sensor  101 . The brightness correction processing section  108  amplifies each pixel value using a given gain in order to correct the difference in brightness (S 305 ). 
       FIG. 6  illustrates the spectral transmittance of the first image sensor  101 .  FIG. 6  illustrates the intensity of the transmitted light with respect to the incident light that has entered the first image sensor  101  using a wavelength axis. The transmittance of light having a wavelength that corresponds to the B signal (see A 3  in  FIG. 6 ) is close to 0% since the light is mainly absorbed by the layer  201 . Likewise, the transmittance of light having a wavelength that corresponds to the G signal (see A 4 ) is close to 0% since the light is mainly absorbed by the layer  202 . The transmittance of light having a wavelength that corresponds to the R signal (see A 5 ) is more than 0% and less than 100% since the light is mainly absorbed by the layer  203 , but the incident light is not completely absorbed by the layer  203 . Therefore, the part of the R signal indicated by A 1  corresponds to the light absorbed by the first image sensor  101 , and the part of the R signal indicated by A 2  corresponds to the light that has passed through the first image sensor  101 . Note that the effects of scattering and the like are not taken into consideration. 
     Even if the light that has passed through the first image sensor  101  has been completely absorbed by the second image sensor  102 , the intensity of the light corresponds to the area indicated by A 2 . On the other hand, light having an intensity that corresponds to the area indicated by A 1  has been absorbed by the first image sensor  101 . Therefore, the second image is normally lower in brightness (brightness value) than the first image. 
     Since an image that has a small brightness value over the entire area has low contrast, such an image is determined to have a larger amount of defocus as compared with an image that has a larger brightness value even if the degree of optical defocus is almost equal. As described above, the difference in the amount of defocus due to a factor other than the in-focus state results in a deterioration in DFD determination accuracy. In the first embodiment, the brightness correction process is performed that causes the brightness of the second image to be substantially identical to that of the first image. Specifically, a gain process is performed using the gain represented by the following expression (2). Note that T is a value obtained by averaging the spectral transmittance illustrated in  FIG. 6  within a band that corresponds to Rch.
 
Gain=(100− T )/ T   (2)
 
     The area indicated by A 2  calculated by performing an integration process using  FIG. 6  may be used as the value T in the expression (2), for example. In this case, the numerator “100−T” included in the right side of the expression (2) is a value that corresponds to the area indicated by A 1 . 
     A diffraction correction process is then performed on the image subjected to the gain process (S 306 ). The effects of diffraction are described below with reference to  FIGS. 7 to 9D . When light passes through the first image sensor  101 , an area of the substrate in which a wire (line) and the like are provided functions as a mask (see  FIG. 7 ). Since the slits (aperture) (through which the light passes) and the masks are provided periodically on a pixel basis, the first image sensor  101  is considered to be a diffraction grating having slits  2   a  at slit intervals of d 1 . 
       FIG. 8  illustrates a state in which light emitted from a point O (point light source) reaches the first image sensor  101  (e.g., diffraction grating) through the imaging lens  100 . Light having a given wavelength emitted from the point light source O forms a spherical wave (spherical wave  1 ), and reaches the imaging lens  100 . The spherical wave  1  is modulated in phase by the imaging lens  100  to form a converging spherical wave (spherical wave  2 ), which reaches the first image sensor  101 . 
       FIGS. 9A to 9D  illustrate a state in which the converging spherical wave is captured by the second image sensor  102 . A spherical wave is considered to be a wave in which plane waves that differ in the incident angle overlap each other. Therefore, when the spherical wave is analyzed using the image of each plane wave that forms the spherical wave, the interference fringes illustrated in  FIG. 9A  are observed for the plane waves that are perpendicularly incident on the image sensor. A point image having an intensity I(m) is formed in the image plane at intervals of a distance mx around a point image having an intensity I(0) that is formed on a straight line that connects the point light source O and the center of the lens. The intensity I(m) and x are represented by the following expression (3). Note that m is a positive integer, N is the number of slits on the first image sensor, and λ is the wavelength of light. 
     
       
         
           
             
               
                 
                   
                     
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     The interference fringes observed for the plane waves incident on the image sensor as illustrated in  FIG. 9B  are shifted to the right relative to the interference fringes illustrated in  FIG. 9A  (indicated by the dotted lines). The amount of shift increases as the incident angle increases. Likewise, the interference fringes observed for the plane waves incident on the image sensor as illustrated in  FIG. 9C  are shifted to the left relative to the interference fringes illustrated in  FIG. 9A  (indicated by the dotted lines). A point image distribution having a smooth slope (see the solid line illustrated in  FIG. 9D ) is obtained by integrating these effects with respect to each incident angle. Since the point image distribution is convoluted into the original defocus image, a process that corrects the dispersion of the point image distribution illustrated in  FIG. 9D  is performed on the image subjected to the gain process. The diffraction correction processing section  109  performs a convolution process on the image subjected to the gain process using an inverse filter calculated in advance from the point spread function. 
     Note that the point spread function may be calculated by integrating the expression (3) with respect to each wavelength and each incident angle, or may be may be empirically acquired by actually capturing the point light source. The inverse filter can be calculated from the point spread function using various methods (e.g., Wiener filter). Note that the calculation cost increases when the number of taps of the designed inverse filter is too large. Therefore, it is preferable to set the number of taps to about 6× in order to use about m=3 for the filter kernel. 
     The object distance is then calculated by applying DFD (S 307 ). The object distance calculation process is described below with reference to the flowchart illustrated in  FIG. 10  and  FIGS. 11A and 11B . In the first embodiment, the method described in Subbarao and G. Surya, “Depth from Defocus: A Spatial Domain Approach”, International Journal of Computer Vision, Vol. 13, No. 3, pp. 271-294, 1994 may be used, for example. Specifically, the Rch image information stored in the first buffer  104  is acquired as the first image (S 401 ), and the corrected image information (see above) is acquired as the second image (S 402 ). The difference between the images is calculated on a pixel basis (S 403 ). The second derivative value of each image is calculated (S 404 ), and the average value thereof is calculated (S 405 ). The following expression (4) is solved using the calculated difference (numerator) and the average second derivative value (denominator) to calculate the spread parameter G that represents the correlation between the amounts of defocus (S 406 ). 
     
       
         
           
             
               
                 
                   
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     Note that g1 is the first image information, g2 is the second image information, and (x, y) is the coordinates within each image. ∇g1 is the second derivative value of the first image information, and ∇g2 is the second derivative value of the second image information. σ1 is the amount of defocus of the first image, and σ2 is the amount of defocus of the second image. The spread parameter G is an expression that calculates the difference in the amount of defocus between the first image and the second image. According to the method described in Subbarao and G. Surya, “Depth from Defocus: A Spatial Domain Approach”, International Journal of Computer Vision, Vol. 13, No. 3, pp. 271-294, 1994, the spread parameter can be calculated from the first image information g1, the second image information g2, and the second derivative values thereof without directly calculating the amount of defocus (see the expression (4)). 
     The spread parameter is calculated by the spread parameter calculation section  110 . The LUT reference section  111  refers to a look-up table (LUT) that stores the spread parameter and the object distance u on a one-to-one basis to calculate the object distance u (S 407 ). 
       FIGS. 11A and 11B  illustrate the relationship between the spread parameter and the object distance.  FIG. 11A  illustrates that the reciprocal of the object distance and the spread parameter have a linear relationship. Since the slope of the function changes (F 1 &lt;F 2 ) (see  FIG. 11B ) due to a change in F-number, it is necessary to provide a table corresponding to the F-number. Note that the spread parameter may be calculated using the following expression (5) without using the table. Note that α in the expression (5) is the slope that changes depending on the F-number, and β is the intercept.
 
 G=αu   −1 +β  (5)
 
     It is possible to eliminate the effects of the difference in brightness and diffraction from the image information obtained by the second image sensor  102  by utilizing the method according to the first embodiment, and implement one-shot DFD with high accuracy using a compact space. 
     According to the first embodiment, the first image sensor  101  is a direct image sensor that sequentially separates the RGB colors in the direction along the optical axis of the imaging lens  100 . 
     Note that the term “direct image sensor” used herein refers to a sensor that sequentially separates a color (i.e., RGB (primary colors)) in the travel direction of light. For example, silicon may be for the photoelectric conversion section (as described above with reference to  FIG. 5 ). Note that an image sensor that includes a photoelectric conversion section in which three organic photoconductive films (that have R, G, or B sensitivity and allow the other colors to pass through) are stacked, may be used as the direct image sensor. Various other modifications may also be made. 
     This makes it possible to use a direct image sensor as the first image sensor  101 . The direct image sensor has a configuration in which the wavelength band of light absorbed by each layer differs from each other (see above). This configuration is implemented by determining the light absorption characteristics and the light transmission characteristics of each layer during the design stage. Specifically, it is possible to control (design) the wavelength band and the intensity of light that passes through the first image sensor  101  (i.e., light that is received by the second image sensor  102 ) by utilizing a direct image sensor as the first image sensor  101 . Therefore, since it is possible to easily adjust the intensity of light that is absorbed by the second image sensor  102 , and easily adjust the clarity of the second image, the method according to the first embodiment that implements DFD using the configuration illustrated in  FIG. 1  has high affinity to the direct image sensor. 
     As illustrated in  FIG. 2 , the imaging device may further include the brightness correction processing section  108  that performs the brightness correction process that amplifies the pixel value of the second image captured by the second image sensor  102  using the gain that has been set based on the light transmittance of the light-receiving section of the first image sensor  101 . 
     This makes it possible to cause the brightness (brightness value) of the second image to be substantially identical to that of the first image. When two images are almost equal in the amount of optical defocus, but differ in the overall brightness value, the image having a larger brightness value has higher contrast as compared with the image having a smaller brightness value, and it is determined that the image having a larger brightness value has a small amount of defocus, and the image having a smaller brightness value has a large amount of defocus (see above). Since the difference in the amount of defocus between the images due to the brightness of the entire image is eliminated by performing the brightness correction process to obtain the first image and the second image that have identical brightness, it is possible to appropriately calculate the difference in the amount of optical defocus between the first image and the second image, and improve the accuracy of the DFD process. 
     When the difference in brightness between the first image and the second image is known in advance, the LUT may be provided taking account of the difference in brightness. In this case, the slope α (see  FIGS. 11A and 11B ) and the intercept β are calculated taking account of the difference in brightness. This makes it possible to compensate for the effects of brightness when converting the spread parameter into the object distance, even if the spread parameter is calculated without performing the brightness correction process. For example, when the transmittance characteristics of the first image sensor  101  (see  FIG. 6 ) are known during the design stage, the LUT may be determined based on the transmittance characteristics. 
     As illustrated in  FIG. 2 , the imaging device may further include the diffraction correction processing section  109  that performs the process that corrects defocus caused by diffraction due to the first image sensor  101  on the second image captured by the second image sensor  102 . 
     According to this configuration, even when defocus that differs from defocus due to the difference in optical path length has occurred in the second image due to the diffraction grating formed by the first image sensor  101 , it is possible to correct the defocus, and appropriately calculate the defocus due to the difference in optical path length (i.e., the difference in focus state). When defocus due to diffraction can be calculated in advance, the LUT may be provided taking account of the effects of defocus due to diffraction. In this case, the diffraction correction processing section  109  can be omitted from the imaging device, and the diffraction correction process can be skipped. 
     When the F-number determined by the lens system that includes the imaging lens  100  is referred to as F, and the size of the permissible circle of confusion is referred to as r, the second image sensor  102  is placed at a given distance L that satisfies I&gt;F×r from the first image sensor  101  in the direction along the optical axis of the imaging lens  100 . 
     According to this configuration, since it is possible to avoid a situation in which both the first image sensor  101  and the second image sensor  102  lie within the depth of focus (see above), it is possible to cause a difference in the amount of defocus to occur between the first image and the second image. This makes it possible to accurately calculate the spread parameter, and improve the accuracy of the object distance calculated by the DFD process. 
     The first embodiment may also be applied to an electronic device that includes the imaging device. The first embodiment may be applied to a digital camera (see  FIG. 19A ), an endoscope apparatus (see  FIG. 19B ), and various other devices that utilize distance information about the distance to the object. When applying the first embodiment to the endoscope apparatus illustrated in  FIG. 19B , an image captured by an imaging section (corresponding to the color image generated by the full-color processing section  106  illustrated in  FIG. 2 ) may be displayed after performing image processing that utilizes the distance information on the image. Examples of the image processing include an enhancement process that enhances the object situated at a specific distance to improve the visibility of the object, and the like. The electronic device according to the first embodiment may be a device that includes a control device  10  (e.g., PC) and an imaging section  20  (see  FIG. 19C ). In this case, the imaging section  20  acquires the first image and the second image using the configuration illustrated in  FIG. 1  or the like, and the control device  10  performs the DFD process to calculate the distance information about the distance to an object OB. The control device  10  performs various processes that utilize the distance information. For example, the control device  10  may perform a process that determines the shape and the size of the object OB in the direction orthogonal to the optical axis using the color image, and determines information about the object OB in the direction along the optical axis using the distance information to generate a 3D model of the object OB. Specifically, the method according to the first embodiment can be applied to various electronic devices that utilize the distance information. 
     The imaging device according to the first embodiment includes a memory that stores information (e.g., program and various types of data), and a processor that operates based on the information stored in the memory. The imaging device includes a first image sensor that is placed to intersect the optical axis of an imaging lens, and captures a first image, a second image sensor that is placed to intersect the optical axis of the imaging lens so as to be situated at a given distance from the first image sensor, and receives light that has passed through the first image sensor to capture a second image, and a processor including hardware, wherein the processor is configured to implement a brightness correction process that amplifies the pixel value of the second image captured by the second image sensor using a gain that has been set based on the light transmittance of a light-receiving section of the first image sensor, and an object distance calculation process that performs the DFD (depth-from-defocus) process based on the pixel value of the first image and the pixel value of the second image subjected to the brightness correction process to calculate the object distance, and the processor is configured to implement the brightness correction process that causes the brightness of the second image to be substantially identical to that of the first image. 
     The processor may implement the function of each section by individual hardware, or may implement the function of each section by integrated hardware, for example. The processor may be a central processing unit (CPU), for example. Note that the processor is not limited to a CPU. Various other processors such as a graphics processing unit (GPU) or a digital signal processor (DSP) may also be used. The processor may be a hardware circuit that includes an application specific integrated circuit (ASIC). The memory may be a semiconductor memory (e.g., SRAM or DRAM), a register, a magnetic storage device (e.g., hard disk drive), or an optical storage device (e.g., optical disk device). For example, the memory stores a computer-readable instruction, and each section of the image processing device is implemented by causing the processor to execute the instruction. The instruction may be an instruction included in an instruction set that is included in a program, or may be an instruction that causes a hardware circuit included in the processor to operate. 
     The operation according to the first embodiment is implemented as described below, for example. The memory stores the first image captured by the first image sensor, and the second image captured by the second image sensor. The processor reads the second image from the memory, performs the brightness correction process on the second image, and writes the second image subjected to the brightness correction process into the memory. The processor reads the first image and the second image subjected to the brightness correction process from the memory, performs the DFD process to calculate the object distance, and writes the calculated object distance into the memory. 
     Each section of the imaging device according to the first embodiment is implemented as a module of a program that operates on the processor. For example, the brightness correction processing section is implemented as a brightness correction processing module that amplifies the pixel value of the second image captured by the second image sensor using the gain that has been set based on the light transmittance of the light-receiving section of the first image sensor. The object distance calculation section is implemented as an object distance calculation module that performs the DFD (depth-from-defocus) process based on the pixel value of the first image and the pixel value of the second image subjected to the brightness correction process to calculate the object distance. 
     The imaging device and the like according to the first embodiment may include a processor and a memory. The processor may be a central processing unit (CPU), for example. Note that the processor is not limited to a CPU. Various other processors such as a graphics processing unit (GPU) or a digital signal processor (DSP) may also be used. The processor may be a hardware circuit that includes an ASIC. The memory stores a computer-readable instruction. Each section of the imaging device and the like according to the first embodiment is implemented by causing the processor to execute the instruction. The memory may be a semiconductor memory (e.g., SRAM or DRAM), a register, a hard disk, or the like. The instruction may be an instruction included in an instruction set that is included in a program, or may be an instruction that causes a hardware circuit included in the processor to operate. 
     3. Second Embodiment 
     The second embodiment is described below. Note that description of the elements of the imaging device according to the second embodiment (see  FIG. 12 ) that are the same as those described above in connection with the first embodiment is omitted, and the differences from the features described above in connection with the first embodiment are mainly described below. As illustrated in  FIG. 12 , the imaging device according to the second embodiment includes a pixel binning processing section  116  in addition to the configuration described above in connection with the first embodiment. 
     The configuration according to the second embodiment is described below taking an example in which the first image sensor  101  includes Bayer-array color filters (see  FIG. 13 ). 
       FIG. 14  illustrates the structure and the arrangement of the first image sensor  101  and the second image sensor  102 .  FIG. 14  is a side view illustrating one row of the first image sensor  101  including the Rch pixels (see the arrow (dotted line) illustrated in  FIG. 13 ). In  FIG. 14 , reference sign  1001  indicates a color filter, reference sign  1002  indicates a photodiode, and reference sign  1003  indicates a substrate and a wiring layer. As illustrated in  FIG. 14 , R color filters and G color filters are arranged alternately. 
     When a Bayer-array image sensor is used as the first image sensor  101 , since light  1006  that is incident on a pixel (i.e., Bch pixel or Gch pixel) other than the Rch pixel enters the color filter that allows light having a wavelength that corresponds to the G signal or the B signal to pass through, the light having a wavelength that corresponds to the R signal (Rch pixel) is blocked by the color filter. The light that is incident on the Bch pixel or the Gch pixel is absorbed by the first image sensor  101  (in the same manner as described above in connection with the first embodiment). Therefore, the light that is incident on a pixel (i.e., Bch pixel or Gch pixel) other than the Rch pixel does not pass through the first image sensor  101  (i.e., is not absorbed by the second image sensor  102 ). 
     Regarding light  1004  that is incident on the Rch pixel, the light having a wavelength that corresponds to the G signal or the B signal is blocked by the color filter, and the light having a wavelength that corresponds to the R signal is absorbed by the first image sensor  101 . In this case, part of the light having a wavelength that corresponds to the R signal passes through the first image sensor  101 , and reaches the second image sensor  102 . Specifically, the DFD process is performed using an image (R image) that corresponds to the Rch pixels of the first image sensor  101 , and an image that corresponds to the light that has passed through the Rch pixels of the first image sensor  101 , and has been received by the second image sensor  102 . 
     In this case, since the first image sensor  101  is configured so that the Rch color filters are arranged every other pixels (i.e., the sampling interval is set to one pixel) in the horizontal direction and the vertical direction (see  FIG. 13 ), the diameter of the permissible circle of confusion necessary for calculating the conditions for determining the distance L 2  between the first image sensor  101  and the second image sensor  102  is d 2  (that corresponds to two pixels) (see  FIG. 15 ). Specifically, the distance L 2  between the first image sensor  101  and the second image sensor  102  used in connection with the second embodiment satisfies the following expression (6) obtained by substituting d 2  for r in the expression (1).
 
 L 2&gt;2 Fd 2  (6)
 
     Diffraction that occurs on the second image sensor  102  due to the diffraction grating formed by the first image sensor  101  is represented by the following expression (7). 
     
       
         
           
             
               
                 
                   
                     
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     Note that the value x in the expression (7) is a parameter that represents the degree of spreading due to diffraction. Therefore, the degree of spreading increases as the value x increases. The number of taps of the inverse filter used for the diffraction correction process increases (i.e., the processing load increases) as the degree of spreading increases. If the diffraction correction process is performed without increasing the number of taps, the accuracy of the diffraction correction process decreases. Since the value d 2  is twice the value d 1  used in connection with the first embodiment, the lower limit of the distance L 2  increases to twice its value (see the expression (6)). Therefore, it may be considered that the value x (that is calculated using the expression in which the distance L 2  is included in the numerator) increases as compared with the first embodiment. However, the value d 2  is included in the expression used to calculate the value x (see the expression (7)). Specifically, the value (L 2 /d 2 ) is almost equal to the value (L 1 /d 1 ) used in connection with the first embodiment. That is, the value x (i.e., the degree of spreading due to diffraction) does not necessarily increases as the distance L 2  increases. Therefore, it is considered that a large difference does not occur with regard to the diffraction correction process between the case of using a direct image sensor as the first image sensor  101  (first embodiment) and the case of using a Bayer-array image sensor as the first image sensor  101  (second embodiment). This also applies to the case where the Rch color filters (pixels) are arranged every two or more pixels (i.e., the sampling interval is set to two or more pixels) in the horizontal direction and the vertical direction. 
     The number of Rch pixels to be sampled by the first image sensor  101  must be identical to the number of pixels of the image acquired by the second image sensor  102  in order to implement DFD. When the ratio of the Rch pixels 1/4 (see  FIG. 13 ), the ratio of the pixels of the first image sensor  101  that contribute to the R image used for DFD is 1/4. On the other hand, all of the pixels of the second image sensor  102  are normally used to generate the R image. In this case, when the first image sensor  101  and the second image sensor  102  are identical to each other as to the pixel pitch, the first image captured by the first image sensor  101  is smaller in the number of pixels than the second image captured by the second image sensor  102 , and it is difficult to make an appropriate determination during DFD. 
     Therefore, the pixel binning processing section  116  illustrated in  FIG. 12  averages the pixel values of the image captured by the second image sensor  102  in units of four pixels (i.e., two pixels in the horizontal direction, and two pixels in the vertical direction). The pixel binning process is described below with reference to  FIG. 15 . The pixels values of the pixels a 1  and a 2  are averaged as the pixels values of the pixels that correspond to the pixel r 1  in the horizontal direction, the pixels values of the pixels a 3  and a 4  are averaged as the pixels values of the pixels that correspond to the pixel r 2  in the horizontal direction, and the pixels values of the pixels a 5  and a 6  are averaged as the pixels values of the pixels that correspond to the pixel r 3  in the horizontal direction. Average values are similarly calculated in the vertical direction. In this case, if the first image sensor  101  and the second image sensor  102  placed so that the pixel r 1  coincides with the pixel a 1  (see  FIG. 16 ), the center C 1  of the pixel r 1  differs in position from the center C 2  of the pixel obtained by performing the pixel binning process on the four pixels (a 1 , a 2 , a′ 1 , a′ 2 ) of the second image sensor  102 . Therefore, it is desirable to place the second image sensor  102  to be shifted by half pixel from the first image sensor  101  in the horizontal direction and the vertical direction (see  FIGS. 14 and 15 ) so that the pixel positions of the first image sensor  101  coincide with the pixel positions of the second image sensor  102  after the pixel binning process. In this case, the center of the pixel of the first image sensor  101  and the center of the pixel of the second image sensor  102  coincide with each other at the point C 3  illustrated in  FIG. 16B . 
     The DFD process is then performed in the same manner as described above in connection with first embodiment using the R image (second image) captured by the second image sensor  102  that has been subjected to the pixel binning process, and the Rch sampling image (first image) captured by the first image sensor  101 . 
     Note that it is possible to make an appropriate determination during DFD as long as the number of pixels of the first image captured by the first image sensor  101  corresponds to (is identical to in a narrow sense) the number of pixels of the second image captured by the second image sensor  102 . Specifically, the process that adjusts the number of pixels is not limited to the pixel binning process described above. For example, the imaging device according to the second embodiment may have the configuration illustrated in  FIG. 20 . In  FIG. 20 , the pixel binning processing section  116  illustrated in  FIG. 12  is omitted, and a pixel sampling processing section  117  is additionally provided. 
     The term “pixel sampling process” used herein refers to a process that adjusts the number of pixels by sampling the pixels while skipping some pixels in either or both of the horizontal direction and the vertical direction. When the number of pixels of the first image is ¼th of that of the second image (see above), the pixel sampling processing section  117  samples the pixels of the second image every other pixels in the horizontal direction, and samples the pixels of the second image every other pixels in the vertical direction. In this case, since the number of pixels of the image subjected to the pixel sampling process is ¼th of that of the image before being subjected to the pixel sampling process, the number of pixels of the first image corresponds to the number of pixels of the second image subjected to the pixel sampling process. 
     In the second embodiment, a microlens  1000  for focusing light may be provided to the first image sensor  101  (see  FIG. 17 ). A microlens for focusing light is also widely used for a normal imaging device that does not perform the DFD process. When the microlens  1000  is provided to the first image sensor  101 , a composite F-number Fc of the F-number of the imaging lens  100  and the Fm of the microlens is used as the value F in the expression (6). 
     Since the composite F-number Fc is normally smaller than the F-number F of the imaging lens  100 , the value on the right side of the expression (6) can be reduced as compared with the case where a microlens is not used, and the distance L 2  can be reduced due to the F-number of the microlens. Therefore, the value x in the expression (7) decreases (i.e., the degree of spreading due to diffraction decreases), and the number of taps of the inverse filter used for the diffraction correction process can be reduced as compared with the case where the microlens  1000  is not used. 
     It is possible to eliminate the effects of the difference in brightness and diffraction from the image information obtained by the second image sensor  102 , and by utilizing the method according to the second embodiment. It is also possible to adjust the number of pixels of the second image captured by the second image sensor  102  so as to coincide with that of the sampling image obtained by the first image sensor  101  through the pixel binning process. This makes it possible to implement one-shot DFD with high accuracy using a compact space. 
     According to the second embodiment, the first image sensor  101  is an image sensor that includes given color filters that are placed in a mosaic-like pattern on a pixel basis (see  FIG. 13 ). 
     Note that the image sensor that includes given color filters that are placed in a mosaic-like pattern on a pixel basis refers to a Bayer-array image sensor in a narrow sense. Note that the image sensor that includes given color filters that are placed in a mosaic-like pattern on a pixel basis is not limited to a Bayer-array image sensor. 
     According to this configuration, it is possible to utilize an image sensor widely used for a known imaging device as the first image sensor  101  according to the second embodiment. This makes it possible to easily and inexpensively implement the first image sensor  101 , for example. 
     The imaging device may further include the microlens  1000  that is provided to the first image sensor  101  on a pixel basis, and used to focus light (see  FIG. 17 ). 
     According to this configuration, the composite F-number Fc can be reduced as compared with the F-number F of the imaging lens  100  (see above), and it is possible to reduce the distance L 2 , and reduce the number of taps (i.e., the number of multipliers provided to a filter (corresponding to the number of filter coefficients)) of the inverse filter used for the diffraction correction process to reduce the filter processing load, for example. 
     The imaging device may further include the pixel binning processing section  116  that performs the pixel binning process on at least one of the first image and the second image so that the number of pixels of the first image corresponds to (is identical to in a narrow sense) the number of pixels of the second image (see  FIG. 12 ). 
     According to this configuration, even when defocus that differs from defocus due to the difference in optical path length has occurred in the second image due to the difference in the number of pixels between the first image and the second image, it is possible to correct the defocus, and appropriately calculate the defocus due to the difference in optical path length (i.e., the difference in focus state). 
     The imaging device may further include the pixel sampling processing section  117  that performs the pixel sampling process on at least one of the first image and the second image so that the number of pixels of the first image corresponds to (is identical to in a narrow sense) the number of pixels of the second image (see  FIG. 20 ). 
     According to this configuration, even when defocus that differs from defocus due to the difference in optical path length has occurred in the second image due to the difference in the number of pixels between the first image and the second image, it is possible to correct the defocus, and appropriately calculate the defocus due to the difference in optical path length (i.e., the difference in focus state). 
     Note that the second image sensor  102  may be an image sensor that has a number of pixels that corresponds to (is identical to in a narrow sense) the number of pixels of the first image sensor  101  that are used to generate the R signal among the RGB signals. 
     The difference in the number of pixels between the first image and the second image described above occurs when the first image sensor  101  and the second image sensor  102  are identical to each other as to the pixel pitch. Note that it is possible to implement a state in which the number of pixels of the first image generated from the Rch pixels of the first image sensor  101  is identical to the number of pixels of the second image generated by the second image sensor  102  without performing the pixel binning process or the like by increasing the pixel pitch (i.e., reducing the number of pixels per unit area) of the second image sensor  102 . When the number of Rch pixels of the first image sensor  101  is ¼th of the total number of pixels (see above), the pixel pitch of the second image sensor  102  may be set to ½ (i.e., the number of pixels per unit area may be set to ¼). 
     4. Third Embodiment 
     The third embodiment is described below. Note that description of the elements of the imaging device according to the third embodiment (see  FIG. 21 ) that are the same as those described above in connection with the first embodiment is omitted, and the differences from the features described above in connection with the first embodiment are mainly described below. As illustrated in  FIG. 21 , the imaging device according to the third embodiment includes a noise reduction processing section  118  in addition to the configuration described above in connection with the first embodiment. 
     When the configuration according to the embodiments of the invention is used, the brightness of the second image captured by the second image sensor is lower than that of the first image captured by the first image sensor (see above). Therefore, the brightness correction processing section (gain processing section)  108  performs the brightness correction process that causes the brightness of the second image to be substantially identical to that of the first image (see the first and second embodiments). Specifically, the gain-up process is performed on the second image. 
     The difference in the amount of defocus due to a factor other than the in-focus state results in a deterioration in DFD determination accuracy (see above). The amount of defocus also changes due to the difference in noise (SN ratio in a narrow sense) in addition to the difference in brightness. Specifically, since noise within the image forms minute contrast, the contrast of the image increases as the amount of noise increases, and the amount of defocus is determined to be smaller than the actual value. The SN ratio of an image normally decreases as the brightness of the image decreases, the first image and the second image differ in SN ratio, and it is likely that the amount of defocus of the second image is determined to be smaller than that of the first image. 
     Since the relationship regarding the SN ratio does not change due to the correction process performed by the brightness correction processing section  108  that causes the brightness of the second image to be substantially identical to that of the first image, the accuracy of the DFD process decreases. 
     In the third embodiment, a given noise reduction process is performed on the second image in order to cause the SN ratio of the second image to be substantially identical to that of the first image. Specifically, the imaging device according to the third embodiment includes the noise reduction processing section  118  that performs the noise reduction process on the output from the brightness correction processing section (gain processing section)  108  (see  FIG. 21 ). 
     The noise reduction processing section  118  performs the noise reduction process at a level sufficient to cancel the difference in SN ratio between the second image subjected to the gain process and the first image. The difference in SN ratio between the second image and the first image is determined by the noise characteristics of the first image sensor and the second image sensor due to the material and the structure, the transmittance of the first image sensor, the quantity (intensity) of incident light, and the like. Therefore, it is desirable to empirically calculate an optimum value, and store the calculated value in the form of a look-up table that uses the pixel value as a key. 
     Note that the noise reduction process may be implemented using an arbitrary method such as a normal method (e.g., bilateral filter). When using a noise reduction filter or the like, the processing level (noise reduction level) can be set by adjusting various parameters. Therefore, the noise reduction conditions are set so that the processing level is sufficient to cause the SN ratio of the second image to be substantially identical to that of the first image. 
     Although  FIG. 21  illustrates an example in which the noise reduction processing section  118  performs the noise reduction process after the brightness correction processing section  108  has performed the brightness correction process, the configuration is not limited thereto. For example, the noise reduction processing section  118  may perform the noise reduction process on the output from the second buffer, and transmit the resulting image to the brightness correction processing section  108 . 
     The first to third embodiments to which the invention is applied and the modifications thereof have been described above. Note that the invention is not limited to the first to third embodiments and the modifications thereof. Various modifications and variations may be made without departing from the scope of the invention. A plurality of elements described above in connection with the first to third embodiments and the modifications thereof may be appropriately combined to achieve various configurations. For example, an arbitrary element may be omitted from the elements described above in connection with the first to third embodiments and the modifications thereof. Arbitrary elements among the elements described above in connection with different embodiments or modifications thereof may be appropriately combined. Any term cited with a different term having a broader meaning or the same meaning at least once in the specification and the drawings can be replaced by the different term in any place in the specification and the drawings. Specifically, various modifications and applications are possible without materially departing from the novel teachings and advantages of the invention.