Patent Publication Number: US-8525914-B2

Title: Imaging system with multi-state zoom and associated methods

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Application No. 60/996,018, filed on Oct. 25, 2007, and entitled: “IMAGING SYSTEM WITH MULTI-STATE ZOOM AND ASSOCIATED METHODS,” which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     Embodiments are directed to an imaging system, more particularly to an imaging system having improved image quality and associated methods. 
     2. Description of Related Art 
     Recently, image capturing devices have become widely used in portable and non-portable devices such as cameras, mobile telephones, webcams and notebooks. These image capturing devices conventionally include an electronic image detector such as a CCD or CMOS sensor, a lens system for projecting an object in a field of view (FOV) onto the detector and electronic circuitry for receiving, processing, and storing electronic data provided by the detector. Resolution and optical zoom are two important performance parameters of such image capturing devices. 
     Resolution of an image capturing device is the minimum distance two point sources in an object plane can have such that the image capturing device is able to distinguish these point sources. Resolution depends on the fact that, due to diffraction and aberrations, each optical system projects a point source not as a point but a disc of predetermined width and having a certain light intensity distribution. The response of an optical system to a point light source is known as point spread function (PSF). The overall resolution of an image capturing device mainly depends on the smaller one of the optical resolution of the optical projection system and the resolution of the detector. 
     Herein, the optical resolution of an optical projection system shall be defined as the full width at half maximum (FWHM) of its PSF. In other words, the peak values of the light intensity distribution of a projection of two point light sources must be spaced at least by the FWHM of the PSF in order for the image capturing device to be able to distinguish the two point light sources. However, the resolution could also be defined as a different value depending on the PSF, e.g. 70% of the width at half maximum. This definition of the optical resolution might depend on the sensitivity of the detector and the evaluation of the signals received from the detector. 
     The resolution of the detector is defined herein as the pitch, i.e., distance middle to middle of two adjacent sensor pixels of the detector. 
     Optical zoom signifies the capability of the image capturing device to capture a part of the FOV of an original image with better resolution compared with a non-zoomed image. Herein, it is assumed that in conventional image capturing devices the overall resolution is usually limited by the resolution of the detector, i.e. that the FWHM of the PSF can be smaller than the distance between two neighboring sensor pixels. 
     Accordingly, the resolution of the image capturing device may be increased by selecting a partial field of view and increasing the magnification of the optical projection system for this partial field of view. For example, ×2 optical zoom refers to a situation where all sensor pixels of the image detector capture half of the image, in each dimension, compared with that of ×1 zoom. 
     Digital still cameras (DSCs) typically employ several groups of lens elements that are mechanically shifted relative to one another in order to create a varying focal length for the whole optical system. In most common multi-use devices having cameras incorporated therein, e.g., mobile telephones, notebook computer, web cameras, etc., the optical system is a fixed-focus system, i.e. there are no moving parts. Thus, it is not possible to dynamically change the system&#39;s focal length. The most widespread zoom solution offered in camera phones is “a digital zoom,” a solution based on cropping the image down to a smaller size and interpolating the cropped image to the original size, where the missing information is completed in various ways. This solution only emulates the effect of a longer focal length and, by definition, adds no new information to the image. 
     Thus, use of digital zoom often results in an obvious loss of detail in the zoomed-in image compared to an optical zoom system. As used herein, “digital zoom” refers to signal interpolation where no additional information is actually provided, whereas “optical zoom” refers to magnification of the projected partial image, providing more information and better resolution. 
     In higher-end devices, a mechanical zoom mechanism, similar to the zoom mechanisms in DSCs, may be employed. These systems may incorporate a small motor, typically based on piezoelectric plates, which enable movement of a lens in the Z direction (along the optical axis) and thus create a varying focal length. Such a motor may be around 3 mm in diameter and more than 15 mm in length. 
     Another technology for achieving optical zoom is a liquid zoom lens. Here, the focal length of a lens changes when a pressure or electro-static force is applied on the liquid inside the lens. For example, changing the lens&#39;s focal length in order to achieve zoom may also affect the focus such that a system of at least two liquid lenses (one for zoom and one for focus correction) may be desirable. 
     SUMMARY 
     Embodiments are therefore directed to a digital camera and associated methods that substantially overcome one or more of the problems due to the limitations and disadvantages of the related art. 
     It is a feature of an embodiment to provide an imaging system having a continuous zoom using a lens system including one or more optical elements disposable into at least first and second discrete states to achieve overall a first range of zoom magnification. 
     It is another feature of an embodiment of the present invention to provide an imaging system having a variable pixel count per field angle across the image sensor, e.g., having a reduced pixel count per field angle at the image borders or a larger pixel-sensor area. 
     It is yet another feature of an embodiment to provide an imaging system realizing optical zoom by having distortion that is later on corrected digitally. 
     At least one of the above and other features and advantages of the present invention may be realized by providing as an embodiment an image capturing device comprising: a detector including a plurality of sensing pixels; and an optical system. Such an optical system may include one or more optical elements disposable into at least two states, the at least two states of the optical system (1) corresponding to at least two angular fields of view, respectively, and (2) projecting at least two distorted images onto the detector corresponding to the at least two angular fields of view, respectively. Such distortion in a given distorted image may manifest as a central portion of the given distorted image consuming (or falling upon) a significantly greater number of sensing pixels (i.e., a significantly greater pixel count) per field angle than are consumed/fallen-upon per field angle by a peripheral portion thereof. 
     For such an image capturing device as noted above: the optical system may produce a zoom magnification, Z j , falling in a first range described according to the following relation,
 
Z min ≦Z j ≦Z max  
 
with Z min  representing a minimum amount of zoom magnification, with
 
Z j  representing a j th  amount of zoom magnification, and with Z max  representing a maximum amount of zoom magnification; and wherein a pixel count, PC, per field angle remains substantially the same regardless of a particular amount of zoom magnification, as described according to the following equation,
 
PC Z     min   ≈PC Z     j   ≈PC Z     max    
 
with PC Z     min    representing a pixel count per field angle at the minimum amount of zoom magnification Z min , with PC Z     j    representing a pixel count per field angle at the j th  amount of zoom magnification Z j , and with PC Z     max    representing a pixel count per field angle at the maximum amount of zoom magnification Z max .
 
     For such an image capturing device as noted above: the optical system may have M states, where M≧2; for a g th  one among the M optical states 0≦g≦M−1, the optical system may produce, without further change from the g th  state, a second range of zoom magnification that is a subset of the first range, the second range being described in terms of the j th  amount of zoom magnification Z j  according to the following relation,
 
Z g   lower ≦Z j ≦Z g   upper ,
 
with Z g   lower  representing a lower bound upon zoom magnification in the second range, and with Z g   upper  representing an upper bound upon zoom magnification in the second range; and at least one of the following conditions may be true for the second range, a first condition of
 
Z min ≦Z g   lower  and Z g   upper &lt;Z max ,
         and a second condition of
 
Z min &lt;Z g   lower  and Z g   upper ≦Z max .
       

     For such an image capturing device as noted above: after a state change to a g+1 state, the optical system may produce, without further change from the g+1 state, a third range described in terms of the j th  amount of zoom magnification Z j  according to the following relation,
 
Z g+1   lower ≦Z j ≦Z g+1   upper ,
 
with Z g+1   lower  representing a lower-bound upon of zoom magnification in the third range, and with Z g+1   upper  representing an upper bound upon of zoom magnification in the third range; and the third range of zoom magnification for the state g+1 relates to the second range of zoom magnification for the gth state according to the following relation,
 
Z g   upper ≦Z g+1   lower .
 
     For such an image capturing device as noted above, the image capturing device may be, e.g., a camera module. And the camera module may be a component, e.g., of one of the following: a stand-alone camera; and a camera-ancillary device. 
     For such an image capturing device as noted above, at least one of the following conditions may be true: the stand-alone camera may be one of a point-and-shoot-type of camera; a single-lens-reflex type of camera; a web cam type of camera; a surveillance camera; a probe-type of camera; and a video camera; and the camera-ancillary device may be one of: a telephone; a personal data assistant device; a personal computer; an MP3 player; a kiosk; an automated teller machine; and a probe. 
     For such an image capturing device as noted above, the optical system may further include an optical zoom mechanism to dispose the one or more optical elements into the at least two states that correspond to the at least two angular fields of view, respectively. Such a zoom mechanism may include at least one of a mechanical zoom mechanism and a liquid zoom lens. 
     For such an image capturing device as noted above, a first number of sensing pixels required to realize a maximal zoom magnification {circumflex over (Z)} at a minimum resolution of the image capturing device may be less than a square of the maximal zoom magnification {circumflex over (Z)} times a second number of sensing pixels required for the minimum resolution. 
     For such an image capturing device as noted above, the first number of sensing pixels may be less than or equal to the second number of sensing pixels times 2 ln({circumflex over (Z)})+1, where {circumflex over (Z)} is the maximal zoom magnification. 
     For such an image capturing device as noted above, the first number of sensing pixels may be equal to about 1.75 times the second number of sensing pixels. 
     For such an image capturing device as noted above, the optical system may be adapted such that a point spread function in the periphery of the field of view has a full width at half maximum substantially the size of a sensing pixel. 
     For such an image capturing device as noted above, the optical system may be adapted such that an optical magnification at the center of the field of view is more than twice an optical magnification at the periphery of the field of view. 
     For such an image capturing device as noted above, the optical system may be adapted to provide the distorted image that is separable in orthogonal directions and/or that is radially symmetric. 
     Such an image capturing device as noted above may further comprise a processor adapted to manipulate electronic information output from the detector. 
     For such an image capturing device as noted above, the first number of sensing pixels may have equal pitch across the detector. 
     For such an image capturing device as noted above, the optical system may includes a plurality of lenses. Each of such lenses may be, e.g., plastic. 
     Such an image capturing device as noted above may be included within a mobile telephone that also includes radio telephony circuitry. 
     Such an image capturing device as noted above may be included within a personal computer that also includes: a processor; and a storage device. 
     At least one of the above and other features and advantages of the present invention may be realized by providing as an embodiment a method of providing continuous zoom ranges to a lens system including one or more optical elements disposable into at least first and second discrete states to achieve overall a first range of zoom magnification. Such a method may include: disposing the one or more optical elements into the first optical state; projecting a distorted image, onto a detector including a plurality of sensing pixels, corresponding to a first angular field of view; wherein distortion in a given distorted image may manifest as a significantly greater pixel count per field angle at a central portion of the given distorted image than at a peripheral portion thereof; and processing image data from the detector representing the first distorted image to provide, without changing away from the first optical state, a continuous second range of zoom magnification that is a subset of the first range, wherein a pixel count per field angle remains substantially the same regardless of a particular amount of zoom magnification. 
     For such a method as noted above, the one or more optical elements may be disposable into M optical states, M≧2, that include the first and second optical states; the first range of zoom magnification may be described according to the following relation,
 
Z min ≦Z j ≦Z max ,
 
with Z min  representing a minimum amount of zoom magnification, Z j  representing a jth amount of zoom magnification, and Z max  representing a maximum amount of zoom magnification; the M optical states correspond to at least M angular fields of view of the lens system, respectively; the first optical state represents a g th  one among the M optical states, 0≦g≦M−1, corresponding to a g th  one of the M angular fields of view, that produces a g th  distorted image on the detector; the second range of zoom magnification may be described in terms of a j th  amount of zoom magnification Z j  according to the following relation,
 
Z g   lower ≦Z j ≦Z g   upper ,
 
with Z g   lower  representing a lower bound upon zoom magnification in the second range, and with Z g   upper  representing an upper bound upon zoom magnification in the second range; and the pixel count (PC) per field angle remains substantially the same regardless of a particular amount of zoom magnification and is described according to the following equation,
 
PC Z     g     lower ≈PC Z     j   ≈PC Z     g     upper  
 
with PC Z     g     lower  representing a pixel count per field angle at the minimum amount of zoom magnification Z g   lower , with PC Z     j    representing a pixel count per field angle at the jth amount of zoom magnification Z j , and with PC Z     g     upper  representing a pixel count per field angle at the maximum amount of zoom magnification Z g   upper .
 
     For such a method as noted above, at least one of the following conditions may be true for the second range, a first condition of
 
Z min ≦Z g   lower  and Z g   upper &lt;Z max ,
 
     and a second condition of
 
Z min &lt;Z g   lower  and Z g   upper ≦Z max .
 
     For such a method as noted above, the second optical state may represent a g+1 state among the M optical states, and the method further may include: disposing the one or more optical elements into a g+1 optical state; projecting a (g+1) th  distorted image onto the detector corresponding to a (g+1) th  one of the M angular fields of view; and processing image data from the detector representing the g+1 distorted image to provide, without changing away from the g+1 optical state, a third range of zoom magnification that is a subset of the first range, the third range being described in terms of the jth amount of zoom magnification Z j  according to the following relation,
 
Z g+1   lower ≦Z j ≦Z g+1   upper ,
 
     with Z g+1   lower  representing a lower bound upon of zoom magnification in the third range, and with Z g+1   upper  representing an upper bound upon of zoom magnification in the third range; wherein the third range of zoom magnification for the g+1 state relates to the second range of zoom magnification for the g th  state according to the following relation,
 
Z g   upper ≦Z g+1   lower .
 
     For such a method as noted above, the lens system may represent a component of a camera module. 
     For such a method as noted above, the processing of image data from the detector may process a first number of sensing pixels required to realize a maximal zoom magnification at a minimum resolution, wherein the first number of sensing pixels may be less than a square of the maximal zoom magnification times a second number of sensing pixels required for the minimum resolution. 
     For such a method as noted above, the first number of sensing pixels may be less than or equal to the second number of sensing pixels times 2 ln({circumflex over (Z)})+1, where {circumflex over (Z)} is the maximal zoom magnification. 
     For such a method as noted above, the first number of sensing pixels may be equal to about 1.75 times the second number of sensing pixels. 
     For such a method as noted above, the first number of sensing pixels may be less than or equal to the second number of sensing pixels times 2 ln({circumflex over (Z)})+1, where {circumflex over (Z)} is the maximal zoom magnification. 
     For such a method as noted above, the first number of sensing pixels may be equal to about 1.75 times the second number of sensing pixels. 
     For such an image capturing device as noted above, the optical system may be adapted such that a point spread function in the periphery of the field of view has a full width at half maximum substantially the size of a sensing pixel. The optical system may be adapted such that an optical magnification at the center of the field of view is more than twice an optical magnification at the periphery of the field of view. 
     At least one of the above and other features may be realized by a method of providing continuous zoom ranges to a lens system including one or more optical elements disposable into at least first and second discrete states to achieve overall a first range of zoom magnification. Such a method may comprise: disposing the one or more optical elements into the first optical state; projecting a distorted image onto the detector corresponding to a first angular field of view; wherein distortion in a given distorted image may manifest as a significantly greater pixel count per field angle at a central portion of the given distorted image than at a peripheral portion thereof; and processing image data from the detector representing the first distorted image to provide, without changing away from the first optical state, a continuous second range of zoom magnification that is a subset of the first range, wherein a pixel count per field angle remains substantially the same regardless of a particular amount of zoom magnification. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other features and advantages will become readily apparent to those of skill in the art by describing in detail example embodiments with reference to the attached drawings, in which: 
         FIGS. 1A and 1B  illustrate a rectangular pattern and a distorted rectangular pattern having distortion that is separable in X &amp; Y coordinates, respectively; 
         FIGS. 2A and 2B  illustrate an example of a circularly symmetric pattern and a distorted circularly symmetric pattern, respectively; 
         FIGS. 3A to 3D  illustrate an object and corresponding displayed images for different zoom levels in accordance with an embodiment; 
         FIG. 4A  illustrates an example of an optical architecture in accordance with an embodiment; 
         FIG. 4B  illustrates grid distortions produced using the optical architecture of  FIG. 4A ; 
         FIG. 4C  illustrates field curvature of the optical architecture of  FIG. 4A ; 
         FIG. 4D  illustrates distortion of the optical architecture of  FIG. 4A ; 
         FIG. 4E  illustrates an example of an optical architecture in accordance with an embodiment; 
         FIG. 4F  illustrates an example of an optical architecture in accordance with an embodiment; 
         FIG. 5  illustrates a flowchart of an operation of the image processor of  FIG. 4A  in accordance with an embodiment; 
         FIG. 6  illustrates an exploded view of a digital camera in accordance with an embodiment; 
         FIG. 7A  illustrates a perspective view of a portable computer with a digital camera integrated therein in accordance with an embodiment; and 
         FIG. 7B  illustrates a front and side view of a mobile telephone with a digital camera integrated therein in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     PCT Application No. PCT/US07/19962, filed on Sep. 14, 2007, and entitled: “IMAGING SYSTEM WITH IMPROVED IMAGE QUALITY AND ASSOCIATED METHODS” is hereby incorporated by reference in it entirety. U.S. Provisional Application No. 60/825,726, filed on Sep. 15, 2006, and entitled: “DIGITAL CAMERA WITH IMPROVED IMAGE QUALITY” is hereby incorporated by reference in it entirety. 
     Embodiments will now be described more fully hereinafter with reference to the accompanying drawings; however, they may be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the embodiments to those skilled in the art. In the figures, the dimensions of layers and regions are exaggerated for clarity of illustration. Like reference numerals refer to like elements throughout. 
     In accordance with embodiments, an optical zoom may be realized using a variable-focus lens combined with post processing for distortion correction. A number of pixels used in the detector may be increased beyond a nominal resolution desired to support zoom capability. First, an initial introduction to the concept of using distortion to realize zoom will be briefly discussed. 
     Commonly assigned, co-pending PCT Application Serial No. EP2006-002864, which is hereby incorporated by reference, discloses an image capturing device including an electronic image detector having a detecting surface, an optical projection system for projecting an object within a field of view (FOV) onto the detecting surface, and a computing unit for manipulating electronic information obtained from the image detector. The projection system projects and distorts the object such that, when compared with a standard lens system, the projected image is expanded in a center region of the FOV and is compressed in a border region of the FOV. 
     As disclosed therein, the projection system may be adapted such that its point spread function (PSF) in the border region of the FOV has a FWHM corresponding essentially to the size of corresponding pixels of the image detector. In other words, this projection system may exploit the fact that resolution in the center of the (FOV) is better than at wide incident angles, i.e., the periphery of the FOV. This is due to the fact that the lens&#39;s point spread function (PSF) is broader in the FOV borders compared to the FOV center. 
     The resolution difference between the on-axis and peripheral FOV may be between about 30% and 50%. This effectively limits the observable resolution in the image borders, as compared to the image center. 
     Thus, the projection system may include fixed-focus optics having a larger magnification factor in the center of the FOV compared to the borders of the FOV. In other words, an effective focal length (EFL) of the lens is a function of incident angle such that the EFL is longer in the image center and shorter in the image borders. Such a projection system projects a distorted image, in which the central part is expanded and the borders are compressed. In other words, distortion in a given distorted image may manifest as a significantly greater pixel count per field angle at a central part of the given distorted image than at a border portion thereof. 
     Since the magnification factor in the image borders is smaller, the PSF in the image borders will become smaller too, spreading on fewer pixels on the sensor, e.g., one pixel instead of a square of four pixels. Thus, there is no over-sampling these regions, and there may be no loss of information when the PSF is smaller than the size of a pixel. In the center of the FOV, however, the magnification factor is large, which may result in better resolution. Two discernable points that would become non-discernable on the sensor due to having a PSF larger than the pixel size may be magnified to become discernable on the sensor, since each point may be captured by a different pixel. 
     The computing unit may be adapted to crop and compute a zoomed, undistorted partial image from the center region of the projected image, taking advantage of the fact that the projected image acquired by the detector has a higher pixel count per field angle at its center than at its border region. For normal pictures of the entire field of view, the center region is compressed computationally. However, if a zoomed partial image of a part of the image close to the center is to be taken, this can be done by simply cropping the partial image and compressing it less or not compressing it at all, depending on the desired zoom and the degree of distortion of the partial image. In other words, with respect to a non-zoomed image, the image is expanded and cropped so that a greater number of pixels may be used to describe the zoomed image. 
     Thus, this zoom matches the definition of optical zoom noted above. However, this optical zoom may be practically limited to about ×2 or ×3. 
     In order to realize larger zoom magnifications, embodiments are directed to exploiting the tradeoff between the number of pixels used and the zoom magnification. In other words, larger zoom magnifications may require increasing the number of pixels in the sensor to avoid information loss at the borders. A number of pixels required to support continuous zoom may be determined from discrete magnifications, where Z 1  is the largest magnification factor and Z P  is the smallest magnification factor. The number of pixels required to support these discrete zoom modes, considering N pixels to cover the whole FOV may be given by Equation 1: 
     
       
         
           
             
               
                 
                   
                     N 
                     ~ 
                   
                   = 
                   
                     N 
                     + 
                     
                       N 
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               ( 
                               
                                 
                                   Z 
                                   2 
                                 
                                 
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                             2 
                           
                         
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                     + 
                     
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                                   Z 
                                   3 
                                 
                                 
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                             2 
                           
                         
                         ) 
                       
                     
                     + 
                     … 
                     + 
                     
                       N 
                       ( 
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               
                                 Z 
                                 P 
                               
                               
                                 Z 
                                 
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                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Rearranging Equation 1, Equation 2 may be obtained as follows: 
     
       
         
           
             
               
                 
                   
                     
                       N 
                       ~ 
                     
                     N 
                   
                   = 
                   
                     P 
                     - 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         
                           P 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               Z 
                               
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                                 + 
                                 1 
                               
                             
                             
                               Z 
                               i 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Substituting Z i −dZ for Z i+1  in order to obtain a continuous function of Z results in Equation 3: 
     
       
         
           
             
               
                 
                   
                     
                       N 
                       ~ 
                     
                     N 
                   
                   = 
                   
                     P 
                     - 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         
                           P 
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                           1 
                         
                       
                       ⁢ 
                       1 
                     
                     - 
                     
                       
                         2 
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                           ⅆ 
                           Z 
                         
                       
                       
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                         i 
                       
                     
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                       2 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Discarding higher power terms, e.g., above the first term, and replacing summation with integration, Equation (4) may be obtained: 
                       N   ~     N     =       P   -     (       (     P   -   1     )     -     2   ⁢       ∫     i   =   1       Z   ^       ⁢       2   ⁢     ⅆ   Z         Z   i             )       =       2   ⁢     ln   ⁡     (     Z   ^     )         +   1               (   4   )               
where {circumflex over (Z)} is the maximal zoom magnification desired.
 
     In other words, for a standard digital camera, i.e., distortion free, with a rectangular sensor of K Mega Pixels ([MP]) producing an image of L [MP] (L&lt;K), the maximum applicable optical zoom (for L[MP] image) for the entire image may be limited to 
                 K   L       .         
In other words, for a desired optical zoom, Z, the number of mega pixels (K) needed is Z 2  times L, K=Z 2 *L.
 
     Thus, when the zoom required is ×2, a standard camera requires four times more pixels. However, in accordance with embodiments, higher zoom may be realized at the center of the image due to the distorting mechanism the optics introduces. Thus, as can be seen from Equation 4 above, only approximately 2.38 times as many pixels may be needed for an ×2 zoom. For example, using a standard 2 MP image sensor, applying ×2 zoom will require 4.77 MP for a completely lossless zoom. Relaxing demands on the quality in image borders, i.e., allowing loss of information, will decrease this number, e.g., down to about 1.75 times as many pixels for ×2 zoom. 
       FIGS. 1A and 1B  illustrate an original rectangular pattern and a projected rectangular pattern as distorted in accordance with an embodiment, respectively. In this specific example, the transformation representing the distortion is separable in the horizontal and vertical axes.  FIGS. 2A and 2B  illustrate an original circularly symmetric pattern and a projected circularly symmetric pattern as distorted in accordance with an embodiment, respectively. As can be seen therein, the patterns are expanded in a central region and compressed in a border region. Other types of distortion, e.g., anamorphic distortion, may also be used. 
       FIGS. 3A to 3D  illustrate a general process of imaging an object, shown in  FIG. 3A , in accordance with embodiments. The object is first projected and distorted by a lens system in accordance with an embodiment and captured by a high resolution, i.e., K[MP] detector, in  FIG. 3B . A corrected lower resolution, i.e., L[MP] image with a ×1 zoom is illustrated in  FIG. 3C . A corrected ×2 zoom image, having the same L[MP] resolution as the ×1 image, is shown in  FIG. 3D . 
     In other words, the optical system can produce a zoom magnification, Z j , falling in a first range described according to the following relation,
 
Z min ≦Z j ≦Z max  
 
with Z min  representing a minimum amount of zoom magnification, Z j  representing a j th  amount of zoom magnification, and Z max  representing a maximum amount of zoom magnification.
 
     Furthermore, in accordance with embodiments, it should be understood that a pixel count, PC, of a corrected image may be uniform across the corrected image, and may remain substantially the same regardless of a particular amount of zoom magnification, as described according to the following equation,
 
PC Z     min   ≈PC Z     j   ≈PC Z     max    
 
with PC Z     min    representing a pixel count per field angle at the minimum amount of zoom magnification Z min , with PC Z     j    representing a pixel count per field angle at the j th  amount of zoom magnification Z j , and with PC Z     max    representing a pixel count per field angle at the maximum amount of zoom magnification Z max .
 
     In accordance with embodiments, an optical system of an image capturing device may have M states. Such an optical system, for a g th  one among the M optical states 0≦g≦M−1, can produce, without further change from the g th  state to another state, a second range of zoom magnification that is a subset of the first range. 
     The second range may described in terms of the j th  amount of zoom magnification Z j  according to the following relation,
 
Z g   lower ≦Z j ≦Z g   upper  
 
with Z g   lower  representing a lower bound upon zoom magnification in the second range, and Z g   upper  representing an upper bound upon zoom magnification in the second range. It is noted that at least one of the following conditions can be true for the second range, namely a first condition of
 
Z min ≦Z g   lower  and Z g   upper ≦Z max ,
         and a second condition of
 
Z min &lt;Z g   lower  and Z g   upper ≦Z max .
       

     Further in accordance with embodiments, such an optical system of such an image capturing device may be operable to change states, e.g., from the g th  state to a g+1 state. After a state change to a g+1 state, the optical system can produce, without further change from the g+1 state, a third range described in terms of the j th  amount of zoom magnification Z j  according to the following relation,
 
Z g+1   lower ≦Z j ≦Z g+1   upper ,
 
     with Z g+1   lower  representing a lower bound upon of zoom magnification in the third range, and with Z g+1   upper  representing an upper bound upon of zoom magnification in the third range. The third range of zoom magnification for the state g+1 may relate to the second range of zoom magnification for the g th  state according to the following relation,
 
Z g   upper ≦Z g+1   lower .
 
There may be no overlap between the third and second ranges. Alternatively, there may be some overlap between the third and second ranges.
 
     As a result, a continuous zoom may be provided such that a user may be able to obtain, in effect, any zoom magnification between the minimum amount of zoom magnification Z min  and the maximum amount of zoom magnification Z max . For example, the second and third ranges together could span the entirety of the first range, i.e., there would be no gap between the second range and the third range. 
     Alternatively, for example, within the first/overall zoom magnification range, it may be that the user is provided with a first range for which magnification options therein are continuous and a second range for which a set of only discrete magnifications are available, or both ranges may be represented by such sets. A benefit of this would be, e.g., to reduce a computational load upon the processor by implementing at least some of the associated distortion-correction calculations via one or more look-up tables. Each such set may correspond to an optical state. 
       FIG. 4A  illustrates an example architecture of an imaging capturing device  400  including an optical system  410  for imaging an object (not shown) onto a detector  475 , i.e., an image plane, that outputs electrical signals in response to the light projected thereon. These electrical signals may be supplied to a processor  485 , which may process, store, and/or display the image. The optical system  410  may include a first lens  420  having second and third surfaces, a second lens  430  having fourth and fifth surfaces, an aperture stop  440  at a sixth surface, a third lens  450  having seventh and eight surfaces, a fourth lens  460  having ninth and tenth surfaces, an infrared (IR) filter  470  having eleventh and twelfth surfaces, all of which image the object onto the image plane  475 . The third lens  450  may be fixed in place, i.e., immovable, and yet may be capable of being disposed into at least two states. 
     For example, the third lens  450  may be a liquid zoom lens operable to change a zoom state according to control signals CTL from the processor  485 . The at least two states of the third lens  450  the imaging capturing device  400  to capture at least two angular fields of view, respectively. Each of the at least two states of the third lens  450  project at least two distorted images onto the detector  475  that correspond to the at least two angular fields of view, respectively. 
     In this particular example, the optical system  410  may have a focal length of 6 mm and an F-number of 3.4. The optical system  410  according to an embodiment may provide radial distortion having image expansion in the center and image compression at the borders for a standard FOV of ±30°. 
     Also in this particular example, the optical coefficients and the apertures of all optical surfaces along with the materials from which the lenses may be made are provided as follows: 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 Radius 
                 Thick 
                   
                 Semi- 
                   
                 Parameter 
                 Parameter 
                 Parameter 
                 Parameter 
                 Parameter 
               
               
                 # 
                 Note 
                 (mm) 
                 (mm) 
                 Medium 
                 Diameter 
                 Conic 
                 X2 
                 X4 
                 X6 
                 X8 
                 X10 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 0 
                 OBJ 
                 Infinite 
                 Infinite 
                 Air 
                 653.2 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
               
               
                 1 
                   
                 Infinite 
                 0.30 
                 Air 
                 4.0 
                 −0.932 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
               
               
                 2 
                 L1 
                 2.900 
                 1.68 
                 Plastic 
                 3.0 
                 −100.00 
                 0.000 
                 0.017 
                 −0.001 
                 0.000 
                 0.000 
               
               
                 3 
                   
                 1000 
                 0.17 
                 Plastic 
                 2.5 
                 −100.00 
                 0.000 
                 0.022 
                 −0.001 
                 0.000 
                 0.000 
               
               
                 4 
                 L2 
                 112.00 
                 1.47 
                 Plastic 
                 2.4 
                 0.455 
                 0.000 
                 −0.027 
                 −0.001 
                 0.000 
                 0.000 
               
               
                 5 
                   
                 2.700 
                 1.68 
                 Plastic 
                 1.6 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
               
               
                 6 
                 APS 
                 Infinite 
                 0.05 
                 Air 
                 0.4 
                 12.800 
                 0.000 
                 −0.067 
                 −0.049 
                 0.000 
                 0.000 
               
               
                 7 
                 L3 
                 3.266 
                 0.80 
                 Plastic 
                 0.6 
                 8.000 
                 0.000 
                 0.066 
                 0.044 
                 0.000 
                 0.000 
               
               
                 8 
                   
                 −3.045 
                 0.63 
                 Plastic 
                 0.9 
                 2.979 
                 0.000 
                 0.000 
                 0.075 
                 0.000 
                 0.000 
               
               
                 9 
                 L4 
                 −2.504 
                 1.51 
                 Plastic 
                 1.1 
                 22.188 
                 0.000 
                 −0.312 
                 0.175 
                 −0.055 
                 0.010 
               
               
                 10 
                   
                 −7.552 
                 0.39 
                 Plastic 
                 1.6 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
               
               
                 11 
                 IRF 
                 Infinite 
                 0.30 
                 N-BK7 
                 1.8 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
               
               
                 12 
                   
                 Infinite 
                 0.23 
                 Air 
                 1.9 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
               
               
                 13 
                 IMG 
                 Infinite 
                 0.00 
                   
                 1.8 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
               
            
           
         
       
     
     Here, surface  0  corresponds to the object, L 1  corresponds to the first lens  420 , L 2  corresponds to the second lens  430 , APS corresponds to the aperture stop  440 , L 3  corresponds to the third lens  450 , L 4  corresponds to the fourth lens  460 , IRF corresponds to the IR filter  460  and IMG corresponds to the detector  475 . Of course, other configurations realizing sufficient distortion may be used. 
     Plastic used to create the lenses may be any appropriate plastic, e.g., polycarbonates, such as E48R produced by Zeon Chemical Company, acrylic, PMMA, etc. While all of the lens materials in Table 1 are indicated as plastic, other suitable materials, e.g., glasses, may be used. Additionally, each lens may be made of different materials in accordance with a desired performance thereof. The lenses may be made in accordance with any appropriate method for the selected material, e.g., injection molding, glass molding, replication, wafer level manufacturing, etc. Further, the IR filter  470  may be made of suitable IR filtering materials other than N-BK7. 
       FIG. 4B  illustrates a grid distortion provided by the optical system  410 .  FIG. 4C  illustrates field curvature of the optical system  410 .  FIG. 4D  illustrates distortion of the optical system  410 . 
       FIG. 4E  illustrates an example architecture of an imaging capturing device  400 ′ including an optical system  410 ′ for imaging an object (not shown) onto a detector  475 , i.e., an image plane, that outputs electrical signals in response to the light projected thereon. The optical system  410 ′ may be similar to the optical system  410 . However, whereas the optical system  410  has the non-movable aperture stop  440  and the non-movable third lens  450 , the optical system  410 ′ may include a movable aperture stop  440 ′ and a movable third lens  450 ′, plus the imaging capturing device  400 ′ further may include moving mechanisms  490  to move the aperture stop  440 ′ and the third lens  450 ′. 
     Moving mechanisms  490  (e.g., piezoelectric plates, MEMS devices, direct drive motor with limit switches, stepper motor, motorized cam assembly, etc.) may be operable (e.g., according to control signals CTL from the processor  485 ′) to move the aperture stop  440 ′ and the third lens  450 ′ as a unit between a first position A (shown using phantom lines in  FIG. 4E ) and a second position B such that the aperture stop  440 ′ and the third lens  450 ′ may be described as exhibiting at least two discrete states. The at least two positions A and B of the aperture stop  440 ′ and the third lens  450 ′ may cause the imaging capturing device  400 ′ to capture at least two angular fields of view, respectively. Each of the at least two positions A and B of the aperture stop  440 ′ and the third lens  450 ′ may project at least two distorted images onto the detector  475  that correspond to the at least two angular fields of view, respectively. It is noted that the light beams of  FIG. 4E  have been depicted relative to the position A, not the position B. 
       FIG. 4F  illustrates an example architecture of an imaging capturing device  400 ″ including an optical system  410 ″ for imaging an object (not shown) onto a detector  475 , i.e., an image plane, that outputs electrical signals in response to the light projected thereon. The imaging capturing device  400 ″ may be similar to the imaging capturing device  400 . However, whereas the imaging capturing device  400  can change optical states via the non-moving third lens  450 , the imaging capturing device  400 ″ may include, e.g., a non-moving third lens  450 ″ (that does not change optical states), an afocal lens system  492  and moving mechanisms  490 ″. 
     An afocal lens system  492  may include: positive/converging lenses  494  &amp;  498 ; and a negative/diverging lens  496  interposed between the positive/converging lenses  494  &amp;  498 . The moving mechanisms  490 ″ may displace the negative/diverging lens  496  back and forth between the positive/converging lenses  494  &amp;  498 . It is noted that the lens  498  is optional and so is depicted with phantom lines. Also, as alternatives, other arrangements are contemplated by which one or more of the lenses  494 - 498  are moved. For example, both of the lens  494  and  496  may be moved via the moving mechanisms  490 , together or independently, the lens  494  may be moved while the lens  496  is fixed in place, etc. 
     As with moving mechanisms  490 , moving mechanisms  490 ″ (e.g., piezoelectric plates, MEMS devices, direct drive motor with limit switches, stepper motor, motorized cam assembly, etc.) may be operable (e.g., according to control signals CTL from the processor  485 ″) to move the negative/diverging lens  496  back and forth between the positive/converging lenses  494  &amp;  498  (shown using a phantom double-headed arrow in  FIG. 4F ). In this regard, e.g., the lens  496  may be described as disposable into at least two discrete states such that the imaging capturing device  400 ″ may be described as exhibiting at least two discrete states. 
     Among other things, the following should be understood: one (e.g., as in FIGS.  4 A &amp;  4 E- 4 F) or (alternatively) more lenses may be used to realize the image distorting mechanism; one (e.g., as in  FIG. 4F ) or (alternatively) more lenses may be moved/displaced to realize the optical zoom; and the one (e.g., as in  FIG. 4E ) or (alternatively) more distortion lenses can be moved/displaced. 
       FIG. 5  illustrates a flowchart of an operation that may be performed by the processor  485 . The processor  485  may include an image signal processing (ISP) chain  510  that receives an image from the detector  475 . This image may be, for example, raw Bayer data or a bitmap image. The image may be supplied to operation  530  via an input interface  520 . Operation  530  may also receive contributing pixel indices from operation  525 , which determines, for every pixel index in an undistorted output image, close neighbors from the distorted input image. Then, knowing the distortion function of the lens system  410 , and since the distortion is fixed, each pixel in the distorted image has a known and fixed magnification factor, thus operation  530  may correct the distortion. Correcting the distortion may be done using known transformations that calculate, according to the preconfigured desired zoom magnification, for every pixel in the desired undistorted image, which pixels from the distorted image contribute to it (as there might not be a pixel-to-pixel matching between the distorted and undistorted image, interpolation between several neighboring distorted pixels may be used to determine the value of the corresponding undistorted pixel). Thus, both 1× magnification, in which the center of the image simply becomes more compressed, and higher magnification factors, where a desired section is cropped from the image center and corrected without compression (or with less compression, according to the desired magnification), may both be realized. 
     For example, when zoom is set to ×1, operation  530  may be adapted to compute an undistorted picture, with fixed L[MP] resolution, of the projected object data received from the detector  475 . The detector  475  may generate data corresponding to the distorted projection of the object to be captured. For this purpose, the distortion generated by the projection system may be known, estimated or measured. When the zoom is higher, operation  530  may adapt the image and crop the desired center of the image, thus receiving the desired zoom with same L[MP] resolution. 
     Operation  530  may use any suitable interpolation method, e.g., bilinear, spline, edge-sense, bicubic spline, etc., and may output the resultant pixel values to an output interface  540 . If needed in accordance with a desired end use, image contrast of the output image may be improved in operation  550 . Then, the output image may be returned to the ISP chain  510 , where further processing may be performed on the image, e.g., denoising or compression, such as JPEG compression or GIF compression. 
     The dashed connector between the input interface  520  and operation  525  may be provided if the image capturing device is to operate in more than one image capture mode, e.g., a normal mode and a zoom mode. If so, different distortion corrections may be needed for each mode, so the input interface  520  might provide the image capture mode information to operation  525 . 
       FIG. 6  illustrates an exploded view of a digital camera  600  in which an optical zoom system in accordance with embodiments may be employed. As seen therein, the digital camera  600  may include a lens system  610  to be secured to a lens holder  620 , which, in turn, may be secured to a sensor  630 . Finally, the entire assembly may be secured to electronics  640 . 
     Portions of the preceding disclosure have been couched in terms of an image capturing device taking the form of a digital still camera (again, DSC). While such a DSC may be a stand-alone camera, it could also be a component of a larger system for which a still camera represents a secondary functionality (“still-camera-ancillary”). Examples of stand-alone cameras include a point-and-shoot-type of camera, a single-lens-reflex type of camera, a web cam type of camera, a surveillance-type of camera, a probe-type camera; etc. Examples of still-camera-ancillary devices include a telephone (e.g., wireless that also includes radio telephony circuitry), a personal data assistant device, a personal computer (e.g., also including a processor and a storage device), an MP3 player, a kiosk, an automated teller machine, a probe, a video camera; etc. 
       FIG. 7A  illustrates a perspective view of a computer  680  having the digital camera  600  integrated therein.  FIG. 7B  illustrates a front and side view of a mobile telephone  690  having the digital camera  600  integrated therein. Of course, the digital camera  600  may be integrated at other locations than those shown. 
     Thus, in accordance with embodiments, an optical zoom may be realized using a fixed-focus lens combined with post processing for distortion correction. A number of pixels used in the detector may be increased beyond a nominal resolution desired to support zoom capability. 
     As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. Further, although terms such as “first,” “second,” “third,” etc., may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer and/or section from another. Thus, a first element, component, region, layer and/or section could be termed a second element, component, region, layer and/or section without departing from the teachings of the embodiments described herein. 
     Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper,” etc., may be used herein for ease of description to describe the relationship of one element or feature to another element(s) or feature(s), as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. 
     As used herein, the singular forms “a,” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and “including” specify the presence of stated features, integers, steps, operations, elements, components, etc., but do not preclude the presence or addition thereto of one or more other features, integers, steps, operations, elements, components, groups, etc. 
     Embodiments of the present invention have been disclosed herein and, although specific terms are employed, they are used and are to be interpreted in a generic and descriptive sense only and not for purpose of limitation. While embodiments of the present invention have been described relative to a hardware implementation, the processing of present invention may be implemented in software, e.g., by an article of manufacture having a machine-accessible medium including data that, when accessed by a machine, cause the machine to undistort the data. Further, while the above discussion has assumed the pixels have an equal pitch across the detector, some or all of the compression may be realized by altering the pitch across the detector. Accordingly, it will be understood by those of ordinary skill in the art that various changes in form and details may be made without departing from the spirit and scope of the present invention as set forth in the following claims.