Patent Publication Number: US-9835821-B1

Title: Five-surface wide field-of-view compound lens and associated camera module

Description:
BACKGROUND 
     Digital camera modules are used in a variety of consumer, industrial, and scientific imaging devices to produce still images and/or video. One such imaging device is a video endoscope, a medical diagnostic instrument used for imaging a ventricle within a patient. It includes a flexible shaft capable of being inserted into the patient through an orifice thereof. The shaft has a tip that includes a light source and a camera for respectively illuminating and capturing images of part of the patient, such as a body cavity or an organ. The endoscope has a field of view by virtue of the imaging lens and image sensor of its camera module. The camera module preferably has a wide field of view (FOV) and produce quality images while being sufficiently small to enable endoscope access to small ventricles of a patient. 
     Conventional compact wide-FOV camera modules are formed of molded glass. A disadvantage of such camera modules is their cost, as conventional processes of molding glass lenses is not compatible with high-volume production methods. 
     SUMMARY OF THE INVENTION 
     In a first embodiment, a five-surface wide FOV compound lens incudes a first lens, a second lens, a third lens, a fourth lens, a fifth lens, a first biplanar substrate, and a second biplanar substrate. The first lens is plano-concave; the second, the third lens, and the fourth lens are plano-convex; the fifth lens is a plano-gull-wing lens. The first biplanar substrate is between the second lens and the third lens. The second biplanar substrate is between the fourth lens and the fifth lens. The Abbe number of the first lens is greater than the Abbe number of the second lens. 
     In a second embodiment, a five-surface wide FOV compound lens includes a first lens, a second lens, a third lens, a fourth lens, a fifth lens, a first biplanar substrate, and a second biplanar substrate. The first lens is plano-concave; the second, the third lens, and the fourth lens are plano-convex; the fifth lens is a plano-gull-wing lens. The first biplanar substrate is between the second lens and the third lens. The second biplanar substrate is between the fourth lens and the fifth lens. The Abbe number of the first lens is greater than the Abbe number of the second lens. The second lens has a focal length F 2 , and the fourth lens has a focal length F 4 , wherein the ratio F 2 /F 4  satisfies 0.65&lt;F 2 /F 4 &lt;0.95. 
     In a third embodiment, a camera module includes the five-surface wide FOV compound lens of either the first or second embodiment, and a glass substrate having a planar surface adjoining a first planar surface of the first lens, the first lens being between the top substrate and the second lens. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  illustrates a five-surface wide FOV compound lens in a use scenario, according to an embodiment. 
         FIG. 2  is a cross-sectional view of an embodiment of the five-surface wide FOV compound lens of  FIG. 1 . 
         FIG. 3  is a cross-sectional view of an imaging system that includes a first embodiment of the five-surface wide FOV compound lens of  FIG. 2 . 
         FIG. 4  shows a table of exemplary parameters of the compound lens of  FIG. 3 . 
         FIG. 5  is a plot of the longitudinal aberration of the compound lens within the imaging system of  FIG. 3 , according to the parameters of  FIG. 4 . 
         FIG. 6  is a plot of the f-theta distortion of the compound lens within the imaging system of  FIG. 3 , according to the parameters of  FIG. 4 . 
         FIG. 7  is a plot of the Petzval field curvature of the compound lens within the imaging system of  FIG. 3 , according to the parameters of  FIG. 4 . 
         FIG. 8  is a plot of the lateral color error of the compound lens within the imaging system of  FIG. 3 , according to the parameters of  FIG. 4 . 
         FIG. 9  is a cross-sectional view of an imaging system that includes a second embodiment of the five-surface wide FOV compound lens of  FIG. 2 . 
         FIG. 10  shows a table of exemplary parameters of the compound lens of  FIG. 9 . 
         FIG. 11  is a plot of the longitudinal aberration of the compound lens within the imaging system of  FIG. 9 , according to the parameters of  FIG. 10 . 
         FIG. 12  is a plot of the f-theta distortion of the compound lens within the imaging system of  FIG. 9 , according to the parameters of  FIG. 10 . 
         FIG. 13  is a plot of the Petzval field curvature of the compound lens within the imaging system of  FIG. 9 , according to the parameters of  FIG. 10 . 
         FIG. 14  is a plot of the lateral color error of the compound lens within the imaging system of  FIG. 9 , according to the parameters of  FIG. 10 . 
         FIG. 15  illustrates a camera module that includes the five-surface wide FOV compound lenses of  FIG. 2 , in an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is a cross-sectional view of a ventricle  190  that includes a lesion  192  imaged by a video endoscope  120  that includes a camera module  110  having an five-surface wide FOV compound lens  100 . 
       FIG. 2  is a cross-sectional view of a five-surface wide FOV compound lens  200 , which is an embodiment of five-surface wide FOV compound lens  100  of  FIG. 1 . Compound lens  200  includes biplanar substrates  262 - 264 , a first lens  210 , a second lens  220 , a third lens  230 , a fourth lens  240 , and a fifth lens  250 . Lens  210  has a planar surface  211  and a concave surface  212 . Lenses  220 ,  230 , and  240  have respective planar surfaces  222 ,  231 , and  242  and respective convex surfaces  221 ,  232 , and  241 . Lenses  220 ,  230 ,  240 , and  250  have respective center thicknesses  223 ,  233 ,  243 , and  253 . Substrates  262 ,  263 , and  264  have respective front surfaces  262 F,  263 F, and  264 F. 
     First lens  210  is a negative lens and second lens  220 , third lens  230 , and fourth lens  240  are each positive lenses. Lens  250  has a planar surface  251  and a gull-wing surface  252  that includes both convex and concave regions. Accordingly, lens  250  is an example of a “plano-gull-wing lens.” The five surfaces referred to by “five-surface wide FOV compound lens”  200  are the non-planar surface of each lens thereof: surfaces  212 ,  221 ,  232 ,  241 , and  252 . 
     Compound lens  200  may include a top substrate  261 , which has a front surface  261 F and a back surface  261 B. Both surfaces  261 F and  261 B may be planar surfaces. Top substrate  261  may have a width  261 W that exceeds an outer diameter  213  of lens  210 , for example, when compound lens  200  is part of a camera module and at least part of top substrate  261  forms an exterior surface of the camera module. Substrate  261  is for example formed of glass, while lens  210  may be formed of UV-curable epoxy, which is less durable than glass and is unlikely to survive a sterilization process. When compound lens  200  with top substrate  261  is incorporated into a camera module, substrate  261  protects lens  210  and provides the camera module a robust top surface (surface  261 F) which, unlike a UV-curable epoxy, can withstand processes of sterilization and also hermitically seal the camera module. 
     Compound lens  200  also may include a coverglass  265 , which has a front surface  265 F and a back surface  265 B. When included in compound lens  200 , cover glass  265  covers a pixel array of an image sensor, not shown, located at image plane  278 . The specific type of pixel array and image sensor may vary and is thus not discussed in detail herein. Alternatively, an embodiment of compound lens  200  not including coverglass  265  may be configured to cooperate with a coverglass  265  to image a scene onto an image sensor to which coverglass  265  is bonded 
     Lenses  210 ,  220 ,  230 ,  240 , and  250  may have a common optical axis  271 . Substrates  262  and  263  may be a single optical element. Without departing from the scope hereof, compound lens  200  may include an optical element between one or more of (i) substrate  262  and lens  220 , (ii) substrate  263  and lens  230 , (iii) substrate  264  and lens  240 , and (iv) substrate  264  and lens  250 . 
     Lenses  210 ,  220 ,  230 ,  240 , and  250  may be formed of a solder-reflow compatible material via a wafer-level optics replication process. A solder-reflow compatible material for example withstands surface-mount technology (SMT) reflow soldering processes occurring at temperatures exceeding 250° C., such that a camera module, including compound lens  200  and an image sensor coupled therewith, may be surface-mounted to a circuit board via a solder-reflow process. Lenses  210 ,  220 ,  230 ,  240 , and  250  may also be formed via injection molding or other methods known in the art. Alternatively, lenses  210 ,  220 ,  230 ,  240 , and  250  may be formed from glass via precision glass molding (also known as ultra-precision glass pressing) or other methods known in the art. 
     At least one of lenses  210 ,  220 ,  230 ,  240 , and  250  may be a singlet lens. At least one of lenses  210 ,  220 ,  230 ,  240 , and  250  may be a non-singlet lens without departing from the scope hereof. At least one of surfaces  212 ,  221 ,  232 ,  241 , and  252  may be an aspheric surface. At least one of surfaces  212 ,  221 ,  232 , and  241  may be a spherical surface without departing from the scope hereof. 
     Second lens  220  has a focal length F 2  and fourth lens  240  has a focal length F 4 . An embodiment of compound lens  200  has a quotient F 2 /F 4  between 0.65 and 0.95. Third lens  230  has a focal length F 3  and fifth lens  250  has a focal length F 5 . An embodiment of compound lens  200  has a quotient F 3 /F 5  satisfying 0.2&lt;|F 3 /F 5 |&lt;0.6. 
     Limiting quotient F 2 /F 4  and |F 3 /F 5 | to the aforementioned ranges balances aberrations, such as astigmatism and distortion, in an image formed by compound lens  200  such that compound lens  200  is capable of forming images of sufficient quality to meet the goals of an endoscopy procedure. 
     First lens  210 , second lens  220 , third lens  230 , fourth lens  240 , and fifth lens  250  are formed of materials having, respectively, a first Abbe number V 1 , a second Abbe number V 2 , a third Abbe number V 3 , a fourth Abbe number V 4 , and a fifth Abbe number V 5 . Herein, all refractive index values and middle wavelength of Abbe numbers correspond to λ d =587.6 nm unless otherwise specified. In compound lens  200 , Abbe number V 1  may each exceed Abbe number V 2 . In one example, Abbe number V 1  exceeds 48 and Abbe number V 2  is less than 35. These constraints on Abbe numbers allow for limiting chromatic aberration in images formed by compound lens  200 . 
     Transparent optical materials with V d &gt;48 include polymethyl methacrylate (PMMA), alicyclic acrylate (e.g., Optrez OZ1230(1)®), and cycloolefin polymers (e.g., APEL™ 5014DP, TOPAS® 5013, ZEONEX® 480R, and Arton FX4727). A lens material with V d &gt;48 may be plastic or non-plastic optical material, such as glass, without departing from the scope hereof. 
     Transparent optical materials with V d &lt;35 include PANLITE® (a brand-name polycarbonate), Udel® P-1700 (a brand-name polysulfone), and OKP-4 (a brand-name optical polyester). A lens material with V d &lt;35 may be plastic or a non-plastic optical material, such as glass, without departing from the scope hereof. 
       FIG. 2  shows compound lens  200  focusing parallel rays  280  onto an image plane  278 . Converging rays  284  exit compound lens  200  at surface  252  of lens  250  and converge at image plane  278 . Extensions of rays  280  and  284  into compound lens  200  intersect at a principal plane  274 .  FIG. 2  shows principal plane  274  intersecting optical axis  271  between lens  250  and image plane  278  for illustrative purposes only. Principal plane  274  may intersect optical axis  271  at different locations without departing from the scope hereof. 
     Compound lens  200  may include an aperture stop  225  between lenses  220  and  230 . Aperture stop  225  is, for example, an opaque coating between substrates  262  and  263 . Including two substrates  262  and  263  between lenses  220  and  230  enables positioning of aperture stop  225  in compound lens  200  to maximize symmetry of compound lens  200  about the aperture stop plane, which, per the symmetric principle known in lens design, minimizes aberrations such as coma, distortion, and lateral color. 
     Compound lens  200  has a FOV  2   a , which corresponds to two times a maximum angle α of an incident ray on its front surface with respect to optical axis  271  that propagates through aperture stop  225  and reaches image plane  278 . The front surface is for example surface  261 F or surface  211 . 
     Compound lens  200  has an effective focal length f eff , between principal plane  274  and image plane  278 . Compound lens  200  has a total track length T between front surface  261 F and image plane  278 . Embodiments of compound lens  200  may have a quotient T/f eff  between 5.0 and 5.8. Limiting the quotient T/f eff  to greater than 5.0 enables compound lens  200  to have a wide field of view. Limiting the quotient T/f eff  to less than 5.8 limits the length of compound lens  200 . 
     First lens  210  has a diameter D 1 , and a sag S 1 . Embodiments of compound lens  200  may have a quotient D 1 /S 1  between 2.5 and 3.2. The lower limit of D 1 /S 1  enables compound lens  200  to have a wide field of view, while the upper limit ensures that lens  210  has dimensions attainable by wafer-level lens manufacturing processes. 
     Five-Surface Wide Field-of-View Compound Lens, Example 1 
       FIG. 3  is a cross-sectional view of a five-surface wide FOV compound lens  300 , which is an embodiment of five-surface wide FOV compound lens  200 . Compound lens  300  includes top substrate  261 , substrates  262 ( 1 )- 264 ( 1 ), a first lens  210 ( 1 ), a second lens  220 ( 1 ), an aperture stop  225 ( 1 ) a third lens  230 ( 1 ), a fourth lens  240 ( 1 ), and a fifth lens  250 ( 1 ). Lenses  210 ( 1 ),  220 ( 1 ),  230 ( 1 ), and  240 ( 1 ) have respective planar surfaces  211 ( 1 ),  222 ( 1 ),  231 ( 1 ),  242 ( 1 ) and  251 ( 1 ) and respective non-planar surfaces  212 ( 1 ),  221 ( 1 ),  232 ( 1 ), and  241 ( 1 ). Lens  250 ( 1 ) has a planar surface  251 ( 1 ) and a gull-wing surface  252 ( 1 ). Lenses  210 ( 1 ),  220 ( 1 ),  230 ( 1 ),  240 ( 1 ), and  250 ( 1 ) are coaxial with a common optical axis  271 ( 1 ). Compound lens  300  may also include coverglass  265 . 
     Herein, a figure element denoted by a reference numeral suffixed by a parenthetical numeral indicates an example of the element indicated by the reference numeral. For example, lens  210 ( 1 ) of  FIG. 3  is an example of lens  210  of  FIG. 2 . 
       FIG. 4  shows a table  400  of exemplary parameters of each surface of compound lens  300  as well as cover glass  265 , with which compound lens  300  is configured to cooperate, or which is included in compound lens  300 . Table  400  includes columns  404 ,  406 ,  408 ,  410 ,  412 , and  421 - 426 . Surface column  421  denotes surfaces of top substrate  261 , substrates  262 ( 1 )- 264 ( 1 ), cover glass  265 , lenses  210 ( 1 ),  220 ( 1 ),  230 ( 1 ),  240 ( 1 ), and  250 ( 1 ) of  FIG. 3 . 
     Column  423  includes center thicknesses of top substrate  261 , substrates  262 ( 1 )- 264 ( 1 ), cover glass  265 , and lenses  210 ( 1 ),  220 ( 1 ),  230 ( 1 ),  240 ( 1 ), and  250 ( 1 ). A thickness value in column  423  in a row denoting a specific surface indicates the on-axis distance between that specific surface and the next surface of the row beneath. For example, on optical axis  271 ( 1 ), surfaces  261 F and  211 ( 1 ) are separated by 0.4000 mm, surfaces  211 ( 1 ) and  212 ( 1 ) are separated by 0.0200 mm, and surfaces  212 ( 1 ) and  221 ( 1 ) are separated by 0.2723 mm. Surface  265 B is 0.045 mm from image plane  278 ( 1 ). Aperture stop  225 ( 1 ) has a diameter  225 D( 1 ) equal to 0.24 mm. 
     It should be appreciated that compound lens  300  need not be configured to cooperate with cover glass  265 , in which case parameters of compound lens  300  may be reoptimized to form an image at an image plane absent cover glass  265 . Likewise, compound lens  300  may be configured to cooperate with a cover glass  265  of thickness or material different from that specified in table  400 , in which case parameters of compound lens  300  may be reoptimized accordingly to form an image at an image plane. 
     Surfaces  211 ( 1 ),  222 ( 1 ),  231 ( 1 ), and  242 ( 1 ) are defined by surface sag z sag , shown in Eqn. 1. 
     
       
         
           
             
               
                 
                   
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     In Eqn. 1, z sag  is a function of radial coordinate r, where directions z and r are shown in coordinate axes  272 ,  FIG. 2 . In Eqn. 1, the parameter c is the reciprocal of the surface radius of curvature r C : 
             c   =       1     r   c       .           
Column  422  of  FIG. 4  lists r C  values for surfaces  212 ( 1 ),  222 ( 1 ),  232 ( 1 ),  241 ( 1 ), and  252 ( 1 ). Parameter k denotes the conic constant, shown in column  426 . Columns  404 ,  406 ,  408 ,  410 , and  412  contain values of aspheric coefficients α 4 , α 6 , α 8 , α 10 , and α 12  respectively. The units of quantities in table  400  are consistent with z sag  in Eqn. 1 being expressed in millimeters.
 
     Column  424  lists values material refractive index n d  at free-space wavelength λ d =587.6 nm, and column  425  lists the corresponding Abbe numbers V d . The refractive index and Abbe numbers corresponding to a surface characterize the material between the surface and the surface in the row beneath. For example, the refractive index and Abbe number between surface  261 F and  211 ( 1 ) are 1.517 and 63.00, respectively, and the refractive index and Abbe number between surface  211 ( 1 ) and  212 ( 1 ) are 1.511 and 57.00, respectively. Non-dispersive materials have an undefined Abbe number, denoted by “--” in column  425 . 
     Compound lens  300  has a working f-number equal to 3.2 and a field of view 2α 1 =140 degrees. At free-space wavelength λ=587.6 nm, compound lens  300  has an effective focal length f eff1 =0.495 mm between principal plane  274 ( 1 ) and image plane  278 ( 1 ). 
     First lens  210 ( 1 ) has a D 1 (1)=0.990, and a sag S 1 (1)=0.330 mm, which corresponds to a ratio D 1 (1)/S 1 (1)=3.0. Compound lens  300  has a total track length T 1 =2.612 mm between surface  261 F and image plane  278 ( 1 ). The ratio of total track length to effective focal length is T 1 /f eff1 =5.3. 
     Second lens  220 ( 1 ) and fourth lens  240 ( 1 ) have focal lengths F 2  and F 4  respectively, which may be approximated using the lensmaker&#39;s equation. Referring to second lens  220 ( 1 ), object-side surface  221 ( 1 ) has a 0.4111-mm radius of curvature, and image-side surface  222 ( 1 ) is has an infinite radius of curvature. Using these radii of curvature, center thickness  223 ( 1 ), and n d =1.59, the lensmaker&#39;s equation yields F 2 ≈0.70 mm. Referring to fourth lens  240 ( 1 ), object-side surface  241 ( 1 ) has a 0.4513-mm radius of curvature, and image-side surface  242 ( 1 ) has an infinite radius of curvature. Using these radii of curvature, center thickness  243 ( 1 ), and n d =1.5110, the lensmaker&#39;s equation yields F 4 ≈0.88 mm. Ratio F 2 /F 4  is approximately 0.79. 
     Third lens  230 ( 1 ) and fifth lens  250 ( 1 ) have focal lengths F 3  and F 5  respectively, which may be approximated using the lensmaker&#39;s equation. Referring to third lens  230 ( 1 ), object-side surface  231 ( 1 ) has an infinite radius of curvature and image-side surface  232 ( 1 ) has a −4.9245-mm radius of curvature. Using these radii of curvature, center thickness  233 ( 1 ), and n d =1.511, the lensmaker&#39;s equation yields F 3 ≈9.64 mm. Referring to fifth lens  250 ( 1 ), object-side surface  251 ( 1 ) has an infinite radius of curvature and image-side surface  252 ( 1 ) has a −9.7369-mm radius of curvature. Using these radii of curvature, center thickness  253 ( 1 ), and n d =1.52, the lensmaker&#39;s equation yields F 5 ≈18.73 mm. Ratio |F 3 /F 5 | is approximately 0.52. 
       FIGS. 5-8  are plots of longitudinal aberration, f-theta distortion, field curvature, and lateral color, respectively, of compound lens  300  as computed by Zemax®. 
       FIG. 5  is a plot of the longitudinal aberration of compound lens  300 . In  FIG. 5 , longitudinal aberration is plotted in units of millimeters as a function of normalized radial coordinate r/r p , where r p =0.0807 mm is the maximum entrance pupil radius. Longitudinal aberration curves  548 ,  558 , and  565  are computed at the blue, green, and red Fraunhofer F-, d- and C-spectral lines: λ F =486.1 nm, λ d =587.6 nm, and λ C =656.3 nm respectively. 
       FIG. 6  is a plot of the f-theta distortion, versus field angle, of compound lens  300 . The maximum field angle plotted in  FIG. 6  is α 1 =70.117°, which is half of lens  300 &#39;s the field of view. Distortion curves  648 ,  658 , and  665  are computed at wavelengths λ F , λ d , and λ C , respectively. 
       FIG. 7  is a plot of the Petzval field curvature, as a function of field angle, of compound lens  300 . The field curvature is plotted for field angles between zero and α 1 . Field curvature  748 -S and field curvature  748 -T (solid lines) are computed at wavelength λ F  in the sagittal and tangential planes, respectively. Field curvature  758 -S and field curvature  758 -T (short-dashed lines) are computed at wavelength λ d  in the sagittal and tangential planes, respectively. Field curvature  768 -S and field curvature  768 -T (long-dashed lines) correspond to field curvature at wavelength λ C  in the sagittal and tangential planes, respectively. 
       FIG. 8  is a plot of the lateral color error, also known as transverse chromatic aberration, versus field height of compound lens  300 . Field height ranges from h min =0 (on-axis) to h max =0.850 mm in image plane  278 ( 1 ). Lateral color is referenced to λ d , and hence the lateral color for λ d  is zero for all field heights. Lateral color  848  is computed at wavelength λ F . Lateral color  865  is computed at wavelength λ C . 
     Five-Surface Wide Field-of-View Compound Lens, Example 2 
       FIG. 9  is a cross-sectional view of a five-surface wide FOV compound lens  900 . Compound lens  900  is an embodiment of five-surface wide FOV compound lens  200 . Compound lens  900  includes top substrate  261 , substrates  262 ( 2 )- 264 ( 2 ), a first lens  210 ( 2 ), a second lens  220 ( 2 ), an aperture stop  225 ( 2 ), a third lens  230 ( 2 ), a fourth lens  240 ( 2 ), and a fifth lens  250 ( 2 ). Lenses  210 ( 2 ),  220 ( 2 ),  230 ( 2 ), and  240 ( 2 ) have respective planar surfaces  211 ( 2 ),  222 ( 2 ),  231 ( 2 ),  242 ( 2 ) and  251 ( 2 ) and respective non-planar surfaces  212 ( 2 ),  221 ( 2 ),  232 ( 2 ), and  241 ( 2 ). Lens  250 ( 2 ) has a planar surface  251 ( 2 ) and a gull-wing surface  252 ( 2 ). Lenses  210 ( 2 ),  220 ( 2 ),  230 ( 2 ),  240 ( 2 ), and  250 ( 2 ) are coaxial with a common optical axis  271 ( 2 ). Compound lens  900  may also include coverglass  265 . 
       FIG. 10  shows a table  1000  of exemplary parameters of each surface of compound lens  900  as well as cover glass  265 , with which compound lens  900  is configured to cooperate, or which is included in compound lens  900 . Table  1000  includes columns  1004 ,  1006 ,  1008 ,  1010 ,  1012 , and  1021 - 1026 . Surface column  1021  denotes surfaces of top substrate  261 , substrates  262 ( 2 )- 264 ( 2 ), cover glass  265 , lenses  210 ( 2 ),  220 ( 2 ),  230 ( 2 ),  240 ( 2 ), and  250 ( 2 ) of  FIG. 9 . Column  1023  includes thickness values, in millimeters, between adjacent surfaces of compound lens  900  on optical axis  271 ( 2 ). Column  1023  includes center thicknesses of top substrate  261 , substrates  262 ( 2 )- 264 ( 2 ), cover glass  265 , and lenses  210 ( 2 ),  220 ( 2 ),  230 ( 2 ),  240 ( 2 ), and  250 ( 2 ). A thickness value in column  1023  in a row denoting a specific surface indicates the on-axis distance between that specific surface and the next surface. Surface  265 B is 0.045 mm from image plane  278 ( 2 ). Aperture stop  225 ( 2 ) has a diameter  225 D( 2 ) equal to 0.204 mm. 
     It should be appreciated that compound lens  900  need not be configured to cooperate with cover glass  265 , in which case parameters of compound lens  900  may be reoptimized to form an image at an image plane absent cover glass  265 . Likewise, compound lens  900  may be configured to cooperate with a cover glass  265  of thickness or material different from that specified in table  1000 , in which case parameters of compound lens  900  may be reoptimized accordingly to form an image at an image plane. 
     Surfaces  211 ( 2 ),  222 ( 2 ),  231 ( 2 ), and  242 ( 2 ) are defined by surface sag z sag , shown in Eqn. 1. Column  1022  of  FIG. 10  lists r c  values for surfaces  212 ( 2 ),  222 ( 2 ),  232 ( 2 ),  241 ( 2 ), and  252 ( 2 ). Parameter k denotes the conic constant, shown in column  1026 . Columns  1004 ,  1006 ,  1008 ,  1010 , and  1012  contain values of aspheric coefficients α 4 , α 6 , α 8 , α 10 , and α 12  respectively. The units of quantities in table  1000  are consistent with z sag  in Eqn. 1 being expressed in millimeters. Column  1024  lists values material refractive index n d  at free-space wavelength λ d =587.6 nm, and column  1025  lists the corresponding Abbe numbers V d . 
     Compound lens  900  has a working f-number equal to 3.6 and a field of view 2α 2 =160 degrees. At free-space wavelength λ=587.6 nm, compound lens  300  has an effective focal length f eff2 =0.450 mm between principal plane  274 ( 2 ) and image plane  278 ( 2 ). 
     First lens  210 ( 2 ) has a D 1 (2)=0.994, and a sag S 1 (2)=0.344 mm, which corresponds to a ratio D 1 (2)/S 1 (2)=2.9. Compound lens  900  has a total track length T 2 =2.549 mm between surface  261 F and image plane  278 ( 2 ). The ratio of total track length to effective focal length is T 2 /f eff2 =5.7. 
     Second lens  220 ( 2 ) and fourth lens  240 ( 2 ) have focal lengths F 2  and F 4  respectively, which may be approximated using the lensmaker&#39;s equation. Referring to second lens  220 ( 2 ), object-side surface  221 ( 2 ) has a 0.4427-mm radius of curvature, and image-side surface  222 ( 2 ) is has an infinite radius of curvature. Using these radii of curvature, center thickness  223 ( 2 ), and n d =1.61, the lensmaker&#39;s equation yields F 2 ≈0.73 mm. Referring to fourth lens  240 ( 2 ), object-side surface  241 ( 2 ) has a 0.4471-mm radius of curvature, and image-side surface  242 ( 2 ) has an infinite radius of curvature. Using these radii of curvature, center thickness  243 ( 2 ), and n d =1.5110, the lensmaker&#39;s equation yields F 4 ≈0.88 mm. Ratio F 2 /F 4  is approximately 0.83. 
     Third lens  230 ( 2 ) and fifth lens  250 ( 2 ) have focal lengths F 3  and F 5  respectively, which may be approximated using the lensmaker&#39;s equation. Referring to third lens  230 ( 2 ), object-side surface  231 ( 2 ) has an infinite radius of curvature and image-side surface  232 ( 2 ) has a −3.0168-mm radius of curvature. Using these radii of curvature, center thickness  233 ( 2 ), and n d =1.511, the lensmaker&#39;s equation yields F 3 ≈5.90 mm. Referring to fifth lens  250 ( 2 ), object-side surface  251 ( 2 ) has an infinite radius of curvature and image-side surface  252 ( 2 ) has a −10.2444-mm radius of curvature. Using these radii of curvature, center thickness  253 ( 2 ), and n d =1.52, the lensmaker&#39;s equation yields F 5 ≈19.70 mm. Ratio |F 3 /F 5 | is approximately 0.30. 
       FIGS. 11-14  are plots of longitudinal aberration, f-theta distortion, field curvature, and lateral color, respectively, of compound lens  900  as computed by Zemax®. 
       FIG. 11  is a plot of the longitudinal aberration of compound lens  900 . In  FIG. 11 , longitudinal aberration is plotted in units of millimeters as a function of normalized radial coordinate r/r p , where r p =0.0807 mm is the maximum entrance pupil radius. Longitudinal aberration curves  1148 ,  1158 , and  1165  are computed at λ F , λ d , and λ C  respectively. 
       FIG. 12  is a plot of the f-theta distortion, versus field angle, of compound lens  900 . The maximum field angle plotted in  FIG. 13  is α 2 =80.008°, which is half of lens  900 &#39;s the field of view. Distortion curves  1248 ,  1258 , and  1265  are computed at wavelengths λ F , λ d , and λ C , respectively. 
       FIG. 13  is a plot of the Petzval field curvature, as a function of field angle, of compound lens  900 . The field curvature is plotted for field angles between zero and α 2 . Field curvature  1348 -S and field curvature  1348 -T (solid lines) are computed at wavelength λ F  in the sagittal and tangential planes, respectively. Field curvature  1358 -S and field curvature  1358 -T (short-dashed lines) are computed at wavelength λ d  in the sagittal and tangential planes, respectively. Field curvature  1365 -S and field curvature  1365 -T (long-dashed lines) correspond to field curvature at wavelength λ C  in the sagittal and tangential planes, respectively. 
       FIG. 14  is a plot of the lateral color error, also known as transverse chromatic aberration, versus field height of compound lens  900 . Field height ranges from h min =0 (on-axis) to h max =0.850 mm in image plane  278 ( 2 ). Lateral color is referenced to λ d , and hence the lateral color for λ d  is zero for all field heights. Lateral color  1448  is computed at wavelength λ F . Lateral color  1465  is computed at wavelength λ C . 
       FIG. 15  is a perspective view of a camera module  1500  that includes five-surface wide FOV compound lens  200 . Camera module  1500  also includes a housing  1590 , an image sensor  1520 , a top window  1561 , and optionally a ball-grid array  1510  electrically connected to image sensor  1520 . Top window  1561  is an example of top substrate  261 , and has a top surface  1561 F and a bottom surface  1561 B. Top surface  1561 F is an example of surface  261 F, and hence may be planar. Housing  1590  is for example formed of metal or plastic. Image sensor  1520  is for example a complementary metal-oxide-semiconductor (CMOS) image sensor. 
     Camera module  1500  has a top surface  1500 T, at least part of which includes top surface  1561 F. Top window  1561  may be bonded to housing  1590 . For example, housing  1590  may include a top ridge  1591  having a bottom surface, facing image sensor  1520 , to which top surface  1561 F may be bonded. Top ridge  1591  has a top surface  1591 T corresponding to a top exterior surface  1590 T of housing  1590 , such that top surface  1500 T includes both top exterior surface  1590 T and the region of top surface  1561 F within an aperture  1591 A formed by top ridge  1591 . Alternatively, housing  1590  includes a ridge  1580  therein to which top window  1561  may be bonded, i.e., such that bottom surface  1561 B is on ridge  1580 . 
     Top window  1561  protects lens  200  and provides camera module  1500  with robust top surface (surface  1561 F) having material hardness (e.g., scratch hardness) that exceeds that of UV-curable epoxy, which may constitute component lenses of lens  200  and can withstand processes of sterilization and also hermitically seal camera module  1500 . Camera module  1500  may be hermitically sealed, for example, for use in medical applications such as endoscopy. 
     Combinations of Features: 
     Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following examples illustrate some possible, non-limiting combinations: 
     (A1) A five-surface wide FOV compound lens includes: a first lens and, in order of increasing distance therefrom and on a same side thereof, a second lens, a third lens, a fourth lens, and a fifth lens. The first, second, third, fourth, and fifth lens are coaxial. The compound lens also includes (i) a first biplanar substrate between the second lens and the third lens and (ii) a second biplanar substrate between the fourth lens and the fifth lens. The first lens is a negative lens. The second, third, and fourth lenses are each positive lenses. The fifth lens is a plano-gull-wing lens. 
     (A2) In the lens denoted by (A1), the first lens may have a first Abbe number that exceeds a second Abbe number of the second lens. 
     (A3) In the lens denoted by (A2), the first Abbe number may exceed 48 and the second Abbe number may be less than 35. 
     (A4) In any lens denoted by one of (A1) through (A3) in which the second lens has a focal length F 2 , the third lens has a focal length F 3 , the fourth lens has a focal length F 4 , and the fifth lens has a focal length F 5 , the ratio F 2 /F 4  may satisfy 0.65&lt;F 2 /F 4 &lt;0.95, and the absolute value of ratio F 3 /F 5  may satisfy 0.2&lt;|F 3 /F 5 |&lt;0.6. 
     (A5) In any lens denoted by one of (A1) through (A4), in which the first lens has a diameter D 1 , and a sag S 1 , the ratio D 1 /S 1  may satisfy 2.5&lt;D 1 /S 1 &lt;3.2. 
     (A6) In any lens denoted by one of (A1) through (A5), the first lens may have a planar surface and a concave surface opposite the planar surface and facing the second lens. 
     (A7) Any lens denoted by one of (A1) through (A6), may have an effective focal length between 0.40 millimeters and 0.55 millimeters. 
     (A8) Any lens denoted by one of (A1) through (A7), may have an f-number between 3.0 and 4.0. 
     (A9) Any lens denoted by one of (A1) through (A8) may further include a top substrate having a planar surface adjoining a first planar surface of the first lens, in which the first lens is between the top substrate and the second lens. 
     (A10) Any lens denoted by one of (A1) through (A9) may have a field of view exceeding 155 degrees. 
     (A11) Any lens denoted by one of (A1) through (A10) may have an effective focal length f eff  such that the compound lens forms an image at an image plane located a distance T from a front surface of the top substrate opposite the first lens, and the ratio T/f eff  may satisfy 5.0&lt;T/f eff &lt;5.8. 
     (A12) A camera module includes a housing and any lens denoted by one of (A9) through (A11). The camera module has a top substrate, formed of glass, that has a second planar surface opposite the planar surface, at least part of the second planar surface being an exterior surface of the camera module. 
     (A13) In the camera module denoted by (A12), the top substrate may provide part of a hermetic seal for the camera module. 
     Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall there between.