Patent Publication Number: US-2007121220-A1

Title: Method for designing and fabricating optical lens unit

Description:
BACKGROUND OF INVENTION  
      1. Field of the Invention  
      The present invention relates to a method for designing and fabricating optical lens unit, more particularly a method that can change the image height of optical lens unit without redesigning the mold assembly for the fabrication of optical lens.  
      2. Description of the Prior Art  
      As shown in  FIG. 1 , a standard camera  1  comprises a lens unit  11 , a sensor  12  and a focusing mechanism (not shown in the figure). The lens unit  11  forms an image on sensor  12  (as shown in  FIG. 1 ) by refracting the light rays from an object. The sensor  12  then converts the refracted light rays into electric signal for reading by a control unit (not shown in  FIG. 1 ) and for it to carry out image processing.  
      In the design and fabrication processes of lens unit  11 , customers oftentimes specify a special size for sensor  12 , and at the same time a specific field of view (which is typically 60 degrees) for the camera  1 . In such case, the lens designer and/or maker needs to design lens unit  11  according to the sensor  12  size and field of view instructed by customer. Sensors  12  presently available on the market come in a variety of sizes, and continue to evolve. The design and fabrication of lens unit  11  would take tremendous amount of manpower and money to meet customer specifications that results in waste of resources.  
      U.S. Pat. No. 6,859,233 and U.S. Pat. No. 6,301,061 disclose a lens that achieves focusing or zooming by switching lens of different thickness to optical path. But the prior art just mentioned uses “assembled” lens unit instead of disclosing the method for designing and fabricating a lens unit. In addition, prior art discloses technology that adjusts the focal length or magnifying power of lens unit on the “same” sensor, not technology that designs lens unit based on sensor of different sizes. In the focusing or zooming process, the prior art only considers the adjustment of lens thickness, but not the corresponding change of air gap between lenses. Moreover, the prior art did not disclose how to design and fabricate the lenses in lens unit to provide proper lens thickness and air gap. According to the prior art mentioned, it becomes necessary to redesign a brand new lens unit if one desires to change the size of sensor (e.g. changing the image height), which results in waste of resources.  
     SUMMARY OF INVENTION  
      The object of the present invention is to provide a method for designing and fabricating a lens unit, which allows changing the image height of lens unit without redesigning the mold assembly for the production of optical lens.  
      In one preferred embodiment according to the present invention, a method for designing and fabricating lens unit comprises the steps of: establishing a set of known parameter values of a properly focused lens unit; inputting an image height desired; calculating a corresponding lens wall thickness and an air gap based on the image height input; and designing and fabricating a new lens unit based on the calculated lens wall thickness and air gap to accord with the image height inputted. As such, the present invention only needs to alter the wall thickness and air gap of optical lens to obtain different image heights. The alteration of wall thickness is achieved by adjusting the space between the male and female molds of the mold assembly; the alteration of air gap is achieved by providing a pad of predetermined thickness on the optical lens without the need to redesign the mold assembly for the fabrication of optical lens. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The details of the present invention will be more readily understood from a detailed description of the preferred embodiments taken in conjunction with the following figures.  
       FIG. 1  is a diagram showing the focusing principle of conventional lens.  
       FIG. 2  depicts the method for designing and fabricating a lens unit according to a preferred embodiment of the invention.  
       FIG. 3  is a diagram showing a known lens unit having a first image height according to the method for designing and fabricating lens unit of the invention.  
       FIG. 4  is a diagram showing a new lens unit having a second image height according to the method for designing and fabricating lens unit of the invention.  
       FIG. 5A  and  FIG. 5B  are diagrams showing changing the lens wall thickness by shifting the gap between the male and female molds in a method for designing and fabricating lens unit according to the invention; wherein  FIG. 5A  is a diagram showing the female mold before shifting, while  FIG. 5B  is a diagram showing the female mold after shifting. 
    
    
     DETAILED DESCRIPTION  
      The main principle of the method for designing and fabricating optical lens unit according to the present invention is to achieve image height adjustment to meet the customer specification of sensor size by changing the wall thickness and air gap of at least one lens in a lens unit without changing the field of view. Because changing the lens wall thickness may be achieved by adjusting the gap between the male and female parts of the mold assembly, while changing the air gap may be achieved by disposing a pad with predetermined thickness on the lens, there is no need to redesign the mold assembly for the production of lens. As such, the designer and manufacturer of optical lens unit can quickly design and fabricate optical lens unit according to customer specifications using available equipment and techniques. So the present invention offers the advantage of effective use of resources, and saves time, resources, and costs.  
       FIGS. 2-4  disclose a method for designing and fabricating optical lens unit according to a preferred embodiment of the invention.  FIG. 2  shows the flow process of the method for designing and fabricating optical lens unit according to a preferred embodiment of the invention.  FIG. 3  is a diagram showing a known lens unit having a first image height according to the method for designing and fabricating lens unit of the invention.  FIG. 4  is a diagram showing a known new lens unit having a second image height according to the method for designing and fabricating lens unit of the invention.  
      As shown in  FIG. 2 , the method for designing and fabricating optical lens unit of the invention comprises the steps of:  
      Step  21 : Establishing a set of known parameter values of a properly focused lens unit. Optical lens unit designers and manufacturers can employ the known parameter values of an existing first lens unit  30  that has been properly focused to create a set of optical functional equations. In this embodiment as shown in  FIG. 3 , the known first lens unit  30  consists of three optical lenses  31 ,  32 ,  33 . The set of functional equations contains a plurality of parameter values to manifest the corresponding relations between parameters, and said plurality of parameter values contain at least an image height  34  (first image height), an air gap  351 ,  352 ,  353  (first air gap) anterior and posterior to the lens, and a wall thickness of the lenses  311 ,  321 ,  331  (first lens wall thickness), refractive index of lens material, and lens curvature.  
      Step  22 : Inputting a new image height  34   a  desired. The new image height  34   a  (second image height) desired is determined based on customer&#39;s instructions for the field of view θ of new lens unit  30   a  and sensor size.  
      Step  23 : Calculating the corresponding lens wall thickness  311   a ,  321   a ,  331   a  and air gap  351   a ,  352   a ,  353   a  according to the image height  34   a  input. Inputting the new image height  34   a  (second image height) into the functional equations and calculating the new parameter values corresponding to the new image height  34   a . Those new parameter values contain at least a new lens wall thickness (one or more of new lens wall thickness  311   a ,  321   a  and  331   a , called second lens wall thickness) of a lens (one or more of lens  31   a ,  32   a , and  33   a ) and a new air gap (one or more of air gap  351   a ,  352   a , and  353   a , called second air gap). Other parameter values, including the number of lens  31   a ,  32   a ,  33   a , and refractive index of lens material and curvature of lens  31   a ,  32   a ,  33   a  stay unchanged, that is, identical to the known parameter values of the properly focused first lens unit  30 .  
      Step  24 : Designing and fabricating a new lens unit  30   a  (second lens unit) as shown in  FIG. 4  based on the new lens wall thickness  311   a ,  321   a ,  331   a  (second lens wall thickness) and new air gap  351   a ,  352   a ,  353   a  (second air gap) to accord with the new image height  34   a  inputted (second image height). In this embodiment, the known lens unit and the new lens unit have the same field of view θ, as well as the same number of lens, refractive index of lens material, and lens curvature.  
       FIGS. 5A and 5B  are diagrams showing changing the lens wall thickness by shifting the gap between the male and female molds according to the method for designing and fabricating lens unit of the invention. As shown in  FIG. 5A , lenses  31 ,  32 ,  33 ,  31   a ,  32   a , and  33   a  are generally fabricated by feeding a photopermeable material having predetermined refractive index into a mold assembly  40  through an inlet  41  and curing the material. The mold assembly  40  typically consists of a male mold frame  42 , a male mold  43  disposed inside the male mold frame  42 , a female mold frame  44 , and a female mold  45  disposed inside the female mold frame  44 . The male mold  43  and female mold  45  have respectively a predetermined curve design for the formation of optical lens with a predetermined curvature. The mold assembly  40  is formed with an accommodation space by closely matching the mold frames  42 ,  44  and molds  43 ,  45 . Subsequently, photopermeable material with predetermined refractive index is fed into the accommodation space of the mold assembly  40  via the inlet  41 . After the photopermeable material is cured, the mold assembly  40  is opened and an optical lens  51  is fabricated after the flashes are removed. The method for designing and fabricating lens unit according to the invention can achieve the objective of image height adjustment by changing the lens wall thickness without changing the lens curvature. Thus as shown in  FIG. 5B , the method disclosed herein simply needs to adjust the gap between male mold and female mold (e.g. shifting the position of female mold  45  in female mold frame  44 ) to fabricate a new lens  51   a  that has a second lens wall thickness without the need to redesign a new mold assembly  40 . In addition, a lens unit that conforms to the second air gap is fabricated by simply disposing a pad of predetermined thickness anterior or posterior to each lens to obtain the second air gap. As such, under the method disclosed herein, the designer and manufacturer of optical lens unit can quickly design and fabricate optical lens unit according to customer specifications using available equipment and techniques. So the present invention offers the advantage of effective use of resources, and saves time, resources, and costs.  
      The lens unit design method and the application of its optical functional equations are described using the known and new lens units shown in  FIG. 3  and  FIG. 4  as examples:  
      (A) Description of Lens Equations  
      First the basic optical functions of lens are introduced.  
      (a1) Single Lens:  
      For single lens, its optical function can be expressed as follows: 
 
 p= 1 /f =( N− 1)((1 /R 1−1 /R 2)−( T/N )(1 /R 1 R 2))  (Eq. 1) 
 
 where f: Lens focal length 
          N: Refractive index of lens material     R 1 , R 2 : Radius of curvature of the front and back surfaces of lens     T: Material thickness        

      (a2) Lens Combination:  
      For a lens unit made of two optical lenses, its optical function can be expressed as follows: 
 
 P= 1 /F =(1 /f 1)+(1 /f 2)−( T/N )/ f 1 f 2  (Eq. 2) 
 
      where F: Effective focal length (EFL) of lens 
          f 1 , f 2 : Focal length of individual lens     N: Material between lenses     T: Distance between lenses        

      The equation for calculating the field of view (FOV) of the lens unit is:  
             FOV   =     2   ⁢           ⁢       tan     -   1       ⁡     (     Y   F     )                 (     Eq   .           ⁢   3     )             
 
      where FOV: Field of view θ
          Y: Image height of lens unit     F: Effective focal length of lens unit        

      By applying Eqs. 1˜3 above, the corresponding lens wall thickness and air gap may be determined by inputting the image height Y to achieve the basic object of the invention.  
      (B) First Preferred Embodiment of Optical Design:  
      Using the example of a known lens unit  30  and a new lens unit  30   a  shown in  FIG. 3  and  FIG. 4 , the image height  34  of the known lens unit  30  is 4.28 mm, while the image height  34   a  of the new lens unit  30   a  is 3.26 mm.  
      To obtain the design where both lens units  30 ,  30   a  have FOV (θ)=60°, the new lens unit  30   a  can be fabricated by changing the lens wall thickness  311 ,  321 ,  331  and air gap  351 ,  352 ,  353  of one or more lenses  31 ,  32 ,  33  of lens unit  30 . Below is the actual calculation:  
      (b1) First, the optical parameter values of the known lens unit  30  shown in  FIG. 3  are as follows:  
                                           Radius of curvature   Thickness (distance)   Glass   Taper                                                 1)   1.952283   0.9456778   1.617290, 60.4   0        2)   4.792914   0.8710841       0       *3) −5.789234   1.047581   1.729150, 46   7.42442       *4) −0.9820674    0.05       −0.677571       *5) −2.074632   0.6335389   1.755200, 27.5   0       *6)   3.758542   1.472101       0.8202025                 where the fields after 1) represent in sequence the radius of curvature of the anterior side (left side) of lens 31, lens thickness, refractive index of glass material, and taper (meaning spherical surface when taper is 0);          # the fields after 2) represent in sequence the radius of curvature of the posterior side (right side) of lens 31, air gap, and taper; similarly the fields after 3) and 4) are respectively the parameter values of the anterior side (left side) and posterior side (right side) of lens 32;        # and the fields after 5) and 6) are respectively the parameter values of the anterior side (left side) and posterior side (right side) of lens 33.          Where the fields with symbol * mean the curvature of the lens is non-spherical.             
 
      (b2) Non-spherical equation:  
             z   =         C   ⁢           ⁢     Y   2         1   +       (     1   -       (     1   +   K     )     ⁢     C   2     ⁢     Y   2         )       1   /   2           +       A   4     ⁢     Y   4       +       A   6     ⁢     Y   6       +       A   8     ⁢     Y   8       +       A   10     ⁢     Y   10       +       A   12     ⁢     Y   12       +       A   14     ⁢     Y   14                 (     Eq   .           ⁢   4     )             
 
      (b3) The anterior side (left side) of lens  32  has non-spherical curvature 3) with the following parameters:  
      A4: −0.1464671  
      A6: 0.01906334  
      A8: −0.051794802  
      A10: 0.013321277  
      A12: −0.015041165  
      A14: 0.025112377  
      (b4) The posterior side (right side) of lens  32  has non-spherical curvature 4) with the following parameters:  
      A4: 0.10882206  
      A6: −0.076525425  
      A8: 0.047715558  
      A10: −0.0088773685  
      A12: −0.011679214  
      A14: 0.0066098526  
      (b5) The anterior side (left side) of lens  33  has non-spherical curvature 5) with the following parameters:  
      A4: 0.0094098806  
      A6: 0.007037218  
      A8: 0.0014927784  
      A10: 0.00042425485  
      A12: −0.0014030275  
      A14: 0.00048301552  
      (b6) The posterior side (right side) of lens  33  has non-spherical curvature 6) with the following parameters:  
      A4: −0.089751199  
      A6: 0.017376604  
      A8: −0.0021373213  
      A10: −4.3719006e-005  
      A12: −0.00015420277  
      A14: 4.6647217e-005  
      (b7) Based on the optical parameters and functions of know lens unit  30  described above and by inputting the new image height 3.26 mm, the parameter values of new lens unit  30   a  as shown in  FIG. 4  may be obtained from functional equations Eqs. 1˜4:  
                                           Radius of curvature   Thickness (distance)   Glass   Taper                                                 1)   1.952283   1   1.617290, 60.4   0        2)   4.792914   0.3820041       0       *3) −5.789234   1.242992   1.729150, 46   7.42442       *4) −0.9820674    0.3089046       −0.677571       *5) −2.074632   0.39   1.755200, 27.5   0       *6)   3.758542   1       0.8202025                 where the fields with symbol * mean the curvature of the lens is non-spherical. Given the non-spherical parameter values of the lenses of new lens unit 30a shown in  FIG. 4  are completely identical to those of known lens unit 30, they will not be reiterated here.             
 
      As described above, among the parameter values of known lens unit  30  ( FIG. 3 ) and new lens unit  30   a  ( FIG. 4 ), only lens wall thickness (thickness) and air gap (distance) between lenses differ, while the rest of parameter values are identical. From Eqs. 1˜3, it is known that for known lens unit  30 , EFL=3.7 mm, FOV=60°, whereas for the new lens unit  30   a , EFL=2.8 mm and FOV=60°.  
      (C) Second Preferred Embodiment of Optical Design:  
      Below is another preferred embodiment that illustrates the simplified application of the lens unit design method according to the invention and its functional equations.  
      Again a known lens unit  30  and a new lens unit  30   a  having three lenses  31 ,  32 ,  33  similar to those shown in  FIG. 3  and  FIG. 4  are used as example. However, the actual shapes and sizes of lenses  31 ,  32 ,  33  in the second preferred embodiment might differ from those shown in  FIG. 3  and  FIG. 4 . Assuming in this simplified embodiment, the image height of known lens unit  30  is 4.28 mm, that is, it is suitable for 4.28 mm sensor. When a customer makes an order, requesting a new lens unit  30   a  having a sensor size applicable to image height of 3.26 mm (assuming the FOV of the new lens unit stays unchanged at 60 degrees as the known lens unit), we can design the new lens unit  30   a  following the steps below:  
      (c1) First the optical parameters of the known lens unit  30  similar to that shown in  FIG. 3  are depicted below: (the units of D, EFL, and AIR are in mm):  
                                                       Known lens       First lens 31   Second lens 32   Third lens 33   unit 30                  N1 = 1.61729   N2 = 1.72915   N3 = 1.7552   Image                   height =                   4.28 mm       R11 = 1.952283   R21 = −5.789234   R31 = −2.074632   EFL = 3.7       R12 = 4.792914   R22 = −0.982067   R32 = 3.758542   AIR1 =                   0.8710841       D1 = 0.945678   D2 = 1.047581   D3 = 0.6335389   AIR2 = 0.05                  
 
      In the above table, N 1 , N 2 , and N 3  represent respectively the refractive index of lens material  31 ,  32 , and  33 ; R 11 , R 21 , and R 31  represent respectively the radius curvature of the posterior side (right side) of lens  31 ,  32 , and  33 ; D 1 , D 2 ; and D 3  represent respectively the thickness of lens  31 ,  32 , and  33 ; EFL is the effective focal length of known lens unit  30 ; AIR 1  is the air gap between the first lens  31  and the second lens  32 ; and AIR 2  is the air gap between the second lens  32  and the third lens  33 .  
      The parameter values of known lens unit  30  depicted in the above table are commonly used by lens manufacturers for lens design.  
      (c2) Calculating EFL of new lens unit  30   a:    
      Using Eq. 3, we can input the image height (3.26 mm) and FOV (60 degrees) requested by the customer for the new lens unit  30   a  and obtain the EFL of the new lens unit  30   a  to be 2.8 mm.  
      (c3) The new lens unit  30   a  needs to change at least the thickness of one lens or the value of an air gap to obtain a EFL of 2.8 mm in step (c2):  
      If we wish to change only the value of an air gap (e.g. AIR 2 ) without changing the other parameters of the lens to obtain the result of 2.8 mm EFL for new lens unit  30   a , we can substitute the parameter values of known lens unit  30  (except for AIR 2 ) coupled with the new EFL of 2.8 mm into Eq. 1 and Eq. 2, and obtain a new AIR 2  of 0.32150565 mm. As such, the optical parameters of the newly designed lens unit  30   a  are depicted in the table below:  
                                                       Known lens       First lens 31a   Second lens 32a   Third lens 33a   unit 30a                  N1 = 1.61729   N2 = 1.72915   N3 = 1.7552   Image                   height =                   3.26 mm       R11 = 1.952283   R21 = −5.789234   R31 = −2.074632   EFL = 3.7       R12 = 4.792914   R22 = −0.982067   R32 = 3.758542   AIR1 =                   0.8710841       D1 = 0.945678   D2 = 1.047581   D3 = 0.6335389   AIR2 =                   0.32150565                  
 
      By comparing the optical parameters of new lens unit  30   a  and known lens unit  30 , it is clear that we only need to change the AIR1 of new lens unit  30   a  for it to work with a sensor 3.26 mm in size, instead of redesigning the lens or remaking the lens mold.  
      Similarly, if we wish to change the thickness of a certain lens in the new lens unit  30   a  to reduce the overall dimensions of new lens unit  30   a , we can input those optical parameters we do not intend to change into Eq. 1 and Eq. 2 to obtain the corresponding thickness (D 1 ) of the lens (e.g. first lens  31   a ) or lenses (e.g. three lenses  31   a ,  32   a ,  33   a ) we wish to change. Thus by changing the thickness of at least one lens or an air gap, we can obtain a new lens unit that is consistent with the new image height desired.  
      While the present invention has been shown and described with reference to the preferred embodiments thereof and in terms of the illustrative drawings, it should not be considered as limited thereby. Various possible modifications and alterations could be conceived of by one skilled in the art to the form and the content of any particular embodiment, without departing from the scope and the spirit of the present invention.