Loupe
This invention relates to magnifying lenses often referred to as loupes, and more particularly relates to loupes of increased power using only three elements. 
     With a loupe, the eye is always the pupil independent of its position. For this reason the loupe must be corrected for aberrations of a large aperture, as well as the aberrations of color, astigmatism, and distortion. Additionally, if a loupe is to be used for reading purposes, such as microfilm, then a further requirement of field flatness must be satisfied to avoid excessive reaccommodations and eye fatigue of the user. 
     Most loupes do not have a flat field. Those that do are complex, having six or more elements. 
     If the magnifying power is large, on the order of 12x or greater, then a wide angle of view on the order of a 22° semi-field angle is extremely difficult to obtain. Thick or spaced lens elements must be individually achromatized for correction of chromatic aberration. This results in increased axial dimension and further complicates the design. 
     The present invention provides a loupe of 12x or greater, where magnifying power is defined as two hundred fifty divided by the equivalent focal length. This is achieved by the provision of a positive lens followed by a cemented doublet. Only one negative element is utilized to provide color correction. A loupe embodying the invention is adequately corrected for all aberrations and has a flat field, making it extremely useful as a microfilm reader. 
     Briefly stated, the invention in one form comprises a first positive group followed by a cemented doublet having the overall shape of a meniscus. Either the cemented surfaces are made aspheric with the outer surfaces spherical or vice versa. However, more aspherics may be added if desired. The positive group preferably comprises a singlet with one aspheric surface, but may be made in the form of a doublet, with or without aspheric surfaces. To achieve the required optical corrections, the surfaces of the lens and certain relationships of surfaces and curvatures are maintained as hereinafter pointed out. 
     An object of this invention is to provide a loupe of increased magnifying power with only three elements and having good optical correction. 
     Another object of this invention is to provide a loupe well corrected for field flatness, and having a wide field angle. 
    
    
     The features of the invention which are believed to be novel are particularly pointed out and distinctly claimed in the concluding portion of this specification. The invention, however, both as to its organization and operation, together with further objects and advantages thereof may best be appreciated by reference to the following detailed description taken in conjunction with the drawings, wherein: 
     FIG. 1 is a diagrammatic side elevation of a loupe embodying the invention; and 
     FIG. 2 is a graphical representation of the influence of a higher order term on the lens surface. 
    
    
     In the drawings, the position of the pupil of the eye is shown at P, the object at O, and the optical axis at A. 
     The loupe comprises a first positive element in the form of a bi-convex element L1, a second bi-convex element L2 and a third bi-concave element L3, having surfaces S1-S5 as indicated. The surfaces S1-S5 are defined on radii R1-R5, at least at the optical axis A. The elements have axial thicknesses D1, D2 and D3. 
     Where the surfaces are made aspheric, the surfaces are defined by the equation: ##EQU1## where X is the sag in the surface measured from a reference plane perpendicular to the optical axis, 
     Y is the radial ordinate from the optical axis, 
     C is the curvature of a lens surface equal to EFL/R where EFL is the equivalent focal length of the overall lens and R is the radius of the lens surface at the optical axis, 
     K is a conic constant, and 
     G is a higher order coefficient. If the surface is a conic section of rotation, G=0. 
     FIG. 2 shows the influence of the term GY 4 . When G=0, the surface will take certain shapes depending on the value of K. 
     Various values of K will produce surfaces as follows: 
     
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K = 0            Spherical                                                
K = -1           Parabolic                                                
K = 0 to -1      Ellipse where smaller axis                               
                 is vertical                                              
K = positive     Ellipse when smaller axis                                
                 is horizontal                                            
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     Generally speaking, if the cemented surface S4 are made aspheric, the outer surfaces of S3 and S5 are spherical and vice versa. However, in Table VII, an example is set forth where all of surfaces S3, S4 and S5 are conics. Either of surfaces S1 or S2 may be made aspheric. 
     Seven examples of the invention are set forth in Tables I-VII with reference to FIG. 1. 
     A 14× loupe of 17.8mm EFL with a semi-field angle of 22.0° is set forth in Table I. 
     
                       TABLE I                                                     
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       Radius of Axial Distance                                           
       Surfaces S1-S5                                                     
                 Between Surfaces                                         
                              N.sub.d V.sub.d                             
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                         21.00mm                                          
      R1      28.371mm                                                    
L1                       7.077      1.491 57.1                            
      R2     -13.176                                                      
                         0.270                                            
      R3      11.331                                                      
L2                       8.052      1.491 57.1                            
      R4     -14.218                                                      
L3                       1.397      1.590 30.8                            
      R5       6.291                                                      
BFL                      6.00                                             
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Aspheric Surfaces  K           G                                          
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S2                 -1.748      0                                          
S3                   .435      0                                          
S5                 - .614      0                                          
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         ______________________________________                                    
Surface Curvatures                                                        
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            C1 =  .620                                                    
            C2 =  -1.351                                                  
            C3 =  1.571                                                   
            C4 =  -1.252                                                  
            C5 =  2.829                                                   
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     A 14× loupe of 18.0mm EFL with a semi-field angle of 22.0° is set forth in Table II. 
     
                       TABLE II                                                    
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       Radius of Axial Distance                                           
       Surfaces S1-S5                                                     
                 Between Surfaces                                         
                              N.sub.d V.sub.d                             
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                         19.00mm                                          
      R1      74.729mm                                                    
L1                       5.683      1.491 57.1                            
      R2     -11.379                                                      
                         0.270                                            
      R3      12.771                                                      
L2                       9.750      1.491 57.1                            
      R4     -4.711                                                       
L3                       1.397      1.590 30.8                            
      R5       9.390                                                      
BFL                      -5.95                                            
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         ______________________________________                                    
Aspheric Surfaces  K           G                                          
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S2                 - .717      .103                                       
S4                 -2.144      .038                                       
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         ______________________________________                                    
Surface Curvatures                                                        
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            C1 =  .238                                                    
            C2 =  -1.564                                                  
            C3 =  1.393                                                   
            C4 =  -3.778                                                  
            C5 =  1.895                                                   
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     A 14× loupe of 17.8mm EFL with a semi-field angle of 22.0° is set forth in Table III. 
     
                       TABLE III                                                   
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       Radius of Axial Distance                                           
       Surfaces S1-S5                                                     
                 Between Surfaces                                         
                              N.sub.d V.sub.d                             
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                         19.00mm                                          
      R1      54.801mm                                                    
L1                       5.708      1.491 57.1                            
      R2     -12.117                                                      
                         0.270                                            
      R3      12.697                                                      
L2                        10.129    1.491 57.1                            
      R4     - 4.457                                                      
L3                       1.397      1.590 30.8                            
      R5       8.951                                                      
BFL                      5.48                                             
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Aspheric Surfaces  K           G                                          
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S2                 -.771        .101                                      
S4                 -2.109      -.025                                      
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Surface Curvatures                                                        
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            C1 =  .324                                                    
            C2 =  -1.467                                                  
            C3 =  1.400                                                   
            C4 =  -4.098                                                  
            C5 =  2.005                                                   
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     A 14× loupe of 17.8mm EFL with a semi-field angle of 22.0° is set forth in Table IV. 
     
                       TABLE IV                                                    
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       Radius of Axial Distance                                           
       Surfaces of S1-S5                                                  
                 Between Surfaces                                         
                              N.sub.d V.sub.d                             
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                         21.00mm                                          
      R1      30.014mm                                                    
L1                       6.857      1.491 57.1                            
      R2     -14.049                                                      
                         0.270                                            
      R3      14.055                                                      
L2                        10.828    1.491 57.1                            
      R4     - 4.577                                                      
L3                       1.397      1.590 30.8                            
      R5       8.958                                                      
BFL                      4.67                                             
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         ______________________________________                                    
Aspheric Surfaces  K           G                                          
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S2                 -1.362      0                                          
S4                 -1.584      0                                          
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Surface Curvatures                                                        
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            C1 =  .592                                                    
            C2 =  -1.267                                                  
            C3 =  1.266                                                   
            C4 =  -3.889                                                  
            C5 =  1.987                                                   
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     A 13× loupe of 20.0mm EFL with a semi-field angle of 19.5° is set forth in Table V. 
     
                       TABLE V                                                     
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       Radius of Axial Distance                                           
       Surface S1-S5                                                      
                 Between Surfaces                                         
                              N.sub.d V.sub.d                             
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                         21.00mm                                          
      R1      28.080mm                                                    
L1                       6.256      1.490 57.1                            
      R2     -13.772                                                      
                          .274                                            
      R3      11.084                                                      
L2                       6.967      1.490 57.1                            
      R4     -14.946                                                      
                         1.397      1.589 30.8                            
      R5       6.422                                                      
BFL                      8.21                                             
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Aspheric Surfaces  K           G                                          
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S2                 -1.759      0                                          
S3                 -0.605      0                                          
S5                 -0.805      0                                          
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         ______________________________________                                    
Surface Curvatures                                                        
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            C1 =  .712                                                    
            C2 =  -1.452                                                  
            C3 =  1.804                                                   
            C4 =  -1.338                                                  
            C5 =  3.115                                                   
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     A 14× loupe of 17.8mm EFL with a semi-field angle of 22.0° is set forth in Table VI. 
     
                       TABLE VI                                                    
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Radius of       Axial Distance                                            
Surfaces S1-S5  Between Surfaces                                          
                              N.sub.d V.sub.d                             
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                        19.00mm                                           
     R1     84.545mm                                                      
L1                      5.621       1.491 57.1                            
     R2     -11.187                                                       
                        0.270                                             
     R3     12.822                                                        
L2                      9.212       1.491 57.1                            
     R4     -- 5.421                                                      
L3                      1.397       1.590 30.8                            
     R5     10.052                                                        
BFL                     6.537                                             
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         ______________________________________                                    
Aspheric Surfaces  K           G                                          
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S2                 - .735      .102                                       
S4                 -2.203      -.069                                      
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 Surface Curvatures                                                       
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C1             =           .210                                           
C2             =           -1.600                                         
C3             =           1.390                                          
C4             =           -3.420                                         
C5             =           1.770                                          
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     A 14× loupe of 17.8mm EFL with a semi-field angle of 22.0° is set forth in Table VII. 
     
                       TABLE VII                                                   
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Radius of       Axial Distance                                            
Surfaces S1-S5  Between Surfaces                                          
                              N.sub.d V.sub.d                             
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                        21.00mm                                           
     R1     29.341                                                        
L1                      6.924       1.491 57.1                            
     R2     -13.877                                                       
                        0.270                                             
     R3     14.118                                                        
L2                      10.639      1.491 57.1                            
     R4     -4.576                                                        
L3                      1.397       1.590 30.8                            
     R5     8.903                                                         
BFL                     4.74                                              
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         ______________________________________                                    
Aspheric Surfaces  K           G                                          
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S2                 -1.470      0                                          
S3                 .070        0                                          
S4                 -1.618      0                                          
S5                 .015        0                                          
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         ______________________________________                                    
 Surface Curvatures                                                       
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C1             =           .606                                           
C2             =           -1.283                                         
C3             =           1.261                                          
C4             =           -3.891                                         
C5             =           2.000                                          
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     In the foregoing tables, L1, L2, L3 are the lens elements, R1-R5 are the radii of the surfaces S1-S5 at the optical axis, N d  is the index of refraction, V d  is the abbe number, P is the pupil position, BFL is the back focal length, and C1-C5 are the curvatures of the surfaces at the optical axis where C = EFL/R. Radii defined from a point to the right are considered positive. 
     In Tables I and IV, the outer surfaces of the doublet are made aspheric while the cemented surfaces are spherical. In Table VII, the cemented surfaces are also aspheric. In Tables II, III, IV and VI, the cemented surfaces are aspheric, and in II and VI are modified by the term GY4. The surface S2 of element L1 is shown as a conic or modified conic in all examples but may be spherical, or L1 can be divided into two elements if desired. 
     The elements may be made of any suitable optically clear plastic such as polymethyl methacrylate, polycyclohexyl methacrylate, polystyrene, or acrylonitrile. 
     Certain relationships of the elements may be noted from the foregoing tables. 
     The curvatures C2 and C3 of surfaces S2 and S3, respectively, differ by no more than .25 and reside within the range 
     
         1.0 &lt; S2,3 &lt; 2.0 
    
     the ratio of the axial thickness D2 and D3 of L2 to L3 is 
     
         4.8 &lt; D2/D3 &lt; 8.0 
    
     such ratio multiplied by the thickness D1 of element L1 is 
     
         60 &gt; D2/D3 · D1 &gt; 25 
    
     the surface curvatures are 
     
         0.2 &lt; C1 &lt; 0.75 
    
     
         1.0 &lt; c2 &lt; 1.7 
    
     
         1.2 &lt; c3 &lt; 1.9 
    
     
         1.0 &lt; c4 &lt; 5.0 
    
     
         1.5 &lt; c5 &lt; 3.5 
    
     where S4 is not aspheric 
     
         |C4| &lt; C3 
    
     
         |c4| &lt; c5 
    
     where S4 is aspheric 
     
         |C4| &gt; C3 
    
     
         |c4| &gt; c5 
    
     the axial thickness D4 of the doublet bears the following relation to D1, the axial thickness of the positive singlet 
     
         2 &gt; D4/D3 &gt; 1 
    
     the first singlet element primarily provides high power for magnifying purposes, while the doublet primarily provides color correction and provides a flat field, as well as correcting other aberrations. 
     To maintain color correction for presently available optical plastics which have Abbe values in a range of 30 to 58, the sum of the absolute value of the curvatures of surfaces S3, S4 and S5 should be in the range of 5.0 to 8.0 or otherwise stated 
     
         8.0 &lt; |C3| + |C4| + |C5| &gt; 5.0 
    
     the elements may be mounted in a housing (not shown) so as to have axial motion for focusing, and means may be provided on such housing or attachable thereto to carry microfilm, microfiche or other items for viewing. 
     The lenses of Tables I-VII also may be defined by the surface curvatures with the axial distance between surfaces of the tables set forth as a function of the EFL of the lens. 
     It may thus be seen that the objects of the invention set forth as well as those made apparent from the foregoing description are efficiently attained. While preferred embodiments of the invention have been set forth for purposes of disclosure, modification to the disclosed embodiments of the invention as well as other embodiments thereof may occur to those skilled in the art. Accordingly, the appended claims are intended to cover all embodiments of the invention and modifications to the disclosed embodiments which do not depart from the spirit and scope of the invention.