Patent Publication Number: US-2021190457-A1

Title: Optical scope

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. application Ser. No. 15/196,376, filed on Jun. 29, 2016 which is a continuation of U.S. application Ser. No. 13/235,588, filed on Sep. 19, 2011 now issued as U.S. Pat. No. 9,417,036, which claims priority to and the benefit of Korean Patent Application No. 10-2010-0094809 filed in the Korean Intellectual Property Office on Sep. 29, 2010, each of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     (a) Field of the Invention 
     The present invention relates to an optical scope, and more particularly, to an optical scope in which a lens having negative power is disposed on an image formation surface of an objective lens, thereby increasing eye-relief. 
     (b) Description of the Related Art 
     In firearms, a sighting means may be coupled to a top portion of the firearm so as to accurately aim an external target. In a particular case of a rifle among the firearms, aiming is achieved by aligning a line of sight between a sight and a bead, in which speed showing how quickly the aiming is achieved to fire an aimed shot and accuracy showing how accurately the aimed shot hits the target are very important. 
     That is, an aimed-shooting method requires complicated procedures and time to acquire and ascertain a target, arrange the line of sight, aim at the target, etc. Also, because the sight and the bead themselves are very small, eyes are turned upon the sight and the bead rather than the target or a frontward situation and therefore a field of view becomes narrow if excessive attention is paid to the alignment for the line of sight in order to accurately align the sight and the bead. 
     Accordingly, an optical scope has been proposed to solve the above cumbersome alignment for the line of sight and improve the accuracy a little more. 
     The optical scope employs a magnifying-power optical system, which includes an objective lens and an objective lens reticle (i.e., the light of sight), to magnify a target, and is thus excellent in discerning the target, thereby enabling steady aiming through the reticle placed inside the scope. 
     Such an optical scope is broadly classified into an erecting prism type and a relay lens type.  FIG. 1  shows structures of these two types. 
     First, referring to  FIG. 1A , the erecting prism type optical scope includes an objective lens  12 , a prism optical system  14 , a reticle  13 , an eyepiece lens  11 , etc. If an image of an external object from the objective lens  12  is formed at a position of the reticle  13 , both the image and the reticle  13  are magnified and viewed through the eyepiece lens  11 , which is the principle of a telescope or scope. At this time, if the image from the objective lens  12  is directly formed at the position of the reticle  13 , the image is viewed as it is inverted. Thus, an erecting prism  14  is provided between the objective lens  12  and the reticle  13  to erect the image viewed through the eyepiece lens  11  by inverting the inverted image again. As the kind of erecting prism  14 , there are an Abbe prism  14   a  (also called a Koenig prism or a Brashear-Hastings prism) as shown in  FIG. 2 , a roofed Pechan prism  14   b  as shown in  FIG. 3 , etc. 
     Referring to a cross-section of the erecting prism shown in  FIG. 4 , which is a roofed Pechan prism  14   b  having a face length of 17.5 mm, a roof having a right-angled prism structure is formed on a top portion of an above prism, thereby serving to invert the left and right images. A total calculated geometrical path is 77.49 mm if an air space between two prisms is 0.70 mm. The shortest distance on an optical axis of this roofed Pechan prism is 21.12 mm, and a expansion amount of the optical path length (OPL) due to the refractive index (1.5168@d-line) of the prism glass BK7 is 
     
       
         
           
             
               
                 
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     so that the geometrical effect on reducing a body tube is 56.37 mm, and a calculated effect on reducing the optical path is 30.21 mm. 
     In general, the erecting prism type is advantageous to shorten the body tube, but difficult to manufacture the prism. 
     Meanwhile,  FIG. 1  illustrates one sheet of the objective lens  12  and one sheet of the eyepiece lens  11 , but many sheets of them are generally provided in practice to remove aberration or the like 
     Referring to  FIG. 1B , the relay lens type optical scope includes an objective lens  12 , a field lens  16 , a reticle  13 , a relay lens  15 , an eyepiece lens  11 , etc. If an image of an external object from the objective lens  12  is formed at a position of the reticle  13 , both the image and the mark of the reticle  13  are formed again in front of the eyepiece lens  11  and magnified and viewed through the eyepiece lens  11 , which is the principle of a relay lens type telescope. That is, if the image from the objective lens  12  is directly formed on the reticle  13 , the image is generally viewed as it is inverted. This inverted image is formed once gain by the relay lens  15  and thus inverted again, so that the image in front of the eyepiece lens  11  can be erect. Then, this erect image is magnified and viewed through the eyepiece lens  11 . 
     Generally, the optical scope includes the objective lens  12 , the eyepiece lens  11 , the reticle  13 , and the relay lens  15  or the erecting prism  14  for erecting the image. In addition, the field lens  16  having the positive power may be interposed between the reticle  13  and the eyepiece lens  11  so as to broaden the field of view. 
     In designing the eyepiece lens of the scope, technology that the field of view through the eyepiece lens  11  is broadened by placing the field lens  16 , which has the positive power and interposed between the reticle  13  and the eyepiece lens  11 , near the reticle  13  has been applied to the scope such as the existing telescope or the like. As the field of view is broadened, eye-relief (refer to ‘D’ in  FIG. 5 ) generally becomes short. Nevertheless, since there is no need for increasing the eye-relief in the existing telescope, this technology has been mostly used. 
     As shown in  FIG. 5 , it is possible to reduce more damage due to recoil of shooting in a firearm G and to quickly acquire motion of a target and its surroundings as eyes of a shooter become distant from the scope  10 . However, a conventional scope  10  employs the objective lens  12 , the eyepiece lens  11 , the reticle  13 , the relay lens  15  or the erecting prism  14  for erecting an image, and the field lens  16  having the positive power, so that a shooter&#39;s eyes gazing upon the scope  10  cannot be sufficiently distant from the scope  10 . 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention is conceived to solve the forgoing problems, and an aspect of the present invention is to provide an optical scope in which a lens having negative power is disposed on an image formation surface of an objective lens in order to increase eye-relief, so that a shooter&#39;s eyes can be sufficiently distant from the scope, thereby reducing damage due to recoil of shooting in a firearm and quickly acquiring motion of a target and its surroundings. 
     An exemplary embodiment of the present invention provides an optical scope comprising an objective lens, an eyepiece lens, and a reticle, wherein a field lens having negative power is disposed in at least one of a front and a back of the reticle disposed on an image formation surface of the objective lens to increase eye-relief. 
     The objective lens, the field lens, the reticle and the eyepiece lens may be arranged in sequence. 
     The field lens may comprise a flat surface opposite to the eyepiece lens, and the reticle may be formed on one surface of a flat lens disposed in parallel with the flat surface of the field lens. 
     The field lens may include a flat surface opposite to the eyepiece lens, and the reticle may be etched on the flat surface of the field lens and formed integrally with the field lens. 
     The objective lens, the reticle, the field lens, and the eyepiece lens may be arranged in sequence. 
     The field lens may include a flat surface opposite to the objective lens, and the reticle may be formed on one surface of a flat lens disposed in parallel with the flat surface of the field lens. 
     The field lens may include a flat surface opposite to the objective lens, and the reticle may be etched on the flat surface of the field lens and formed integrally with the field lens. 
     The field lens may include a first field lens and a second field lens each having negative power, and the objective lens, the first field lens, the reticle, the second field lens, and the eyepiece lens may be arranged in sequence. 
     At least one of the first field lens and the second field lens may include a flat surface opposite to the reticle, and the reticle may be formed on one surface of a flat lens disposed in parallel with the flat surface of the field lens. 
     At least one of the first field lens and the second field lens may include a flat surface opposite to the reticle, and the reticle may be etched on a flat surface of the first field lens or second field lens and formed integrally with the first field lens or second field lens. 
     The optical scope may further include an erecting optical system interposed between the objective lens and the reticle and erecting an image. 
     The erecting optical system may include an erecting prism. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are a structural view of a conventional optical scope according to its kinds, 
         FIG. 2  is a structural view of an Abbe prism, 
         FIG. 3  is a structural view of a roofed Pechan prism, 
         FIG. 4  is a view showing an example of a practical manufacturing size of the roofed Pechan prism, 
         FIG. 5  is a conception view showing an eye-relief of a scope, 
         FIG. 6  is a cross-section view of an optical scope according to an exemplary embodiment of the present invention, 
         FIG. 7  is a layout showing a paraxial optical lens for calculating power of a field lens in the optical scope according to an exemplary embodiment of the present invention, 
         FIG. 8  shows an example of a program calculation, 
         FIG. 9  is a ray tracing view of an eyepiece lens in the optical scope according to an exemplary embodiment of the present invention, 
         FIG. 10  is a ray tracing view of an objective lens in the optical scope according to an exemplary embodiment of the present invention, 
         FIG. 11  is a ray tracing view of the optical scope according to an exemplary embodiment of the present invention, 
         FIG. 12  is a ray tracing view of when a field lens having negative power is removed from the optical scope according to an exemplary embodiment of the present invention, 
         FIG. 13  is a view showing modulation transfer function (MTF) characteristics of the optical scope according to an exemplary embodiment of the present invention, 
         FIG. 14  is a cross-section view of an optical scope according to a second exemplary embodiment of the present invention, and 
         FIGS. 15 and 16  are cross-section views of an optical scope according to a third exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Prior to description, elements will be representatively explained in an embodiment and only different configurations will be described in another embodiment, in which like reference numerals refer to like elements throughout the embodiments. 
     Hereinafter, an optical scope according to a first exemplary embodiment of the present invention will be described with reference to the accompanying drawings. 
     Among the accompanying drawings,  FIG. 6  is a cross-section view of an optical scope according to an exemplary embodiment of the present invention. 
     As shown therein, the optical scope in this exemplary embodiment includes an eyepiece lens  110 , an objective lens  120 , a reticle  130 , a field lens  140  having negative power, and an erecting optical system  150 . 
     In this exemplary embodiment, the field lens  140  having negative power is disposed between the eyepiece lens  110  and the objective lens  120 , so that a space between the eyepiece lens  110  and a user&#39;s eyes, i.e., eye-relief can be increased. 
     Before detailed descriptions about configuration of the present invention, the rationale of increasing the eye-relief is as follows. 
     Referring to  FIG. 7 , let a focal distance of an objective lens be f o , a focal distance of a field lens be f f , a focal distance of an eyepiece lens f e , eye-relief be dis eye , an incident height of a chief ray in the field lens be y f  an incident height of the chief ray in the eyepiece lens be y e , a refractive angle of the chief ray passing through the objective lens be u o , an incident angle and a refractive angle of the chief ray in a space before and after the field lens be u f  and u′ f , and an incident angle and a refractive angle of the chief ray in a space before and after the eyepiece lens be Ue and U e, the following equations are expanded by the length TL of the tube body, magnification mag, and paraxial ray tracing equations. 
     
       
         
           
             
               
                 
                   
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     In the foregoing equations (1) to (7), the length TL of the tube body and the magnification mag are determined by a user of the scope, and a view angle u 0  of the scope, i.e., the incident angle of the chief ray in the objective lens is determined by the diameter and length of the tube body a user wants. Thus, necessary initial design values for the field lens can be calculated in the equations (3), (6) and (7) with the tube body length TL, the magnification mag and the view angle u 0  of the scope which are determined initially. In accordance with practical calculation, the power (i.e., the reciprocal number of the focal distance) of the necessary field lens is changed from a positive value to a negative value as the eye-relief dis eye  increases. 
     Here, it will be understood that the eye-relief can be increased by using a lens having negative power instead of a general field lens. Therefore, there is provided a rationale for replacing the field lens of the existing scope by the lens having negative power in order to increase the eye-relief. 
       FIG. 8  shows initial values determined by programming the above equations according to an exemplary embodiment, in which the values were determined when the tube body length TL=144 mm, the magnification mag=−3, the scope view angle u 0 =2.5 degrees, and a desired eye-relief dis eye =90 mm. That is, the initial values are determined under the condition that the objective lens has a focal distance f o =108 mm, the field lens has a focal distance f f =−30.86 mm, the eyepiece lens has a focal distance f e =36 mm, the chief ray in the field lens has an incident height y f =4.71 mm, the chief ray in the eyepiece lens has an incident height y e =11.78 mm, the chief ray before and after the field lens has an incident angle u f =2.5 degrees and a refractive angle u′ f =11.25 degrees. On the basis of the obtained initial values, the objective lens and the eyepiece lens are designed together with the field lens having the negative power and combined, thereby completing the design of the scope having the eye-relief of 90 mm. 
     At this time, the lenses may be arranged as follows.
         1) The object lens  120 , the erecting optical system  150 , the field lens  140  having the negative power, the reticle  130 , and the eyepiece lens  110  are arranged in sequence (refer to  FIG. 6 )   2) The object lens  120 , the erecting optical system  150 , the reticle  130 , the field lens  140  having the negative power, and the eyepiece lens  110  are arranged in sequence (refer to  FIG. 14 )   3) The object lens  120 , the erecting optical system  150 , a first field lens  141  having the negative power, the reticle  130 , a second field lens  142  having the negative power, and the eyepiece lens  110  are arranged in sequence (refer to  FIG. 15 ) Among the foregoing various arrangements, the arrangement where the object lens  120 , the erecting optical system  150 , the field lens  140  having the negative power, the reticle  130 , and the eyepiece lens  110  are arranged in sequence will be described below as a first exemplary embodiment.
 
&lt;Design of the Eyepiece Lens Having Eye-Relief of 90 mm&gt;
       

     With reference to  FIG. 9 , the eyepiece lens  110  is configured as follows. 
     The specification of the eyepiece lens  110  determined by the initial values of the scope may include the focal lens f e =36 mm, a distance of 90 mm from a caliber stop (a pupil of an eye) to a first lens  111 , a chief ray at a view angle of 7.5 degrees (2.5 degrees×3) having an incident height of 4.71 mm and an incident angle of 11.25 degrees on the reticle, and so on. As glass for a lens used in an early design, a lens having positive power was BK7, and a lens having negative power was SF11, so that chromatic aberration in the visible region for recognition by human eyes could be controlled well. The design was performed to obtain 177.37 mm by adding a geometrical distance increasing effect of 56.37 mm in the erecting optical system  150  (i.e., an erecting prism (e.g., a roofed Pechan prism)) to a total length of 121 mm, and dividing 177.37 mm in a ratio of 3:1 to regard a length of about 44 mm as a total length of the eyepiece lens  110 . That is, while using a distance 44.0 mm from the first lens  111  of the eyepiece lens  110  to the reticle  130  (having the maximum thickness of 2.0 mm) as a fixed variable, and using the distance, thickness and curvature between a second lens  112  and a fourth lens  114  arranged between the first lens  111  and the reticle  130  as variables, optimization was achieved so that a chief ray at the view angle of 7.5 degrees can have an incident height of 4.71 mm and an incident angle of 11.25 degrees on the reticle  130  with the minimum finite ray aberration. Since the reticle  130  was configured by etching on a surface facing the eyepiece lens  110  of the field lens  140 , or etching a flat lens of BK7 having the maxim thickness of 2.00 mm and facing the field lens  140  and bonding it to or arranging the etched flat lens in parallel with the field lens  140 , the design was achieved to make the reticle  130  have a thickness of 2.0 mm. After such primary optimization, the whole is optimized once again by using a distance from the first lens  111  of the eyepiece lens  110  to the last reticle  130  as a variable in order to control remained aberration. 
     It starts with three sheets of the first lens  111  having the positive power, the second lens  112  having the positive power, and the third lens  113  having the negative power, but after the optimization it was concluded with the first lens  111  having the positive power, the second lens  112  having the positive power as a doublet lens, the third lens  113  having the negative power, and a meniscus-type fourth lens  114  having weak positive power. This means that the meniscus type fourth lens  114  having the weak positive power has to be lastly added to maintain the incident angle at 11.25 degrees on the reticle  130 . The chromatic aberration is sufficiently controlled by a +/−adhesion lens of the second lens  112  and the third lens  113 , and the first lens  111  serves as a power lens for maintaining the focal distance f e =36 mm. 
     Thus, design data and primary optical values of the eyepiece lens  110 , which has a configuration optimized with the first lens  111  to the fourth lens  114  and eye-relief of 90 mm, were shown in [Table 1] and a ray tracing view thereof was shown in  FIG. 9 . Referring to this, it will be appreciated that there is a little difference at a final optimization stage, for example, the distance from the first lens  111  of the eyepiece lens  110  to the last reticle  130  is 47.60 mm (obtained by subtracting the eye-relief of 90 mm from the total length of 137.60 mm), the chief ray at the angle of 7.5 degrees has an incident height of 4.74 mm and an incident angle of 11.11 degrees on the reticle  130 . 
                     TABLE 1               [Design data and primary optical       values for optimized eyepiece lens]                                    EFL = 36.000 WAVELENGTHS[nm] 587.60 656.30 486.10                                         #SURF   RADIUS   THICK   INDEX1   V   CLR RAD   GLASS               1 S   Plane   0.000   1.000000       2.833       2 S   53.475   90.000   1.000000       15.367       3 S   −53.475   7.000   1.516798   64.14   15.323   S-BK7       4 S   35.960   2.500   1.000000       13.895       5 S   −38.019   9.000   1.516798   64.14   12.841   S-BK7       6 S   169.670   3.000   1.784713   25.75   11.934   S-SF11       7 S   26.708   2.000   1.000000       11.500       8 S   30.861   6.000   1.516798   64.14   11.500   S-BK7       9 S   Plane   16.102   1.000000       11.500       10 S   Plane   2.000   1.516798   64.14   11.500   S-BK7       11 S   Plane   0.000   1.000000       11.500                         Infinite Conjugates                             BFL 0.00005   EFL 36.00006   FNO. 6.35370   FFL 53.69115                 At used Conjugates(Infinite Object Distance and Finite Focus)                             MAG   0.00000               OBJ NA   0.00000       IMAG NA   −0.07869        OBJ DIST   undefined       IMG DIST   0.00005       TRACK   undefined       THKNESS   137.602         IMG HT   4.73950       IMG ANG   −11.10865                  Entrance Pupil Diameter and Distance from First Surface                             DIA 5.66600   DIST 0.00000                         Exit Pupil Diameter and Distance from Last Surface                    
&lt;Design of the Objective Lens with Field Lens Having Negative Power&gt;
 
     Next, the configuration of the objective lens  120  with the field lens  140  having the negative power will be described with reference to  FIG. 10 . 
     The objective lens  120  has to have a focal distance of 108 mm, the chief ray corresponding to a view angle of 2.5 degrees on the scope has to be emergent at an angle of 11.11 on the last image formation surface so that the image can have a height of 4.74 mm, and the image formation surface of the field fens  140  has to be flat so that the reticle  130  can be etched and attached on to the image formation surface of the field lens  140  having the negative to power. In this exemplary embodiment, the objective lens  120  and the field lens  140  having the negative power were provided in the form of a doublet lens as one set of two sheets so as to reduce the chromatic aberration, and BK7 and SF2 easy to get were used as glass. The design data and the primary optical values of the objective lens  120  designed in such a manner were shown in [Table 2] and a ray tracing view thereof was shown in  FIG. 10 . Referring to this, it will be appreciated that the optimized objective lens  120  has an effective aperture of 17.0 mm and a total length of 129.803 mm. If it is considered that the tube body length of the erecting optical system  150  (e.g., the erecting prism) has a geometrical decreasing effect of a 56.37 mm, the total length is changed into 73.433 mm.  FIG. 10  illustrates the ray tracing view in the state that an optical path of the erecting optical system  150  (e.g., the erecting prism) is spread out. 
     As a result of the optimization, the focal distance becomes 108 mm, but there is a little difference from an initial limit condition as the chief ray corresponding to a scope&#39;s view angle of 2.5 degrees has an emergent angle of 11.21 degrees and the image has a height of 4.72 mm. This difference is within an allowance derived when a design error is considered to allow design of the eyepiece lens  110  considering the reticle  130  having the thickness of 2.0 mm, the objective lens  120  considering the reticle  130  having the thickness of 0.0 mm configured by etching the surface of the field lens  140  facing the eyepiece lens  110  in order to accept a user&#39;s demand for forming the reticle  130  by etching the surface of the field lens  140  facing the eyepiece lens  110  or by etching the flat lens BK7 having the maximum thickness of 2.00 mm and facing the field lens  140  and bonding it to or arranging the etched flat lens in parallel with the field lens  140 . Further, it will be appreciated in the optimization that such a difference brings a little difference in the path of rays entering an observer&#39;s eyes in light of combination of the objective lens  120  and the eyepiece lens  110 , but has little effect on the performance of the optical system. 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 [Design data and primary optical values for the objective 
               
               
                 lens with the field lens having optimized negative power] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
            
               
                 EFL = 108.002 WAVELENGTHS[nm] 587.60 656.30 486.10 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 #SURF 
                 RADIUS 
                 THICK 
                 INDEX1 
                 V 
                 CLR RAD 
                 GLASS 
               
               
                   
               
               
                 1 S 
                 62.396 
                 0.000 
                 1.000000 
                   
                 8.500 
               
               
                 2 S 
                 −44.961  
                 5.500 
                 1.516798 
                 64.14 
                 11.500 
                 S-BK7 
               
               
                 3 S 
                 −130.412  
                 2.000 
                 1.647686 
                 33.83 
                 11.500 
                 S-SF2 
               
               
                 4 S 
                 Plane 
                 31.809 
                 1.000000 
                   
                 11.500 
               
               
                 5 S 
                 Plane 
                 29.874 
                 1.516798 
                 64.14 
                 11.500 
                 S-BK7 
               
               
                 6 S 
                 Plane 
                 0.700 
                 1.000000 
                   
                 11.500 
               
               
                 7 S 
                 Plane 
                 46.919 
                 1.516798 
                 64.14 
                 11.500 
                 S-BK7 
               
               
                 8 S 
                 −24.297  
                 8.000 
                 1.000000 
                   
                 11.500 
               
               
                 9 S 
                 12.606 
                 2.000 
                 1.647686 
                 33.83 
                 11.500 
                 S-SF2 
               
               
                 10 S 
                 Plane 
                 3.000 
                 1.516798 
                 64.14 
                 11.500 
                 S-BK7 
               
               
                 11 S 
                 Plane 
                 0.001 
                 1.516798 
                 64.14 
                 11.500 
               
               
                   
               
            
           
           
               
            
               
                 Infinite Conjugates 
               
            
           
           
               
               
               
               
            
               
                 BFL 0.00068 
                 EFL 108.002 
                 FNO 6.35307 
                 FFL −490.379 
               
            
           
           
               
            
               
                 At used Conjugates (Infinite Object Distance and Finite Focus) 
               
            
           
           
               
               
               
               
            
               
                 MAG 
                 0.00000 
                   
                   
               
               
                 OBJ NA 
                 0.00000 
               
               
                 IMAG NA 
                 −0.07870  
               
               
                 OBJ DIST 
                 undefined 
               
               
                 IMG DIST 
                 0.00068 
               
               
                 TRACK 
                 undefined 
               
               
                 THKNESS 
                 129.803   
               
               
                 IMG HT 
                 4.71547 
               
               
                 IMG ANG 
                 11.21297  
               
            
           
           
               
            
               
                 Entrance Pupil Diameter and Distance from First Surface 
               
            
           
           
               
               
               
               
            
               
                 DIA 17.00000 
                 DIST 0.00000 
                   
                   
               
            
           
           
               
            
               
                 Exit Pupil Diameter and Distance from Last Surface 
               
            
           
           
               
               
               
               
            
               
                 DIA 3.74412 
                 DIST −36.07950 
               
               
                   
               
            
           
         
       
     
     &lt;Combination of the Objective Lens and the Eyepiece Lens&gt; 
     As shown in  FIG. 11 , it is possible to configure the optical scope, the eye-relief of which is increased, by combining the objective lens and the eyepiece lens. Since the eyepiece lens  110  is designed to place the reticle  130  on the right, the eyepiece lens  110  has to combine lens data inversely when combining the objective lens  120  and the eyepiece lens  110 . 
       FIG. 12  shows the effect of the present invention, which illustrates that the eye-relief decreases from 90 mm to 40.6 mm when the field lens  140  having the negative power is removed. 
       FIG. 13  shows a modulation transfer function (MTF) of a combination optical system, in which the X axis refers to a cycles/rad axis of which the maximum is 2000 cycles/rad and the Y axis refers to an MTF value of which the maximum is 1.0. That is, it will be understood that resolution is good since more than 900 cycles/rad are obtained at an MTF of 50%. 
     Below, an optical scope according to a second exemplary embodiment of the present invention will be described. 
       FIG. 14  is a cross-section view of an optical scope according to a second exemplary embodiment of the present invention. As shown therein, the optical scope according to the second exemplary embodiment is different from that of the foregoing exemplary embodiment in that an objective lens  120 , an erecting optical system  150 , a reticle  130 , a field lens  140  having negative power, and an eyepiece lens  110  are arranged in sequence. 
     Here, the field lens  140  having the negative power has a flat surface opposite to the objective lens  120 , so that it can be bonded to or arranged in parallel with the reticle  130  of the flat lens. With this configuration, the eye-relief is increased by the field lens  140  having the negative power like that of the foregoing exemplary embodiment, thereby having the same effect as that of the first exemplary embodiment. 
     Although it is not shown, the field lens  140  having the negative power may have a flat surface facing the objective lens  120 , and the reticle  130  may be etched on the flat surface of the field lens  140 , so that the field lens  140  and the reticle  130  can be formed as a single body, thereby omitting the flat lens. 
     Below, an optical scope according to a third exemplary embodiment of the present invention will be described. 
       FIG. 15  is a cross-section view of an optical scope according to a third exemplary embodiment of the present invention. 
     The optical scope according to the third exemplary embodiment is different from that of the foregoing exemplary embodiments in that a field lens  140  is divided into a first field lens  141  having negative power and a second field lens  142  having negative power, and an objective lens  120 , an erecting optical system  150 , the first field lens  141  having the negative power, a reticle  130 , the second field lens  142  having the negative power, and an eyepiece lens  110  are arranged in sequence. 
     Here, the first field lens  141  and the second field lens  142  each having the negative power have flat surfaces opposite to the reticle  130 , so that they can be configured as being bonded to or arranged in parallel with the reticle  130  of the flat lens. 
     Further, the first field lens  141  and the second field lens  142  may have flat surfaces facing the reticle  130 , and the reticle  130  is etched on one of the flat surfaces of the first and second field lenses  141  and  142 , so that the first field lens  141  or the second field lens  142  can be integrated with the reticle  130 , thereby omitting the flat lens. 
     As described above, an optical scope in which a lens having negative power is disposed on an image formation surface of an objective lens in order to increase eye-relief, so that a shooter&#39;s eyes can be sufficiently distant from the scope, thereby reducing damage due to recoil of shooting in a firearm and quickly acquiring motion of a target and its surroundings. 
     While this invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.