Patent Publication Number: US-2010110549-A1

Title: Optical Element and Method for Machining Die for Optical Element

Description:
FIELD OF THE INVENTION 
     The present invention relates to an optical element and method for machining a die for an optical element. 
     BACKGROUND ART 
     In recent years, a high-precision optical element such as an objective lens for an optical pickup device is produced in such a way that a diffraction surface is formed on the optical surface, and the optical characteristics are improved by the diffraction effect of this structure. In this case, the diffraction structure is generally arranged in a grooved structure. When plastics are used as materials to form an optical element by injection molding and other methods, a subtle groove must be formed on the die. When a groove is formed for this die, an NC machine is sometimes used, for example, as shown in the Patent Literature 1. A fly cutting method or shaping method is used when machining the die with the NC machine. 
     In both the fly cutting method and shaping method, the die surface is machined at a predetermined pitch. Accordingly, a microscopically roughened structure is formed as cutting indentations (sculp) on the surface after machining. A difference in the height of the microscopically roughened structure forms the sculpture height of the optical element surface. 
     In one of the proposals having been made so far, when the sculpture height is equal to or greater than a predetermined height, the pitch in the cutting die is reduced, whereby the sculpture height is reduced, in the conventional method. Alternatively, the surface of the optical element is coated with another material, whereby the sculpture height is made less conspicuous. 
     Patent Literature 1: Japanese Unexamined Patent Application Publication No. Hei 11-248906 
     DISCLOSURE OF THE INVENTION 
     Problems to be Solved by the Invention 
     Incidentally, in the coating method, a coating process is added, and this prolongs the production time. Further, the equipment for ensuring uniform coating is expensive and the coated thickness reaches 0.2 μm. Thus, this method is not applicable to a structure on the order of submicrons. 
     In the meantime, when the method for reducing the pitch at the time of cutting is utilized, the existing equipment can be used and the need of a coating step can be eliminated. Thus, this method is applicable to the structure on the order of submicrons. However, since the pitch is reduced, the machining distance is increased, hence the production time is prolonged. If the production time is prolonged, the workpiece will be subjected to changes in temperature and humidity for a long period of time during the machining operation, and a misalignment will occur at the contact point of the cutting tool and die, with the result that the precision of the profile will deteriorate. 
     The object of the present invention is to provide cutting differences between the portion of the optical surface making a greater contribution to improvements in efficiency and other portions in such a way that the processing time is reduced and the precision of the profile is improved, whereby the total efficiency is maintained at a maximum. 
     Means for Solving the Problems 
     The first structure is an optical element having a phase structure provided on an optical surface of the optical element, the phase structure being formed of a plurality of optical function surfaces divided through a plurality of stepped portions, wherein each sculpture height of the plurality of stepped portions is set smaller than each sculpture height of the plurality of the optical function surfaces. 
     The second structure is the optical element described in Claim  1  wherein the each sculpture height of the optical function surfaces is 50 nm or more without exceeding 300 nm and that the each sculpture height of the plurality of stepped portions is 5 nm or more and less than 50 nm. 
     The third structure is an optical element having a phase structure provided on an optical surface of the optical element, the phase structure being formed of a plurality of optical function surfaces divided through a plurality of stepped portions, wherein each sculpture height on a periphery of the optical surface is set smaller than a sculpture height at a center of the optical surface. 
     The fourth structure is the optical element described in Claim  3  wherein the sculpture height at the center of the optical surface is 50 nm or more without exceeding 300 nm and the each sculpture height on the periphery is 5 nm or more and less than 50 nm. 
     The fifth structure is an optical element having a phase structure provided on an optical surface of the optical element, the phase structure being formed of a plurality of optical function surfaces divided through a plurality of stepped portions, wherein a sculp pitch on the plurality of optical function surfaces is smaller than a sculp pitch on the plurality of stepped portions. 
     The sixth structure is the optical element described in Claim  5  wherein the sculp pitch on the optical function surfaces is set in such a way that each sculpture height of the optical function surfaces will be 50 nm or more without exceeding 300 nm, and the sculp pitch on the plurality of stepped portions is set in such a way that each sculpture height of the plurality of stepped portions will be 5 nm or more and less than 50 nm. 
     The seventh structure is an optical element having a phase structure provided on an optical surface of the optical element, the phase structure being formed of a plurality of optical function surfaces divided through a plurality of stepped portions, wherein a sculp pitch on the periphery of the optical surface is set smaller than a sculp pitch at a center of the optical surface. 
     The eighth structure is the optical element described in Claim  7  wherein the sculp pitch at the center of the optical surface is set in such a way that a sculpture height at the center of the optical surface is 50 nm or more without exceeding 300 nm, and the sculp pitch on the periphery of the optical surface is set in such a way that a sculpture height on the periphery of the optical surface is 5 nm or more and less than 50 nm. 
     The ninth structure is the optical element described in any one of the Claims  3 ,  4 ,  7  and  8  wherein the periphery of the optical surface is an area ranging from the edge of a concentric circle having a diameter two thirds of an effective diameter of the optical surface to the effective diameter, and an angle between a normal line with respect to an optical axis of the optical element and the tangential line to the optical surface in the area is equal to or greater than 20 degrees. 
     The tenth structure is a method for machining a die for an optical element used to mold an optical element having a phase structure provided on an optical surface of the optical element, the phase structure being formed of a plurality of optical function surfaces divided through a plurality of stepped portions, wherein a cutting condition for cutting portions corresponding to the plurality of stepped portions with respect to a base material of the die is different from a cutting condition for cutting portions corresponding to the optical function surfaces with respect to the base material of the die. 
     The eleventh structure is the method for machining a die for an optical element described in Claim  10 , wherein the cutting condition is a cutting feed pitch of a cutting tool with respect to the base material of the die. 
     The twelfth structure is the method for machining dies for an optical element described in Claim  11 , wherein the cutting feed pitch for cutting the portion corresponding to the plurality of stepped portions is smaller than the cutting feed pitch for cutting the portions corresponding to the optical function surfaces. 
     The thirteenth structure is the method for machining a die for an optical element described in Claim  12 , wherein the cutting feed pitch for cutting the portions corresponding to the optical function surfaces is set in such a way that each sculpture height of the optical function surfaces is 50 nm or more without exceeding 300 nm, and the cutting feed pitch for cutting the portions corresponding to the plurality of stepped portions is set in such a way that each sculpture height of the plurality of stepped portions is 5 nm or more and less than 50 nm. 
     The fourteenth structure is the method for machining a die for an optical element described in Claim  10 , wherein the cutting condition is a radius of a tip end of a cutting tool. 
     The fifteenth structure is a method for machining a die for an optical element used to mold an optical element having a phase structure provide on the optical surface of the optical element, the phase structure being formed of a plurality of optical function surfaces divided through a plurality of stepped portions, wherein a cutting condition for cutting a center portion corresponding to a center of the optical surface with respect to a base material of the die is different from a cutting condition for cutting a periphery portion corresponding to the periphery of the optical surface with respect to the base material of the die. 
     The sixteenth structure is the method for an optical element described in Claim  15 , wherein the cutting condition is a cutting feed pitch of a cutting tool with respect to the base material of the die. 
     The seventeenth structure is the method for machining a die for an optical element described in Claim  16 , wherein the cutting feed pitch for cutting the center portion corresponding to the center of the optical surface is smaller than the cutting feed pitch for cutting the periphery portion corresponding to the periphery. 
     The eighteenth structure is the method for machining a die for an optical element described in Claim  12 , wherein the cutting feed pitch for cutting the portion corresponding to the center is set in such a way that the sculpture height at the center is 50 nm or more without exceeding 300 nm, and the cutting feed pitch for cutting the portion corresponding to the periphery is set in such a way that the sculpture height on the periphery is 5 nm or more and less than 50 nm. 
     The nineteenth structure is the method for machining a die for an optical element described in Claim  15 , wherein the cutting condition is a radius of a tip end of a cutting tool. 
     The twentieth structure is the method for machining a die for an optical element described in any one of the Claims  15  through  19 , wherein the periphery portion is an area ranging from the edge of a concentric circle having a diameter two thirds of an effective diameter of the optical surface to the effective diameter, and an angle between a normal line with respect to an optical axis of the optical element and the tangential line to the optical surface in the area is equal to or greater than 20 degrees. 
     The twenty-first structure is the method for machining a die for an optical element described in any one of the Claims  10  through  20 , wherein a fly cutting method is used to cut the base material of the die. 
     EFFECTS OF THE INVENTION 
     According to the present invention, the sculpture height is reduced only on the face (the center of the optical surface and stepped portion) making a greater contribution to the improvement in the efficiency of using light. This arrangement reduces the cutting distance at the time of producing the optical element die as compared to the case wherein the sculpture heights of all the faces are uniform, hence reduces prolongation of the production time. Thus, profile precision is prevented from deteriorating due to a prolonged production time. 
     The sculpture height is formed smaller on the face making a greater contribution to the improvement in the efficiency of using light. This structure ensures the maximum light usage efficiency of the entire optical element. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a conceptual diagram representing the schematic configuration of the optical element of the present embodiment, wherein (a) is a front view and (b) is a side view; 
         FIG. 2  is an enlarged view inside the circle S of  FIG. 1  ( b ); 
         FIG. 3  is a enlarged view of the cross section perpendicular to the scanning direction of a cutting tool, representing the profile of the surface having been machined in a pick-feed mode according to the fly cutting or shaping method using a cutting tool; 
         FIG. 4  is an explanatory diagram representing the schematic configuration of a machine used to implement the method of machining the die for an optical element in the present invention; 
         FIG. 5  is an explanatory diagram representing the schematic configuration of the cutting tool provided on the machine of  FIG. 4 , wherein (a) is a front view, (b) is a side view and (c) is an enlarged view of the circle S 3  of (b); 
         FIG. 6  is an explanatory diagram representing a variation of the machine shown in  FIG. 4 ; and 
         FIG. 7  is an explanatory diagram representing the center and periphery of the optical element, wherein (a) is a front view and (b) is a side view. 
     
    
    
     DESCRIPTION OF REFERENCE NUMERALS 
     
         
         
           
               1 . Optical element 
               2 . Optical face 
               21 . Diffraction grating 
               22 . Level difference portion 
               23 . Optical function face 
               24  and  25 . Scalp 
               26 . Effective diameter 
               27 . Concentric circle 
               28 . Optical axis 
               29 . Normal line to optical axis 
               30 . Tangential line 
               31 . Periphery 
               32 . Center 
               100 . Machine 
               101 . Base material for die 
               102 . Chuck 
               103 . X-Y table 
               104 . Cutting tool 
               105 . Drive table 
           
         
       
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     The following describes the embodiments of the present invention with reference to the drawings. 
     In the first place, the optical element of the present invention will be described.  FIG. 1  is a conceptual diagram representing the schematic configuration of the optical element  1 , wherein (a) is a front view and (b) is a side view. 
     The “optical element” is exemplified by a lens, prism, diffraction grating optical element (including a diffraction lens, diffraction prism, phase filter, chromatic aberration, and correction element), optical filter (including a space low-pass filter, wavelength band pass filter, wavelength low-pass filter, and wavelength by-pass filter), and polarizing filter (including an analyzer, azimuth rotator, and polarizing/separation prism), without the optical element being restricted thereto. Further, the optical element can be one that separates light by transmission and converges light onto a different position, or one that separates light by reflection and converges light onto a different position. 
     As shown in  FIG. 1 , the optical element  1  is formed in a disk, and a plurality of diffraction gratings  21  running in one direction (lateral direction of  FIG. 1 ) are formed on the optical surface  2  thereof.  FIG. 2  is an enlarged view inside the circle S of  FIG. 1  ( b ). As shown in  FIG. 2 , a plurality of optical function faces  23  divided through a stepped portion  22  are formed on the optical surface  2 . 
       FIG. 3  is an enlarged view of the cross section perpendicular to the scanning direction of a cutting tool, representing the profile of the surface having been machined in a pick-feed mode according to the fly cutting or shaping method using a cutting tool. As shown in  FIG. 3 , a plurality of minute microscopically roughened structures are shaped on the stepped portion  22  and optical function face  23 . These microscopically roughened structures represent sculps  24  and  25 . They are formed by transferring the microscopically roughened structures on the surface of the die when the optical element  1  is molded. The height of the sculps  24  and  25  (height from the common tangential lines L 1  and L 2  of the circles S 2  constituting the sculps  24  and  25 ) is called the sculpture height. The pitch of the sculps  24  and  25  (center-to-center distance of the circles S 2  constituting the sculps  24  and  25 ) is called the sculp pitch. 
     The sculpture height H 1  of the stepped portion  22  is formed smaller than the sculpture height H 2  of the optical function face  23 . To put it more specifically, the sculpture height H 2  of the optical function face  23  is 50 nm or more without exceeding 300 nm, and the sculpture height H 1  of the stepped portion  22  is 5 nm or more to less than 50 nm exclusively. 
     The sculpture height H 1  can be made different from the sculpture height H 2  when the diameters of the circles S 2  are made different. If the diameters of the circles S 2  are constant, the sculpture height H 1  can be made different from the sculpture height H 2  by making the sculp pitches different. In this case, the sculpture height H 1  of the stepped portion  22  can be made smaller than the sculpture height H 2  of the optical function face  23  by making the sculp pitch P 1  of the stepped portion  22  smaller than the sculp pitch P 2  of the optical function face  23 . Further, it is preferred in this case that the sculp pitch P 2  of the optical function face  23  should be set in such a way that the sculpture height H 2  of the optical function face  23  is 50 nm or more without exceeding 300 nm, and the sculp pitch P 1  of the stepped portion  22  should be set in such a way that the sculpture height H 1  of the stepped portion  22  is 5 nm or more to less than 50 nm exclusively. 
     If the sculpture heights H 1  and H 2  exceed the aforementioned upper limit, high-order diffracted light beam and flare in the relevant optical element  1  may be subjected to deterioration in optical performance in addition to deterioration in efficiency. 
     If the sculpture heights H 1  and H 2  are below the aforementioned lower limit, there will be a huge increase in the number of cuttings (the number of cutting lines) in the pick-feed mode, and the machining time will be unrealistic. 
     The following describes the method of machining the die for the optical element in order to mold the optical element  1 . 
     In the first place, the machine used to implement the method of machining the die for the optical element will be described.  FIG. 4  is an explanatory diagram representing the schematic configuration of the machine. The machine  100  is a fly-cutting machine. As shown in  FIG. 4 , the machine  100  is provided with a chuck  102  for holding the base material for the die  101 , an X-Y table  103  for supporting the chuck  102  movable in the horizontal direction, and an elevating drive table  105  for rotatably holding the cutting tool  104 . 
     The X-Y table  103  is designed in such a way that the chuck  102  is moved in the direction (the lateral direction in the drawing: X-direction) wherein the base material for the die  101  is connected and disconnected from the cutting tool  104  and the direction (Y-direction) horizontally perpendicular to the X-direction. 
     The drive table  105  allows a groove to be formed on the machined surface  106  of the base material for the die  101  by rotating the cutting tool  104 . 
     To put it more specifically, the chuck  102  is moved in the X-direction in such a way that the machined surface  106  of the base material for the die  101  is brought in contact with the cutting tool  104  when the drive table  105  has rotated the cutting tool  104 . This movement ensures that the machined surface  106  of the base material for the die  101  will be cut by the cutting tool  104 . If the chuck  102  is moved in the Y-direction when the cutting operation is maintained, the machined surface  106  is cut, and one groove line is formed in the Y-direction. When one groove line has been formed, the chuck  102  is moved in the X-direction, in such a way that the machined surface  106  is removed from the cutting tool  104 . 
     Then the drive table  105  is raised or lowered by a predetermined pitch. After that, the chuck  102  is moved in the X-direction in such a way that the machined surface  106  of the base material for the die  101  is brought in contact with the cutting tool  104 , and the machined surface  106  of the base material for the die  101  is cut by the cutting tool  104 . If the chuck  102  is moved in the Y-direction with the cutting operation being maintained, one groove line is formed on the machined surface  106 . Repetition of this procedure allows the optical surface  2  of the optical element  1  to be formed on the machined surface  106  of the base material for the die  101 . 
     The aforementioned sculps  24  and  25  of the optical element  1  are formed by the groove formed on the machined surface  106  of the base material for the die  101  by the cutting tool  104 . The cutting conditions for cutting the stepped portion that corresponds to the stepped portion  22  with respect to the base material for the die  101  is different from the optical function face portion that corresponds to the optical function face  23  with respect to the base material for the die  101  in such a way that the sculpture height H 1  of the stepped portion  22  in the optical element  1  and the sculpture height H 1  of the optical function face  23  will have the aforementioned set values. 
     The cutting conditions are exemplified by the cutting feed pitch of the cutting tool with respect to the base material for the die  101  and the tip radius of the cutting tool. 
     When the cutting condition is to be changed by making the cutting feed pitch different, the cutting feed pitch corresponding to cutting the stepped portion is set smaller than the cutting feed pitch corresponding to cutting the optical function face portion. To put it more specifically, the cutting feed pitch corresponds to the sculp pitch. Accordingly, the cutting feed pitch for cutting the corresponding optical function face portion is set in such a way that the sculpture height of the optical function face is 50 nm or more without exceeding 300 nm, and the cutting feed pitch for cutting the corresponding stepped portion is set in such a way that the sculpture height of the stepped portion is 5 nm or more to less than 50 nm exclusively. 
     In the case of a fly-cutting machine  100 , the cutting feed pitch can be classified into line feed pitch and main feed pitch. The line feed pitch is the pitch based on the vertical movement of the drive table  105 . The main feed pitch is the pitch based on the movement of the chuck  102  in the Y-direction. Both of these pitches are set to meet the aforementioned conditions. 
     In the case of line feed pitch, for example, assume that the tool tip radius is “r” (nm), and the elevation pitch of the drive table  105  (the aforementioned predetermined pitch) is “fp” (nm). Then, the tool tip radius and elevation pitch is determined so as to meet the Formula (1). 
       5(nm)≦ r −( r   2 −( fp/ 2) 2 ) 1/2 ≦50(nm)  (1) 
     In the Formula (1), the tool tip radius is preferably further characterized in that one third of the microscopically small structure or less is kept within the range of 10 nm or more without exceeding 1 μm. The microscopically small structure in the sense in which it is used here refers to the length of one stepped portion  22 , for example. 
     In the meantime, for the main feed pitch, assume that the tool swing radius is “R” (nm), the feed rate of the chuck  102  is “f” (nm/s), and the tool rotation speed is “M” (rps). Then, for the main feed pitch sp, the tool swing radius, feed rate, and tool rotation speed are determined so as to meet the following Formulas (2) and (3). 
         sp=f/M   (2) 
       50(nm)&lt; R −( R   2 −( sp/ 2) 2 ) 1/2 ≦300(nm)  (3) 
     In Formulas (2) and (3), the tool rotation speed is preferably kept in the range of 150 rps or more without exceeding 650 rps. 
     To put it more specifically, in the present embodiment, numerical values were substituted into the Formulas (1), (2), and (3) on the assumption that the tool tip radius r is 100 nm, the tool rotation speed M is 170 rps, and the tool swing radius R is 15,000,000 nm, whereby the feed rate f and elevation pitch fp best suited to each of the corresponding stepped portions and the corresponding optical function face portion were obtained. In this embodiment, the feed rate f at the corresponding stepped portion is 5,000,000 nm/s, the elevation pitch fp is 150 nm, the feed rate f of the optical function face is 20,000,000 nm, and the elevation pitch fp is 200 nm. 
     When the cutting condition is changed by making the tool tip radius of the cutting tool  104  different, in the meantime, changes are preferably made within the range of 10 nm or more without exceeding 1 μm, as described above. 
       FIG. 5  is an explanatory diagram representing the schematic configuration of the cutting tool  104 , wherein (a) is a front view, (b) is a side view and (c) is an enlarged view of the circle S 3  of (b). The front face of the cutting tool  104  in a tool traveling direction is a tooth face  111 , and the face adjacent to the tooth face  111  is a flank  112 . The aforementioned tool tip radius is the radius on the tip portion  113  of the tooth face  111 . It is preferred that the tip angle of the tooth face  111  should be between one to five degrees smaller than the smallest of the angles formed by the stepped portion  22  of the optical element  1  and the optical function face  23 . This arrangement will prevent the cutting operation from being subjected to geometric interference. 
     If the die produced under the aforementioned conditions is used to manufacture an optical element, the aforementioned optical element  1  will be molded. In the case of the aforementioned optical element  1 , the sculpture height is formed smaller only on the stepped portion  22  thus making a greater contribution to the improvement in the efficiency of using light. This arrangement reduces the cutting distance in producing the die for the optical element  1 , as compared to the case wherein the sculpture heights of all faces are made uniform, and therefore, reduces prolongation of the production time. Thus, precision of the profile is prevented from deteriorating due to a prolonged production time. 
     Further, since the sculpture height is formed smaller only on the stepped portion  22  thus making a greater contribution to the improvement in the efficiency of using light, the light usage efficiency of the entire optical element is improved on a high level. 
     It goes without saying that the present invention can be modified as appropriate, without being restricted to the aforementioned embodiment. 
     For example, the present embodiment has been described with reference to the case of producing a die for an optical element, using a machine  100  wherein the angle of the cutting tool  104  is fixed. However, the angle of the cutting tool  104  can be changed. To put it more specifically, the drive table  105  is provided with an angle changing shaft  121  capable of changing the angle of the cutting tool  104 . This shaft permits the angle of the cutting tool  104  to be changed to a desired angle. 
     Further, a fly-cutting machine  100  was used as an example to describe the present embodiment. However, it is possible to use a shaping machine capable of cutting a groove by moving the machined surface  106  of the base material for the die  101  in the Y-direction, without the cutting tool  104  being rotated. 
     As compared to the machine wherein the angle of the cutting tool  104  can be changed, the fly-cutting machine illustrated in the present embodiment is preferably used because precise positioning of the tip of the cutting tool  104  can be achieved. 
     As compared to the shaping machine, the fly-cutting machine illustrated in the present embodiment is preferably characterized by a smaller load on the tool during the cutting operation, and a reduced amount of burrs produced. 
     Further, the present embodiment has been described with reference to the case wherein the sculpture height on the stepped portion  22  of the optical surface  2  is different from that on the optical function face  23  in the optical element  1 . However, it is also possible to make such arrangements that the sculpture height at the center of the optical surface  2  is different from that on the periphery thereof. 
       FIG. 7  is an explanatory diagram representing the center and periphery of the optical element, wherein (a) is a front view of the optical element and (b) is a side view of the optical element. As shown in  FIG. 7 , the periphery  31  of the optical surface  2  in the optical element  1  is the area ranging from the edge of the concentric circle  27  having a diameter equivalent to two thirds of the diameter of the effective diameter  26  of the optical surface  2  to the effective diameter  26 . Further, the periphery  31  is the area wherein the angle β formed between the normal line  29  of the optical element  1  with respect to the optical axis  28  and the tangential line  30  to the optical surface  2  in the aforementioned area is 20 degrees or more. The center  32  is located inside the periphery  31 . 
     The sculpture height on the periphery  31  of the optical surface  2  is formed smaller than the sculpture height of the center  32 . To put it more specifically, the sculpture height of the center  32  of the optical surface  2  is 50 nm or more without exceeding 300 nm, and the sculpture height of the periphery  31  is 5 nm or more to less than 50 nm exclusively. 
     As described above, the sculpture pitch can be changed by making the sculpture pitches different. In this case, if the sculp pitch of the periphery  31  is formed smaller than the sculp pitch of the center  32 , the sculpture height of the periphery  31  is formed smaller than the sculpture height of the center  32 . Further, in this case, the sculp pitch of the center  32  is preferably set in such a way that the sculpture height of the center  32  is 50 nm or more without exceeding 300 nm. The sculp pitch of the periphery  31  is preferably set in such a way that the sculpture height of the periphery  31  is 5 nm or more to less than 50 nm exclusively. 
     When a die for the optical element is to be machined to mold such an optical element  1 , the cutting condition for cutting the center section corresponding to the center  32  of the optical surface  2  with respect to the base material for the die  101  is made different from the cutting condition for cutting the periphery portion corresponding to the periphery  31  of the optical surface  2  with respect to the base material for the die  101 . 
     If the cutting condition is the cutting feed pitch, the cutting feed pitch for cutting the corresponding center portion is set smaller than the cutting feed pitch for cutting the corresponding periphery portion. To put it more specifically, the cutting feed pitch for cutting the corresponding center portion is set in such a way that the sculpture height of the center  32  is 50 nm or more without exceeding 300 nm, and the cutting feed pitch for cutting the corresponding periphery portion is set in such a way that the sculpture height of the periphery  31  is 5 nm or more to less than 50 nm exclusively. 
     In this case, if the aforementioned fly-cutting machine  100  is used for cutting, the feed rate f and elevation pitch fp of the corresponding periphery portion and corresponding center portion can be obtained from Formulas (1), (2), and (3). To put it more specifically, in the present embodiment, numerical values were substituted into the Formulas on the assumption that the tool tip radius r is 100 nm, the tool rotation speed M is 170 rps, and the tool swing radius R is 15,000,000 nm, whereby the feed rate f and elevation pitch fp best suited to each of the corresponding periphery portion and corresponding center portion were obtained. In this embodiment, the feed rate f of the corresponding periphery portion is 5,000,000 nm/s, the elevation pitch fp is 150 nm, the feed rate f of the corresponding center portion is 20,000,000 nm, and the elevation pitch fp is 200 nm. 
     As described above, if the sculpture height of the periphery  31  of the optical surface  2  is set smaller than that of the center  32 , the sculpture height is formed smaller only on the periphery  31  making a greater contribution to the improvement in the efficiency of using light. This arrangement reduces the cutting distance when producing the die for the optical element  1 , as compared to the case wherein the sculpture heights of all the faces are made uniform, and therefore, reduces prolongation of the production time. Thus, precision of the profile is prevented from deteriorating due to a prolonged production time. 
     The sculpture height is formed smaller on the face making a greater contribution to the improvement in the efficiency of using light. This structure ensures maximum light usage efficiency of the entire optical element.