Abstract: A method of producing a mold for a microlens array with a cutting tool rotating around a rotation axis, microlenses having the substantially same shapes. A z-axis of an (x, y, z) coordinate system is in the direction of the central axis of a surface of the mold. The method includes the steps of cutting a surface of the mold while each of angle ? between the rotation axis of the cutting tool and a straight line passing through a point on the rotation axis and parallel to the z-axis and angle ? of a plane containing the rotation axis and the straight line around the straight line is kept constant; and cutting the plural surfaces while the values of angle ? and angle ? are determined such that a variance of the values of at least one of angle ? and angle ? is greater than a predetermined value.

Abstract: A mold machining method using an endmill, the contour of a cross section of the mold being concave and continuous in an area, a ratio of the maximum to the minimum of radius of curvature of the contour of a portion of the area (a first area) being 2 or greater, and a blade of the endmill having a second area where the contour of a cross section is similar to the contour of the first area, the method comprising the steps of determining a spiral path of the endmill such that each point of the first area is machined by a portion of the second area, corresponding to said each point in the similarity, and a radial interval between the spiral tool path is maximized while keeping surface roughness of the machined mold at or below a predetermined value; and machining the mold along the path.

Abstract: A method for manufacturing a mold for a retroreflective element, the mold having plural polygonal faces having a common vertex, the method including the steps of: roughing of a polygonal face in which cutting is carried out such that a predetermined cutting amount in a finishing process is left with respect to a desired shape; and finishing of the polygonal face in which a blade portion is made to move relatively towards the vertex while an angle of relief of the blade portion is kept within 1 degree so as to carry out cutting of the predetermined cutting amount, wherein a depth of cut for each one-time cutting operation is 2 micrometers or smaller, and the movement of the blade portion is a combination of a motion towards the vertex and an oscillation.

Abstract: A diffuser provided with plural shapes obtained by translation on an xy plane of at least one of z=g(x, y) and z=?g(x, y), z=g(x, y) being a smooth function within a rectangle having sides of length of s in x direction and sides of length of t in y direction, the origin being the center of the rectangle, wherein on the sides of the rectangle, g ? ( x , y ) = 0 , ? ? g ? ( x , y ) ? x = 0 , ? ? g ? ( x , y ) ? y = 0 , ? ? 2 ? g ? ( x , y ) ? x 2 = 0 , and ? 2 ? g ? ( x , y ) ? y 2 = 0 , and wherein z=g(x, y) has a single vertex at (xv,yv) g(x,y)=h1(x)·h2(y), first derivative of z=h1(x) is continuous in ( - s 2 , s 2 ) , second derivative of z=h1(x) has a single point of discontinuity in ( - s 2 , x v ) and ? ( x v , s 2 ) , first derivative of z=h2(y) is continuous in ( - t 2 , t 2 ) , and second derivative of z=h2(y) has a single

Abstract: Provided is a mold manufacturing method that is capable of manufacturing a mold of a complex shape particularly of an optical element with sufficient shape accuracy and within a relatively short time. This mold manufacturing method includes: a step for forming a base made of metal into a first shape through machining; a step for coating the base with a resin layer; a step for forming the resin layer into a second shape; and a step for forming the base into a third shape through dry-etching.

Abstract: A mold machining method using an endmill, the contour of a cross section of the mold being concave and continuous in an area, a ratio of the maximum to the minimum of radius of curvature of the contour of a portion of the area (a first area) being 2 or greater, and a blade of the endmill having a second area where the contour of a cross section is similar to the contour of the first area, the method comprising the steps of: determining a spiral path of the endmill such that each point of the first area is machined by a portion of the second area, corresponding to said each point in the similarity, and a radial interval between the spiral tool path is maximized while keeping surface roughness of the machined mold at or below a predetermined value; and machining the mold along the path.

Abstract: Provided is a mold manufacturing method that is capable of manufacturing a mold of a complex shape particularly of an optical element with sufficient shape accuracy and within a relatively short time. This mold manufacturing method includes: a step for forming a base made of metal into a first shape through machining; a step for coating the base with a resin layer; a step for forming the resin layer into a second shape; and a step for forming the base into a third shape through dry-etching.

Abstract: A diffuser provided with plural shapes obtained by translation on an xy plane of at least one of z=g(x, y) and z=?g(x, y), z=g(x, y) being a smooth function within a rectangle having sides of length of s in x direction and sides of length of t in y direction, the origin being the center of the rectangle, wherein on the sides of the rectangle, g ? ( x , y ) = 0 , ? ? g ? ( x , y ) ? x = 0 , ? ? g ? ( x , y ) ? y = 0 , ? ? 2 ? g ? ( x , y ) ? x 2 = 0 , and ? 2 ? g ? ( x , y ) ? y 2 = 0 , and wherein z=g(x, y) has a single vertex at (xv,yv) g(x,y)=h1(x)·h2(y), first derivative of z=h1(x) is continuous in ( - s 2 , s 2 ) , second derivative of z=h1(x) has a single point of discontinuity in ( - s 2 , x v ) and ? ( x v , s 2 ) , first derivative of z=h2(y) is continuous in ( - t 2 , t 2 ) , and second derivative of z=h2(y) has a sin

Abstract: A microlens array includes N microlenses arranged in a predetermined direction on an x-y plane. A projection onto the x-y plane of the vertex of each microlens is arranged in the vicinity of a lattice point of a reference lattice on the x-y plane, the lattice spacing of the reference lattice in the predetermined direction being D/M (millimeters) where M is a positive integer. A distance between two sides of a lens facing each other is approximately equal to D, and a distance between the projection onto the x-y plane of the vertex of the lens and the projection onto the x-y plane of a side of the lens is D/2+?i. Letting n represent the refractive index of the material of each microlens and letting f (millimeters) represent the focal length of each microlens, the following relationships are satisfied. 0.0042 D < D 2 ? ? f = D ? ( n - 1 ) 2 ? ? R 0.0048 ? f ? { 1 + ( D / 2 ? ? f ) 2 } < ? < 0.

Abstract: A microlens array includes N microlenses arranged in a predetermined direction on an x-y plane. A projection onto the x-y plane of the vertex of each microlens is arranged in the vicinity of a lattice point of a reference lattice on the x-y plane, the lattice spacing of the reference lattice in the predetermined direction being D/M (millimeters) where M is a positive integer. A distance between two sides of a lens facing each other is approximately equal to D, and a distance between the projection onto the x-y plane of the vertex of the lens and the projection onto the x-y plane of a side of the lens is D/2+?i. Letting n represent the refractive index of the material of each microlens and letting f (millimeters) represent the focal length of each microlens, the following relationships are satisfied. 0.0042 D < D 2 ? ? f = D ? ( n - 1 ) 2 ? ? R 0.0048 ? f ? { 1 + ( D / 2 ? ? f ) 2 } < ? < 0.