Abstract:
An optical system includes, in order from an object side to an image side, a first lens unit having a positive refractive power and a second lens unit having a negative refractive power, the second lens unit being moved during focusing, wherein the first lens unit has a diffractive optical element of positive refractive power and a first lens subunit of positive refractive power, and the first lens subunit consists of at least one positive lens and at least one negative lens, the optical system satisfying the following conditions: 
     
       
         0.005&lt;φ D /φ 1a &lt;0.05 
       
     
     
       
         50&lt;ν 1ap &lt;75 
       
     
     
       
         25&lt;ν 1an &lt;60 
       
     
     where 
     φ D : a refractive power of the diffractive optical element of positive refractive power in the first lens unit, 
     φ 1a : a refractive power of the first lens subunit, 
     ν 1ap : an Abbe number of a material of the positive lens, or a mean value of Abbe numbers of materials of positive lenses, included in the first lens subunit, 
     and 
     ν 1an : an Abbe number of a material of the negative lens, or a mean value of Abbe numbers of materials of negative lenses, included in the first lens subunit.

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an image forming optical system having a diffractive optical element and, more particularly, to a photographic optical system of the telephoto type having a large relative aperture with a refractive optical element and a diffractive optical element used in combination to improve imaging performance, suited to silver-halide photographic cameras, video cameras, electronic still cameras, etc. 
     Description of Related Art 
     In general, in long-focal-length or telephoto lenses, as the focal length becomes longer, various aberrations, especially, longitudinal chromatic aberration and lateral chromatic aberration, tend to worsen. To correct these chromatic aberrations, there has been a previous proposal for combining a positive lens made of a low-dispersion material, which has an extraordinary partial dispersion, such as fluorite, with a negative lens made of a high dispersion material, so as to obtain achromatism. Such a method has found its use in many telephoto lenses. 
     Optical glasses of extraordinary partial dispersion such as fluorite are advantageous for correcting chromatic aberrations, but have a disadvantage that they are very expensive. In specific gravity, too, they are relatively greater than the other low-dispersion glasses whose partial dispersions are not extraordinary. Therefore, the use of fluorite leads also to a drawback that the whole lens system becomes heavier. (For example, fluorite is 3.18 and FK01 is 3.63 in specific gravity. In contrast, FK5 that has a small extraordinary partial dispersion is 2.46 and BK7 is 2.52 in specific gravity.) Moreover, the extraordinary partial dispersion glass surface is relatively susceptible to scratches. Further, FK01 or the like, when made in the form of large relative aperture lenses, gives rise to another drawback that these lenses are liable to crack when the ambient temperature changes rapidly. 
     Telephoto lenses in which chromatic aberration is corrected only by using a glass having no extraordinary partial dispersion have been proposed in Japanese Laid-Open Patent Applications No. Hei 6-324262 and No. Hei 6-331887. 
     The telephoto lens disclosed in the above Japanese Laid-Open Patent Application No. Hei 6-324262 is composed of at least one diffractive optical element having a positive refractive power, at least one refractive optical element having a positive refractive power, and at least one refractive optical element having a negative refractive power, has an F-number of F2.8 or thereabout and is corrected relatively well for chromatic aberration. Also, the telephoto lens disclosed in the above Japanese Laid-Open Patent Application No. Hei 6-331887 is composed of a combination of a diffractive optical element and refractive optical elements, has an F-number of F2.8 or thereabout and is corrected relatively well for chromatic aberration. 
     In telephoto lenses adapted to be mounted on cameras having the automatic focusing function, which are extensively being developed in recent years, it has become general that focusing is effected by moving along an optical axis a lens unit disposed in a relatively rear portion, which is light in weight and provides little load on the lens barrel. 
     In a case where, in the photographic optical system disclosed in the above Japanese Laid-Open Patent Application No. Hei 6-324262, focusing is made to be effected by moving a rear lens unit, various aberrations including chromatic aberration become worse. Therefore, such a photographic optical system is difficult to use as a telephoto lens adapted for cameras having the automatic focusing function. 
     Further, in the optical system of the telephoto lens disclosed in the above Japanese Laid-Open Patent Application No. Hei 6-331887, as shown in FIG. 10 or FIG. 12 thereof, there is provided, as a lens unit that is relatively light in weight and has relatively little variation of monochromatic aberration during focusing, a lens unit disposed slightly in the rear (image side) of the middle point of the optical system and that consists of a cemented lens composed of a positive lens and a negative lens and having a negative refractive power as a whole. However, such a telephoto lens is not necessarily sufficient for the distribution of refractive power between the diffraction surface (diffractive optical element) and the refractive optical element and for setting of glass materials. Therefore, if the above negative lens unit is used for focusing, the variation of chromatic aberration becomes large. 
     BRIEF SUMMARY OF THE INVENTION 
     An object of the invention is to provide an image forming optical system, such as a telephoto lens, which is capable of making chromatic aberrations sufficiently small. 
     Another object of the invention is to provide an image forming optical system, such as a telephoto lens, whose chromatic aberrations vary to a small extent with focusing. 
     To attain the above objects, in accordance with an aspect of the invention, there is provided an optical system that comprises, in order from an object side to an image side, a first lens unit having a positive refractive power and a second lens unit having a negative refractive power, the second lens unit being moved during focusing, wherein the first lens unit has a diffractive optical element of positive refractive power and a first lens subunit of positive refractive power, and the first lens subunit comprsises at least one positive lens and at least one negative lens, the optical system satisfying the following conditions: 
     
       
         0.005&lt;φ D /φ 1a &lt;0.0 5  (1) 
       
     
     
       
         50&lt;ν 1ap &lt;75  (2) 
       
     
     
       
         25&lt;ν 1an &lt;60  (3) 
       
     
     where 
     φ D : the refractive power of the diffractive optical element of positive refractive power in the first lens unit, 
     φ 1a : the refractive power of the first lens subunit, 
     ν 1ap : the Abbe number of a material of the positive lens, included in the first lens subunit when there is only one positive lens in the first lens subunit or the mean value of Abbe numbers of materials of positive lenses, included in the first lens subunit included in the first lens subunit when there is more than one positive lens in the first lens subunit, 
     and 
     ν 1an : the Abbe number of a material of the negative lens included in the first lens subunit when there is only one negative lens in the firs lens subunit, or the mean value of Abbe numbers of materials of negative lenses, included in the first lens subunit when there is more than one negative lens in the first lens subunit. 
     In accordance with another aspect of the invention, there is provided an optical system that comprises, in order from an object side to an image side, a first lens unit having a positive refractive power and a second lens unit having a negative refractive power, the second lens unit being moved toward the image side along an optical axis during focusing from an infinitely distant object to a closest object, wherein the first lens unit has a diffractive optical element of positive refractive power composed of a diffraction grating of revolution symmetry with respect to the optical axis and a first lens subunit of positive refractive power, and the first lens subunit consists of at least one positive lens and at least one negative lens, the optical system satisfying the following conditions: 
     
       
         0.005&lt;φ D /φ 1a &lt;0.05 
       
     
     
       
         50&lt;ν 1ap &lt;75 
       
     
     
       
         25&lt;ν 1an &lt;60 
       
     
     where 
     φ D : the refractive power of the diffractive optical element of positive refractive power in the first lens unit, 
     φ 1a : the refractive power of the first lens subunit, 
     ν 1ap : then Abbe number of a material of the positive lens, or the mean value of Abbe numbers of materials of positive lenses, included in the first lens subunit included in the first lens subunit when there is more than one positive lens in the first lens subunit, 
     and 
     ν 1an : the Abbe number of a material of the negative lens included in the first lens subunit when there is only one negative lens in the first lens subunit, or the mean value of Abbe numbers of materials of negative lenses, included in the first lens subunit when there is more than one negative lens in the first lens subunit. 
     In accordance with a further aspect of the invention, the optical system further satisfies the following condition: 
     
       
         0.5&lt;φ 1a /φ&lt;5 
       
     
     where φ is a refractive power of the entirety of the optical system. 
     In accordance with a further aspect of the invention, the second lens unit has one positive lens and one negative lens, and the optical system further satisfies the following conditions: 
      −5&lt;φ 2 /φ&lt;−1 
     
       
         20&lt;ν 2p &lt;30 
       
     
     
       
         30&lt;ν 2n &lt;50 
       
     
     where 
     φ: the refractive power of the entirety of the optical system, 
     φ 2 : the refractive power of the second lens unit, 
     ν 2p : the Abbe number of a material of the positive lens included in the second lens unit, and 
     ν 2n : the Abbe number of a material of the negative lens included in the second lens unit. 
     In accordance with a further aspect of the invention, the first lens subunit consists of, in order from the object side to the image side, a positive lens, a positive lens and a negative lens. 
     In accordance with a further aspect of the invention, the first lens unit has a negative lens of meniscus form concave toward the image side disposed on the image side of the first lens subunit. 
     The above and further objects and features of the invention will become apparent from the following detailed description of preferred embodiments thereof taken in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     FIG. 1 is a schematic diagram of the paraxial arrangement of an optical system, for explaining the principles of the invention. 
     FIGS. 2A,  2 B and  2 C are graphs for explaining the correction of chromatic aberrations in the invention. 
     FIG. 3 is a longitudinal section view of a numerical example 1 of the optical system of the invention. 
     FIG. 4 is a longitudinal section view of a numerical example 2 of the optical system of the invention. 
     FIG. 5 is a longitudinal section view of a numerical example 3 of the optical system of the invention. 
     FIG. 6 is a longitudinal section view of a numerical example 4 of the optical system of the invention. 
     FIG. 7 is a longitudinal section view of a numerical example 5 of the optical system of the invention. 
     FIG. 8 is a longitudinal section view of a numerical example 6 of the optical system of the invention. 
     FIG. 9 is a longitudinal section view of a numerical example 7 of the optical system of the invention. 
     FIG. 10 is a longitudinal section view of a numerical example 8 of the optical system of the invention. 
     FIG. 11 is a longitudinal section view of a numerical example 9 of the optical system of the invention. 
     FIGS.  12 A 1  to  12 A 4  and FIGS.  12 B 1  to  12 B 4  are graphic representations of the longitudinal aberrations of the numerical example 1 of the invention during focusing for an infinite distance and during focusing for an object distance of 4 meters, respectively. 
     FIGS.  13 A 1  to  13 A 4  and FIGS.  13 B 1  to  13 B 4  are graphic representations of the longitudinal aberrations of the numerical example 2 of the invention during focusing for an infinite distance and during focusing for an object distance of 6 meters, respectively. 
     FIGS.  14 A 1  to  14 A 4  and FIGS.  14 B 1  to  14 B 4  are graphic representations of the longitudinal aberrations of the numerical example 3 of the invention during focusing for an infinite distance and during focusing for an object distance of 3 meters, respectively. 
     FIGS.  15 A 1  to  15 A 4  and FIGS.  15 B 1  to  15 B 4  are graphic representations of the longitudinal aberrations of the numerical example 4 of the invention during focusing for an infinite distance and during focusing for an object distance of 4 meters, respectively. 
     FIGS.  16 A 1  to  16 A 4  and FIGS.  16 B 1  to  16 B 4  are graphic representations of the longitudinal aberrations of the numerical example 5 of the invention during focusing for an infinite distance and during focusing for an object distance of 6 meters, respectively. 
     FIGS.  17 A 1  to  17 A 4  and FIGS.  17 B 1  to  17 B 4  are graphic representations of the longitudinal aberrations of the numerical example 6 of the invention during focusing for an infinite distance and during focusing for an object distance of 3 meters, respectively. 
     FIGS.  18 A 1  to  18 A 4  and FIGS.  18 B 1  to  18 B 4  are graphic representations of the longitudinal aberrations of the numerical example 7 of the invention during focusing for an infinite distance and during focusing for an object distance of 4 meters, respectively. 
     FIGS.  19 A 1  to  19 A 4  and FIGS.  19 B 1  to  19 B 4  are graphic representations of the longitudinal aberrations of the numerical example 8 of the invention during focusing for an infinite distance and during focusing for an object distance of 6 meters, respectively. 
     FIGS.  20 A 1  to  20 A 4  and FIGS.  20 B 1  to  20 B 4  are graphic representations of the longitudinal aberrations of the numerical example 9 of the invention during focusing for an infinite distance and during focusing for an object distance of 3 meters, respectively. 
     FIG. 21 is a fragmentary sectional view in enlarged scale of a diffractive optical element according to the invention. 
     FIG. 22 is a graph of the wavelength-dependent characteristics of the diffractive optical element shown in FIG.  21 . 
     FIG. 23 is a graph of the MTF characteristic of the diffractive optical element shown in FIG.  21 . 
     FIG. 24 is a fragmentary sectional view in an enlarged scale of another diffractive optical element according to the invention. 
     FIG. 25 is a graph of the wavelength-dependent characteristics of the diffractive optical element shown in FIG.  24 . 
     FIG. 26 is a graph of the MTF characteristic of the diffractive optical element shown in FIG.  24 . 
     FIG. 27 is a fragmentary sectional view in an enlarged scale of a further diffractive optical element according to the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Hereinafter, preferred embodiments of the invention will be described in detail with reference to the drawings. 
     Referring to FIG. 1, an optical system having a diffractive optical element according to the invention is illustrated as a thin system with the paraxial refractive power arrangement shown to explain optical actions in the normal state. In the present embodiment, the optical system takes the form of a telephoto lens, comprising a refractive optical system part M and a diffractive optical element having a diffraction grating formed in a surface D thereof. P represents a paraxial on-axial ray of light, and Q represents a pupil paraxial ray of light. (Here, for the purpose of simply treating problems, the diffraction surface D is assumed to be disposed on the object side of the refractive optical system part M, and the refractive optical system part M is considered as a thin single lens.) 
     FIGS. 2A,  2 B and  2 C are graphs for explaining the correction of chromatic aberrations in the invention. 
     FIGS. 3 to  11  in block diagram show numerical examples 1 to 9 of the invention, respectively. FIGS.  12 A 1  to  12 A 4  and  12 B 1  to  12 B 4  through FIGS.  20 A 1  to  20 A 4  and  20 B 1  to  20 B 4  graphically show the aberrations of the numerical examples 1 to 9 of the invention, respectively. Of the aberration graphs, the ones whose figure numbers contain letter “A” are obtained during focusing on an infinitely distant object and the others whose figure numbers contain letter “B” are obtained during focusing on an object at a finite distance. 
     In FIGS. 3 to  11 , D•O denotes a diffractive optical element having a positive refractive power composed of a diffraction grating of revolution symmetry with respect to an optical axis of the optical system. L 1  denotes a first lens unit having a positive refractive power. L 2  denotes a second lens unit having a negative refractive power, which is made to axially move toward the image side during focusing from an infinitely distant object to an object at the minimum distance. L 3  denotes a third lens unit having a positive refractive power. SP stands for a stop, and G stands for a glass block, such as optical filter or face plate. 
     In the numerical examples 1, 2, 4, 5, 7 and 8 shown in FIGS. 3,  4 ,  6 ,  7 ,  9  and  10 , respectively, the first lens unit L 1  is composed of the diffractive optical element D•O, a first lens subunit L 1   a  of positive refractive power, a positive lens L 1   p , and a negative lens L 1   n  of meniscus form concave toward the image side. 
     In the numerical examples 3, 6 and 9 shown in FIGS. 5,  8  and  11 , respectively, the first lens unit L 1  is composed of the diffractive optical element D•O, a first lens subunit L 1   a  of positive refractive power, and a negative lens L 1   n  of meniscus form concave toward the image side. 
     In the numerical examples 1 to 9, the first lens subunit L 1   a  has a bi-convex positive lens G 1 , a positive lens G 2 , and a bi-concave negative lens G 3 . 
     The second lens unit L 2  is constructed with a cemented lens composed of a positive lens and a negative lens. 
     In the numerical examples 1, 3, 4, 6, 7 and 9 shown in FIGS. 3,  5 ,  6 ,  8 ,  9  and  11 , respectively, on the image side of the second lens unit L 2  there is provided a third lens unit L 3 , which is constructed with a cemented lens composed of a positive lens and a negative lens. 
     Next, referring to FIG. 1, the features of the optical system of the invention are explained. 
     At first, on the diffraction surface D and the refractive optical system part M in combination, the formulae for the longitudinal chromatic aberration coefficient (L) and the lateral chromatic aberration coefficient (T) are obtained as follows: 
      L=h D   2 φ D /ν D +h M   2 φ M ν M   (4) 
     
       
         T=h D {overscore (h)} D φ D /ν D +h M {overscore (h)} M φ M /ν M   (5) 
       
     
     where 
     φ D : the refractive power for the diffracted light in the design diffraction order of the diffraction surface D, 
     φ M : the refractive power of the refractive optical system M, 
     ν D : the reduced Abbe number (equivalent to −3.45) of the diffraction surface D, 
     ν M : the Abbe number of the refractive optical system part M (the thin single lens), 
     h D : the height of incidence of the paraxial on-axial ray on the diffraction surface D, 
     h M : the height of incidence of the paraxial on-axial ray on the refractive optical system part M, 
     {overscore (h)} D : the height of incidence of the pupil paraxial ray on the diffraction surface D, and 
     {overscore (h)} M : the height of incidence of the pupil paraxial ray on the refractive optical system part M. 
     In actual practice, the refractive optical system part M is constructed with a plurality of lens surfaces i (where i=1, . . . and n). Therefore, the second terms of the equations (4) and (5) each should be expressed by the total sum of the aberration coefficients of all the surfaces, i.e., the first surface to the n-th surface, as follows:              L   =         h   D   2            φ   D     /     ν   D         +       ∑     i   =   1     n                       h   Mi   2            φ   Mi     /     ν   Mi                     (   6   )               T   =         h   D            h   _     D            φ   D     /     ν   D         +       ∑     i   =   1     n                       h   Mi            h   _     Mi            φ   Mi     /     ν   Mi                     (   7   )                                
     Now, since the equations (6) and (7) have their second terms concerned with the refractive optical system part M, because its overall refractive power is substantially positive, the second terms of the equations (6) and (7) take, in most cases, values of the same sign as that of the single lens model. Therefore, a discussion may be provided of the equations (4) and (5) for the single lens model without causing any particular inconvenience. So, in the following, an explanation is provided by using the equations (4) and (5). 
     In the equation (4), the second term is for the longitudinal chromatic aberration coefficient of the refractive optical system part M. 
     Since φ M &gt;0 and ν M &gt;0, the following relation is obtained: 
     
       
         h M   2 φ M /ν M &gt;0 
       
     
     In order to reduce the longitudinal chromatic aberration coefficient of the entire optical system, therefore, the first term for the longitudinal chromatic aberration coefficient of the diffraction surface D must take a negative value. That is, the following relation is obtained: 
      h D   2 φ D /ν D &lt;0 
     Here, since ν D &lt;0, the refractive power of the diffraction surface D should be as follows: 
     
       
         φ D &gt;0 
       
     
     In this instance, in the equation (5), the first term for the lateral chromatic aberration coefficient of the diffraction surface D is found from 
     
       
         h D &gt;0, {overscore (h)} D &gt;0 and ν D &lt;0, 
       
     
     to be 
     
       
         h D {overscore (h)} D φ D /ν D &lt;0. 
       
     
     Also, in the equation (5), the second term for the lateral chromatic aberration coefficient of the refractive optical system part M is found from 
     
       
         h M &gt;0, {overscore (h)} M &gt;0, φ M &gt;0 and ν M &gt;0, 
       
     
     to be 
     
       
         h M {overscore (h)} M φ M /ν M &gt;0. 
       
     
     Accordingly, the lateral chromatic aberration coefficient of the refractive optical system part M is canceled by the lateral chromatic aberration coefficient of the diffraction surface D, thus making it possible to reduce the lateral chromatic aberration coefficient of the entire optical system to a minimum. 
     In conclusion, as the refractive power of the diffraction surface D is given a positive value, the refractive optical system part M has its longitudinal and lateral chromatic aberration coefficients canceled in each at once, so that it becomes possible to improve the achromatism of the entire optical system. 
     On this account, what is to be considered is that the heights of incidence of the paraxial on-axial ray and the pupil paraxial ray both have positive values, and the absolute values of them are large. In this sense, the first lens unit of positive refractive power makes a large contribution to chromatic aberration. Hence, it becomes a necessary condition to provide the first lens unit with at least one diffraction surface having a positive refractive power, so that chromatic aberration is corrected well in at least a reference setting. 
     The discussion of the above-described type of achromatism by the chromatic aberration coefficients is concerned with two wavelengths and is not always valid in the entire visible spectrum. Including the variation of chromatic aberrations with focusing, the chromatic correction has to further improve over the entire visible spectrum. For this purpose, certain rules of design are to set forth as described below. 
     First, a case where the refractive optical system part M is corrected for longitudinal chromatic aberration in itself without using the extraordinary partial dispersion glass is considered. In this case, the spectrum curve is usually of the shape shown in FIG. 2A, whose curvature is convex downward and which crosses the abscissa at a design wavelength and another one wavelength, or is achromatized in two colors. That is, it becomes the so-called “achromatic type” spectrum curve. 
     Next, a spectrum curve the diffraction surface D can give is considered. 
     The phase shape ψ D  of the diffraction surface D can be given by the following polynomial expression: 
     
       
         ψ D (h, m)=(2π/(mλ 0 )(C 1 h 2 +C 2 h 4 +C 3 h 6   + . . . )   (8) 
       
     
     where 
     h: the height in a direction vertical to the optical axis, 
     m: an order number of the diffracted ray, 
     λ 0 : the design wavelength, and 
     C i : phase coefficients (i=1, 2, 3, . . . ). 
     Such a shape gives the diffraction surface D a refractive power φ D  which can be defined for an arbitrary wavelength λ and an arbitrary order number m by using the phase coefficient C 1  as follows: 
     
       
         φ D  (λ, m)=−2C 1  mλ/λ 0   (9) 
       
     
     If, in the equation (9), the diffraction order number m is taken at, for example, “1”, and the phase coefficient is chosen to be a negative value, the refractive power of the diffraction surface D can be made positive. As is apparent from the equation (9), it is in a wavelength region of “λ&gt;λ 0 ” that, as the wavelength increases, the positive refractive power of the diffraction surface D increases as a linear function of variation of the wavelength. Conversely, in the other wavelength region of “λ&lt;λ 0 ”, as the wavelength decreases, the positive refractive power of the diffraction surface D decreases as a linear function of variation of the wavelength. 
     In other words, on the assumption that the refractive optical system M is free from longitudinal chromatic aberration, then it results that, as the ray of the design wavelength λ 0  is focused at a position of the image plane of the entire optical system, the paraxial rays whose wavelengths are longer than the design wavelength λ 0  have their focuses falling ahead of the image plane, while the paraxial rays whose wavelengths are shorter than the design wavelength λ 0  have their focuses behind the image plane and, moreover, that the focus position shifts as a linear function of variation of the wavelength. (see FIG. 2B) 
     This leads to provide a possibility of canceling the residual chromatic aberration of the refractive optical system part M by the diffraction surface D to allow achromatization for the entire visible spectrum. For this purpose, because the diffraction surface D alone cannot give any solution for the spectrum of upward convex curvature, it has after all been found out that there is need to adjust the designing of the refractive optical system part M to the linear correction characteristic of the diffraction surface D so that longitudinal chromatic aberration, which shifts linearly in the slope reverse to the linear correction characteristic of the diffraction surface D, is beforehand produced in the visible spectrum by the refractive optical system part M. 
     In order to assure the above, it becomes necessary that the first lens unit L 1  of the refractive optical system part M be provided with the first lens subunit L 1   a  consisting of at least one positive lens and at least one negative lens and having a positive refractive power as a whole, and that the conditions (1), (2) and (3) described before be satisfied. 
     By setting forth such rules of design, the spectrum curve of the refractive optical system part M can be controlled with the design wavelength at the center so that the longer wavelength region than the design wavelength is made more under-corrected and the shorter wavelength region is made more over-corrected. With this control, the position of the minimum point of the spectrum curve can be made to shift to shorter wavelengths. As a result, the spectrum curve of the refractive optical system part M becomes almost linear in shape over the entire visible spectrum (see FIG.  2 C). In addition, the condition (1) described before is taken into account in determining the refractive power of the diffraction surface D. Achromatization for the entire visible spectrum, including good stability of chromatic correction with focusing, can thus be achieved. 
     The conditions (1), (2) and (3) are explained below. 
     The inequalities of condition (1) are concerned with the ratio of the refractive powers of the diffraction surface D and the first lens subunit L 1   a . When the upper limit of the condition (1) is exceeded, as this means that the refractive power of the diffraction surface D is too strong, the longitudinal chromatic aberration spectrum line of the diffraction surface D becomes a large absolute value of the slope. In conformity with the large absolute value of the slope, the spectrum curve of the refractive optical system part M, too, has to decline largely, while keeping the linear shape. Spherical aberration, color spherical aberrations and other aberrations are caused to worsen, which the diffraction surface D cannot sufficiently correct by its aspherical effect (corresponding to the terms for the phases in higher degrees of the equation (8)). Also, as is understandable from the first terms of the equations (5) and (6), as the refractive power of the diffraction surface D increases, the absolute value of the chromatic aberration coefficient of the diffraction surface D, too, increases. As a result, for the object movement, too, the chromatic aberration coefficient of the diffraction surface D varies greatly. The rear stage of the diffraction surface D, i.e., the first and second lens units, cannot fully correct the variation of chromatic aberration. Further, the pitch of the diffraction grating becomes much too fine to manufacture economically. So, the violation is objectionable. Conversely, when the refractive power of the diffraction surface D is weaker than the lower limit of the condition (1), as this implies that the absolute value of the slope of the longitudinal spectrum line of the diffraction surface D is too small, the slope of the spectrum curve of the refractive optical system part M cannot be made small while keeping a linear shape. In the shorter wavelength region than the design wavelength, therefore, a tough curvature convex downward is produced, making it impossible for the diffraction surface D to cancel the longitudinal chromatic aberration. So, the violation is objectionable. 
     The inequalities of conditions (2) and (3) have such an aim that, while keeping the refractive optical system part M good in aberrations other than chromatic aberration, the spectrum curve, especially with respect to the longitudinal chromatic aberration, is given a proper slope and its curvature is made looser to sustain an almost linear shape. When the upper limit of the condition (2) or the lower limit of the condition (3) is exceeded, as this implies that the spectrum curve in the shorter wavelength region than the design wavelength is too much tough in curvature, it becomes difficult for the diffraction surface D to fully correct chromatic aberration. When the lower limit of the condition (2) or the upper limit of the condition (3) is exceeded, the spectrum curve is improved in linearity, but each of the constituent lenses of the refractive optical system part M suffers collapsing of the distribution of the refracting powers over its surfaces, making it impossible to correct aberrations other than chromatic aberration in good balance. So, the violation is objectionable. Along with this, it also becomes necessary to strengthen the refractive power of the diffraction surface D. Therefore, the chromatic aberration coefficient of the diffraction surface D, too, is caused to increase in absolute value. As a result, the chromatic aberration coefficient for the object movement of the diffraction surface D varies to a large extent. Such a variation of the chromatic aberration is hard to correct fully by the rear stage, i.e., the second lens unit. 
     For more desired results, it is preferred that the conditions (1), (2) and (3) have their numerical ranges for the values φ D /φ 1a , ν 1ap  and ν 1an  respectively more restricted as follows: 
     
       
         0.009&lt;φ D /φ 1a &lt;0.021  (10) 
       
     
     
       
         56&lt;ν 1ap &lt;71  (11) 
       
     
     
       
         30&lt;ν 1an &lt;50  (12) 
       
     
     The satisfaction of the above conditions (10), (11) and (12) can further improve the correction of chromatic aberration and other aberrations and also their variations with focusing. 
     Further, in the present invention, in order to further reduce the range of variation of aberrations with focusing and to obtain a high image quality over the entire area of the image frame, it is preferred to satisfy at least one of the following conditions: 
     (i) The refractive power φ 1a  of the first lens subunit L 1   a  lies within the following range: 
     
       
         0.5&lt;φ 1a /φ&lt;5  (13) 
       
     
     where φ is the refractive power of the entire optical system. 
     The inequalities of condition (13) are valid after the conditions (1), (2) and (3) are satisfied and have an aim to improve the chromatic aberration and the other various aberrations and their variations with focusing. 
     Either when the upper limit of the condition (13) is exceeded or when the lower limit thereof is exceeded, all of the chromatic aberration and the other various aberrations become difficult to further improve. 
     For more desired results, the numerical range of the condition (13) is preferably made to be altered as follows: 
     
       
         0.95&lt;φ 1a /φ&lt;1.9  (13) 
       
     
     (ii) The second lens unit L 2  has one positive lens and one negative lens and satisfies the following conditions: 
     
       
         −5&lt;φ 2 /φ&lt;−1  (14) 
       
     
     
       
         20&lt;ν 2p &lt;30  (15) 
       
     
     
       
         30&lt;ν 2n &lt;50  (16) 
       
     
     where 
     φ 2 : the refractive power of the second lens unit, 
     ν 2p : the Abbe number of a material of the positive lens included in the second lens unit, and 
     ν 2n : the Abbe number of a material of the negative lens included in the second lens unit. 
     The conditions (14), (15) and (16) are valid after the conditions (1), (2) and (3) or the condition (13) is satisfied and have an aim to further improve the chromatic aberration and the other various aberrations and their variations with focusing and have another aim to make the optical system adaptable to the camera having an auto-focus capability by reducing the weight and shortening the forward movement of the focusing lens unit. 
     The inequalities of condition (14) give a proper range for the ratio of the refractive powers of the second lens unit and the entire optical system. When the upper limit of the condition (14) is exceeded, as this means that the refractive power of the second lens unit is too strong, an increase of the refractive power of the first lens unit, too, results. Although the diameter and the focusing movement of the second lens unit decrease, the aberration in the reference setting and the variation of aberrations with focusing both are caused to worsen objectionably. Conversely, when the refractive power of the second lens unit weakens beyond the lower limit of the condition (14), an advantage is produced for correction of the aberrations, but the diameter and the focusing movement of the second lens unit increases objectionably. 
     The conditions (15) and (16) are set forth for the purpose of correcting the variation of chromatic aberration well. Either when the upper limit is exceeded or when the lower limit is exceeded, the range of variation of chromatic aberration increases greatly. So, these factors are better made to fall within the numerical ranges specified. 
     For more desired results, it is preferred that the conditions (14), (15) and (16) have their numerical ranges for the values φ 2 /φ, ν 2p  and ν 2n  respectively more restricted as follows: 
     
       
         −2.8&lt;φ 2 /φ&lt;−1.7  (17) 
       
     
     
       
         22&lt;ν 2p &lt;25  (18) 
       
     
     
       
         33&lt;ν 2n &lt;47  (19) 
       
     
     Also, upon having satisfied the conditions (1), (2) and (3), especially the conditions (10), (11) and (12), or the condition (13), or the conditions (14), (15) and (16), especially the conditions (17), (18) and (19), it is preferred to construct the first lens subunit L 1   a  with, in order from the object side to the image side, a positive lens, a positive lens and a negative lens, totaling three lenses, thereby producing an advantage of correcting well spherical aberration, coma, and astigmatism and their variations with focusing. 
     Further, a negative lens of meniscus form concave toward the image side may be added on the image side of the first lens subunit L 1   a , thereby improving the variation of mainly spherical aberration with focusing much more. 
     Next, nine numerical examples 1 to 9 of the invention are shown. In the numerical data for the examples 1 to 9, ri is the radius of curvature of the i-th lens surface, when counted from the object side, di is the axial distance between the i-th and (i+1)st surfaces in the reference setting, when counted from the object side, and ni and vi are respectively the refractive index and Abbe number for the spectral d-line of the i-th lens element, when counted from the object side. Incidentally, f stands for the focal length and Fno stands for F-number, and 2ω stands the field angle. 
     It is to be noted in each numerical example that the phase shape ψ of the diffraction surface is expressed by the following equation: 
     
       
         ψ(h, m)=(2π/mλ 0 )(C 1 h 2 +C 2 h 4 +C 3 h 6 + . . . ) 
       
     
     where 
     h: the height in a direction vertical to the optical axis, 
     m: the order number of the diffracted rays, 
     λ 0 : the design wavelength, and 
     C i : the phase coefficients (i=1, 2, 3, . . . ). 
     In each numerical example, the order number “m” of the diffracted rays is taken at “1”, and the design wavelength λ 0  is taken at the spectral d-line (587.56 nm). 
     Numerical Example 1: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 f = 390.000 Fno = 1:2.91 2ω = 6.35° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 7.70 
                 n1 = 1.45867 
                 ν1 = 67.9 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 160.719 
                 d3 = 23.00 
                 n2 = 1.51633 
                 ν2 = 64.2 
               
               
                 r4 = −669.066 
                 d4 = 1.09 
               
               
                 r5 = 131.417 
                 d5 = 16.00 
                 n3 = 1.51633 
                 ν3 = 64.2 
               
               
                 r6 = 541.953 
                 d6 = 5.89 
               
               
                 r7 = −1579.038 
                 d7 = 7.00 
                 n4 = 1.83170 
                 ν4 = 37.0 
               
               
                 r8 = 184.386 
                 d8 = 40.19 
               
               
                 r9 = 92.935 
                 d9 = 14.50 
                 n5 = 1.51633 
                 ν5 = 64.2 
               
               
                 r10 = 326.653 
                 d10 = 3.97 
               
               
                 r11 = 69.383 
                 d11 = 6.50 
                 n6 = 1.77154 
                 ν6 = 32.1 
               
               
                 r12 = 52.352 
                 d12 = 18.12 
               
               
                 r13 = 286.035 
                 d13 = 7.50 
                 n7 = 1.85000 
                 ν7 = 23.0 
               
               
                 r14 = −252.113 
                 d14 = 3.50 
                 n8 = 1.79541 
                 ν8 = 34.4 
               
               
                 r15 = 94.805 
                 d15 = 34.02 
               
               
                 r16 = 370.404 
                 d16 = 3.00 
                 n9 = 1.71909 
                 ν9 = 28.3 
               
               
                 r17 = 137.065 
                 d17 = 6.50 
                 n10 = 1.86089 
                 ν10 = 26.8 
               
               
                 r18 = 600.357 
                 d18 = 26.36 
               
               
                 r19 = Stop 
                 d19 = 25.00 
               
               
                 r20 = ∞ 
                 d20 = 2.00 
                 n11 = 1.51633 
                 ν11 = 64.2 
               
               
                 r21 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = −2.4877 × 10 −5   
                 C 2  = 2.6305 × 10 −10   
                 C 3  = −5.5461 × 10 −14   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 2: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 f = 585.000 Fno = 1:4.12 2ω = 4.24° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 7.50 
                 n1 = 1.45867 
                 ν1 = 67.9 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 184.160 
                 d3 = 25.00 
                 n2 = 1.51633 
                 ν2 = 64.2 
               
               
                 r4 = −584.658 
                 d4 = 3.94 
               
               
                 r5 = 225.610 
                 d5 = 14.61 
                 n3 = 1.51633 
                 ν3 = 64.2 
               
               
                 r6 = 1433.116 
                 d6 = 10.92 
               
               
                 r7 = −567.224 
                 d7 = 7.00 
                 n4 = 1.80656 
                 ν4 = 37.7 
               
               
                 r8 = 268.227 
                 d8 = 124.53 
               
               
                 r9 = 108.895 
                 d9 = 10.80 
                 n5 = 1.51633 
                 ν5 = 64.2 
               
               
                 r10 = 499.231 
                 d10 = 0.15 
               
               
                 r11 = 69.080 
                 d11 = 5.00 
                 n6 = 1.63138 
                 ν6 = 33.5 
               
               
                 r12 = 57.497 
                 d12 = 33.43 
               
               
                 r13 = 257.060 
                 d13 = 6.00 
                 n7 = 1.85000 
                 ν7 = 23.0 
               
               
                 r14 = −645.982 
                 d14 = 2.80 
                 n8 = 1.85339 
                 ν8 = 43.1 
               
               
                 r15 = 106.748 
                 d15 = 53.07 
               
               
                 r16 = Stop 
                 d16 = 27.76 
               
               
                 r17 = ∞ 
                 d17 = 2.00 
                 n9 = 1.51633 
                 ν9 = 64.2 
               
               
                 r18 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = −1.8736 × 10 −5   
                 C 2  = 9.8274 × 10 −11   
                 C 3  = −1.8124 × 10 −14   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 3: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
             
           
               
                   
               
               
                 f = 389.988 Fno = 1:2.91 2ω = 8.46° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 7.30 
                 n1 = 1.51633 
                 ν1 = 64.1 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 159.485 
                 d3 = 22.50 
                 n2 = 1.51015 
                 ν2 = 68.0 
               
               
                 r4 = −690.349 
                 d4 = 1.39 
               
               
                 r5 = 131.363 
                 d5 = 15.70 
                 n3 = 1.48700 
                 ν3 = 70.4 
               
               
                 r6 = 540.029 
                 d6 = 6.05 
               
               
                 r7 = −1588.857 
                 d7 = 6.60 
                 n4 = 1.83889 
                 ν4 = 42.9 
               
               
                 r8 = 184.941 
                 d8 = 44.75 
               
               
                 r9 = 91.738 
                 d9 = 14.30 
                 n5 = 1.50435 
                 ν5 = 68.6 
               
               
                 r10 = 323.430 
                 d10 = 6.57 
               
               
                 r11 = 72.191 
                 d11 = 6.50 
                 n6 = 1.75649 
                 ν6 = 33.3 
               
               
                 r12 = 53.128 
                 d12 = 20.01 
               
               
                 r13 = 242.801 
                 d13 = 7.50 
                 n7 = 1.85000 
                 ν7 = 23.0 
               
               
                 r14 = −379.075 
                 d14 = 3.50 
                 n8 = 1.78390 
                 ν8 = 34.4 
               
               
                 r15 = 93.301 
                 d15 = 52.87 
               
               
                 r16 = 183.128 
                 d16 = 3.00 
                 n9 = 1.64392 
                 ν9 = 32.4 
               
               
                 r17 = 78.710 
                 d17 = 6.50 
                 n10 = 1.87376 
                 ν10 = 32.9 
               
               
                 r18 = 196.287 
                 d18 = 12.56 
               
               
                 r19 = Stop 
                 d19 = 25.00 
               
               
                 r20 = ∞ 
                 d20 = 2.00 
                 n11 = 1.51633 
                 ν11 = 64.2 
               
               
                 r21 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = −3.7600 × 10 −5   
                 C 2  = 2.0170 × 10 −9   
               
               
                 C 3  = −3.0380 × 10 −13   
                 C 4  = 8.1254 × 10 −19   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 4: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
             
           
               
                   
               
               
                 f = 292.506 Fno = 1:2.91 2ω = 6.35° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 6.00 
                 n1 = 1.45867 
                 ν1 = 67.9 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 120.922 
                 d3 = 16.50 
                 n2 = 1.51633 
                 ν2 = 64.2 
               
               
                 r4 = −712.166 
                 d4 = 1.36 
               
               
                 r5 = 102.601 
                 d5 = 15.16 
                 n3 = 1.51633 
                 ν3 = 64.2 
               
               
                 r6 = −721.270 
                 d6 = 1.86 
               
               
                 r7 = −492.775 
                 d7 = 4.50 
                 n4 = 1.82739 
                 ν4 = 30.7 
               
               
                 r8 = 259.377 
                 d8 = 26.36 
               
               
                 r9 = 57.444 
                 d9 = 5.00 
                 n5 = 1.63981 
                 ν5 = 40.7 
               
               
                 r10 = 46.599 
                 d10 = 15.47 
               
               
                 r11 = −321.564 
                 d11 = 5.30 
                 n6 = 1.85000 
                 ν6 = 23.0 
               
               
                 r12 = −103.619 
                 d12 = 3.20 
                 n7 = 1.61666 
                 ν7 = 42.6 
               
               
                 r13 = 83.998 
                 d13 = 33.99 
               
               
                 r14 = 1109.063 
                 d14 = 2.50 
                 n8 = 1.52539 
                 ν8 = 53.0 
               
               
                 r15 = 127.516 
                 d15 = 5.70 
                 n9 = 1.63751 
                 ν9 = 58.7 
               
               
                 r16 = −209.995 
                 d16 = 3.00 
               
               
                 r17 = Stop 
                 d17 = 33.50 
               
               
                 r18 = ∞ 
                 d18 = 2.00 
                 n10 = 1.51633 
                 ν10 = 64.2 
               
               
                 r19 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = −2.3125 × 10 −5   
                 C 2  = 2.1079 × 10 −10   
               
               
                 C 3  = −4.8078 × 10 −14   
                 C 4  = 2.9442 × 10 −18   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 5: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
             
           
               
                   
               
               
                 f = 585.002 Fno = 1:4.12 2ω = 4.24° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 7.50 
                 n1 = 1.51633 
                 ν1 = 64.1 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 185.594 
                 d3 = 25.00 
                 n2 = 1.50451 
                 ν2 = 68.5 
               
               
                 r4 = −574.943 
                 d4 = 4.41 
               
               
                 r5 = 227.587 
                 d5 = 15.90 
                 n3 = 1.48700 
                 ν3 = 70.4 
               
               
                 r6 = 1634.485 
                 d6 = 11.16 
               
               
                 r7 = −539.171 
                 d7 = 7.00 
                 n4 = 1.78460 
                 ν4 = 39.8 
               
               
                 r8 = 285.254 
                 d8 = 121.49 
               
               
                 r9 = 104.508 
                 d9 = 10.80 
                 n5 = 1.48739 
                 ν5 = 70.4 
               
               
                 r10 = 459.797 
                 d10 = 0.62 
               
               
                 r11 = 70.658 
                 d11 = 5.00 
                 n6 = 1.60934 
                 ν6 = 42.0 
               
               
                 r12 = 57.996 
                 d12 = 33.98 
               
               
                 r13 = 249.265 
                 d13 = 6.00 
                 n7 = 1.82293 
                 ν7 = 23.7 
               
               
                 r14 = −1054.298 
                 d14 = 2.80 
                 n8 = 1.81745 
                 ν8 = 46.1 
               
               
                 r15 = 104.889 
                 d15 = 53.09 
               
               
                 r16 = Stop 
                 d16 = 27.76 
               
               
                 r17 = ∞ 
                 d17 = 2.00 
                 n9 = 1.51633 
                 ν9 = 64.2 
               
               
                 r18 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = 1.8170 × 10 −5   
                 C 2  = 1.0117 × 10 −10   
               
               
                 C 3  = −1.6581 × 10 −14   
                 C 4  = 5.2668 × 10 −19   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 6: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
             
           
               
                   
               
               
                 f = 292.500 Fno = 1:2.91 2ω = 8.46° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 6.00 
                 n1 = 1.51633 
                 ν1 = 64.1 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 119.545 
                 d3 = 16.50 
                 n2 = 1.51148 
                 ν2 = 67.9 
               
               
                 r4 = −737.740 
                 d4 = 1.96 
               
               
                 r5 = 104.417 
                 d5 = 14.75 
                 n3 = 1.48700 
                 ν3 = 70.4 
               
               
                 r6 = −717.698 
                 d6 = 1.89 
               
               
                 r7 = −498.380 
                 d7 = 4.50 
                 n4 = 1.84276 
                 ν4 = 33.1 
               
               
                 r8 = 272.750 
                 d8 = 32.11 
               
               
                 r9 = 57.112 
                 d9 = 5.00 
                 n5 = 1.61594 
                 ν5 = 52.3 
               
               
                 r10 = 46.182 
                 d10 = 14.81 
               
               
                 r11 = −368.144 
                 d11 = 5.30 
                 n6 = 1.85283 
                 ν6 = 23.9 
               
               
                 r12 = −112.781 
                 d12 = 3.20 
                 n7 = 1.59518 
                 ν7 = 45.1 
               
               
                 r13 = 82.135 
                 d13 = 31.19 
               
               
                 r14 = 555.034 
                 d14 = 2.50 
                 n8 = 1.54830 
                 ν8 = 46.2 
               
               
                 r15 = 92.937 
                 d15 = 5.70 
                 n9 = 1.66817 
                 ν9 = 56.2 
               
               
                 r16 = −305.554 
                 d16 = 3.00 
               
               
                 r17 = Stop 
                 d17 = 33.50 
               
               
                 r18 = ∞ 
                 d18 = 2.00 
                 n10 = 1.51633 
                 ν10 = 64.2 
               
               
                 r19 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = −3.6388 × 10 −5   
                 C 2  = 2.0260 × 10 −9   
               
               
                 C 3  = −2.7330 × 10 −13    
                 C 4  = 3.8783 × 10 −18   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 7: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
             
           
               
                   
               
               
                 f = 389.998 Fno = 1:2.91 2ω = 6.35° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 7.30 
                 n1 = 1.51633 
                 ν1 = 64.1 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 162.526 
                 d3 = 22.50 
                 n2 = 1.51823 
                 ν2 = 59.0 
               
               
                 r4 = −637.861 
                 d4 = 0.90 
               
               
                 r5 = 132.222 
                 d5 = 15.70 
                 n3 = 1.50137 
                 ν3 = 56.4 
               
               
                 r6 = 561.248 
                 d6 = 5.48 
               
               
                 r7 = −1421.030 
                 d7 = 6.60 
                 n4 = 1.81274 
                 ν4 = 36.3 
               
               
                 r8 = 183.908 
                 d8 = 39.41 
               
               
                 r9 = 92.593 
                 d9 = 14.30 
                 n5 = 1.48700 
                 ν5 = 70.4 
               
               
                 r10 = 355.839 
                 d10 = 4.40 
               
               
                 r11 = 74.407 
                 d11 = 6.50 
                 n6 = 1.67681 
                 ν6 = 29.9 
               
               
                 r12 = 54.010 
                 d12 = 18.75 
               
               
                 r13 = 365.814 
                 d13 = 7.50 
                 n7 = 1.85000 
                 ν7 = 23.0 
               
               
                 r14 = −222.882 
                 d14 = 3.50 
                 n8 = 1.79168 
                 ν8 = 34.1 
               
               
                 r15 = 101.096 
                 d15 = 60.40 
               
               
                 r16 = 923.368 
                 d16 = 3.00 
                 n9 = 1.54224 
                 ν9 = 47.2 
               
               
                 r17 = 112.581 
                 d17 = 6.50 
                 n10 = 1.88500 
                 ν10 = 41.0 
               
               
                 r18 = 753.908 
                 d18 = 20.78 
               
               
                 r19 = Stop 
                 d19 = 25.00 
               
               
                 r20 = ∞ 
                 d20 = 2.00 
                 n11 = 1.51633 
                 ν11 = 64.2 
               
               
                 r21 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = −2.1950 × 10 −5   
                 C 2  = 2.2712 × 10 −10   
               
               
                 C 3  = −4.4010 × 10 −14   
                 C 4  = 2.8811 × 10 −18   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 8: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
             
           
               
                   
               
               
                 f = 585.000 Fno = 1:4.12 2ω = 4.24° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 7.00 
                 n1 = 1.51633 
                 ν1 = 64.1 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 188.883 
                 d3 = 24.50 
                 n2 = 1.51823 
                 ν2 = 59.0 
               
               
                 r4 = −541.325 
                 d4 = 3.70 
               
               
                 r5 = 228.625 
                 d5 = 14.00 
                 n3 = 1.51112 
                 ν3 = 60.5 
               
               
                 r6 = 1667.988 
                 d6 = 10.12 
               
               
                 r7 = −541.274 
                 d7 = 6.50 
                 n4 = 1.78813 
                 ν4 = 34.9 
               
               
                 r8 = 270.504 
                 d8 = 128.24 
               
               
                 r9 = 100.617 
                 d9 = 10.80 
                 n5 = 1.48700 
                 ν5 = 70.4 
               
               
                 r10 = 478.068 
                 d10 = 0.15 
               
               
                 r11 = 70.049 
                 d11 = 5.50 
                 n6 = 1.58574 
                 ν6 = 38.8 
               
               
                 r12 = 56.777 
                 d12 = 32.50 
               
               
                 r13 = 242.722 
                 d13 = 5.50 
                 n7 = 1.85000 
                 ν7 = 23.0 
               
               
                 r14 = −743.445 
                 d14 = 2.80 
                 n8 = 1.84379 
                 ν8 = 43.9 
               
               
                 r15 = 101.782 
                 d15 = 53.44 
               
               
                 r16 = Stop 
                 d16 = 27.90 
               
               
                 r17 = ∞ 
                 d17 = 2.00 
                 n9 = 1.51633 
                 ν9 = 64.2 
               
               
                 r18 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = 1.7925 × 10 −5   
                 C 2  = 1.3699 × 10 −10   
               
               
                 C 3  = −1.7985 × 10 −14   
                 C 4  = 4.8512 × 10 −19   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     Numerical Example 9: 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
             
           
               
                   
               
               
                 f = 292.585 Fno = 1:2.91 2ω = 8.46° 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 r1 = ∞ 
                 d1 = 5.00 
                 n1 = 1.51633 
                 ν1 = 64.1 
               
               
                 *r2 = ∞ 
                 d2 = 1.00 
               
               
                 r3 = 118.867 
                 d3 = 16.20 
                 n2 = 1.51633 
                 ν2 = 64.1 
               
               
                 r4 = −658.466 
                 d4 = 0.15 
               
               
                 r5 = 117.413 
                 d5 = 14.50 
                 n3 = 1.51823 
                 ν3 = 59.0 
               
               
                 r6 = −501.987 
                 d6 = 1.57 
               
               
                 r7 = −401.282 
                 d7 = 4.50 
                 n4 = 1.87130 
                 ν4 = 31.6 
               
               
                 r8 = 270.797 
                 d8 = 37.59 
               
               
                 r9 = 58.230 
                 d9 = 5.00 
                 n5 = 1.53513 
                 ν5 = 49.1 
               
               
                 r10 = 47.229 
                 d10 = 14.66 
               
               
                 r11 = −337.610 
                 d11 = 4.50 
                 n6 = 1.85000 
                 ν6 = 23.0 
               
               
                 r12 = −119.558 
                 d12 = 3.20 
                 n7 = 1.55484 
                 ν7 = 44.8 
               
               
                 r13 = 83.468 
                 d13 = 29.68 
               
               
                 r14 = 1305.135 
                 d14 = 2.50 
                 n8 = 1.57147 
                 ν8 = 41.1 
               
               
                 r15 = 121.977 
                 d15 = 5.30 
                 n9 = 1.73544 
                 ν9 = 52.1 
               
               
                 r16 = −304.382 
                 d16 = 3.00 
               
               
                 r17 = Stop 
                 d17 = 33.50 
               
               
                 r18 = ∞ 
                 d18 = 2.00 
                 n10 = 1.51633 
                 ν10 = 64.2 
               
               
                 r19 = ∞ 
               
             
          
           
               
                 Aspheric Phase Coefficients: 
               
             
          
           
               
                 C 1  = −3.7400 × 10 −5   
                 C 2  = 2.3674 × 10 −9   
               
               
                 C 3  = −2.5645 × 10 −13   
                 C 4  = 3.0641 × 10 −18   
               
               
                   
               
               
                 *: Diffraction Surface  
               
             
          
         
       
     
     
       
         
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Condition 
                 Numerical Example 
                   
               
             
          
           
               
                   
                 Factor 
                 1 
                 2 
                 3 
               
               
                   
                   
               
               
                   
                 φ D   
                  4.9754E-05 
                  3.7472E-05 
                  7.5200E-05 
               
               
                   
                 φ 1a   
                  2.7930E-03 
                  1.8793E-03 
                  6.3617E-03 
               
               
                   
                 φ 
                  2.5641E-03 
                  1.7094E-03 
                  3.4187E-03 
               
               
                   
                 φ 2   
                 −5.0512E-03 
                 −4.5674E-03 
                 −7.7767E-03 
               
               
                   
                 φ D /φ 1a   
                  0.0178 
                  0.0199 
                  0.0118 
               
               
                   
                 ν 1ap   
                 64.20 
                 64.20 
                 64.20 
               
               
                   
                 ν 1an   
                 37.00 
                 37.70 
                 30.70 
               
               
                   
                 φ 1a /φ 
                  1.0893 
                  1.0994 
                  1.8608 
               
               
                   
                 φ 2 /φ 
                 −1.9700 
                 −2.6719 
                 −2.2747 
               
               
                   
                 ν 2p   
                 23.00 
                 23.00 
                 23.00 
               
               
                   
                 ν 2n   
                 34.40 
                 43.10 
                 42.60 
               
               
                   
                   
               
             
          
           
               
                   
                 Condition 
                 Numerical Example 
                   
               
             
          
           
               
                   
                 Factor 
                 4 
                 5 
                 6 
               
               
                   
                   
               
               
                   
                 φ D   
                  4.6250E-05 
                  3.6340E-05 
                  7.2776E-05 
               
               
                   
                 φ 1a   
                  2.5346E-03 
                  1.8977E-03 
                  6.0034E-03 
               
               
                   
                 φ 
                  2.5642E-03 
                  1.7094E-03 
                  3.4188E-03 
               
               
                   
                 φ 2   
                 −4.5493E-03 
                 −4.3626E-03 
                 −7.3117E-03 
               
               
                   
                 φ D /φ 1a   
                  0.0182 
                  0.0191 
                  0.0121 
               
               
                   
                 ν 1ap   
                 69.20 
                 69.45 
                 69.15 
               
               
                   
                 ν 1an   
                 42.90 
                 39.80 
                 33.10 
               
               
                   
                 φ 1a /φ 
                  0.9885 
                  1.1102 
                  1.7560 
               
               
                   
                 φ 2 /φ 
                 −1.7742 
                 −2.5521 
                 −2.1387 
               
               
                   
                 ν 2p   
                 23.00 
                 23.70 
                 23.90 
               
               
                   
                 ν 2n   
                 34.40 
                 46.10 
                 45.10 
               
               
                   
                   
               
             
          
           
               
                   
                 Condition 
                 Numerical Example 
                   
               
             
          
           
               
                   
                 Factor 
                 7 
                 8 
                 9 
               
               
                   
                   
               
               
                   
                 φ D   
                  4.3900E-05 
                  3.5850E-05 
                  7.4800E-05 
               
               
                   
                 φ 1a   
                  2.7288E-03 
                  1.8972E-03 
                  5.6838E-03 
               
               
                   
                 φ 
                  2.5641E-03 
                  1.7094E-03 
                  3.4178E-03 
               
               
                   
                 φ 2   
                 −5.1350E-03 
                 −4.6495E-03 
                 −6.7224E-03 
               
               
                   
                 φ D /φ 1a   
                  0.0161 
                  0.0189 
                  0.0132 
               
               
                   
                 ν 1ap   
                 57.70 
                 59.75 
                 61.55 
               
               
                   
                 ν 1an   
                 36.30 
                 34.90 
                 31.60 
               
               
                   
                 φ 1a /φ 
                  1.0642 
                  1.1099 
                  1.6630 
               
               
                   
                 φ 2 /φ 
                 −2.0026 
                 −2.7200 
                 −1.9669 
               
               
                   
                 ν 2p   
                 23.00 
                 23.00 
                 23.00 
               
               
                   
                 ν 2n   
                 34.10 
                 43.90 
                 44.80 
               
               
                   
                   
               
             
          
         
       
     
     It should be noted in connection with the embodiment of the invention that the diffraction surface of positive refractive power is the first one, but an additional diffraction surface may be used to thereby obtain a better optical performance. The diffraction surface to add may be either positive or negative in refractive power. Particularly, in the case of adding a diffraction surface of negative refractive power, it is better placed near to the image plane of the optical system at a position where the pupil paraxial ray is incident relatively high, and the paraxial on-axial ray is incident relatively low. By this arrangement, lateral chromatic aberration is even better corrected. It should be also noted that every diffraction surface is applied to a parallel flat plate of glass (except to the filter which, although being a parallel flat glass plate, has no diffraction surface applied), as a base on one side thereof. However, the spherical lens or the aspherical lens may be used as the base for the diffraction surface, and both surfaces of the base may be formed as diffraction surfaces. Further, the diffraction surface may be applied to a cementing surface of a cemented lens. The material of the base may be anything but glass in particular, provided it is transparent for light. 
     In the embodiment described above, the diffraction grating  101  of the diffractive optical element is of kinoform as shown in FIG.  21 . FIG. 22 shows the wavelength-dependent characteristics of the diffraction efficiency in the first order of the diffractive optical element shown in FIG.  21 . An actual example of the diffraction grating is constructed on a surface of a substrate  102  with a layer of ultra-violet ray setting resin applied thereon. A diffraction grating  103  is thus formed to such a thickness “d” that the diffraction efficiency in the first order becomes 100% at a wavelength of 530 μm. As is apparent from FIG. 22, the diffraction efficiency in the design order decreases as the wavelength goes away from the optimized one, or 530 μm. Meanwhile, in the neighborhood of the design order, that is, in the zero and second orders, the amount of diffracted rays increases. Such an increase of the diffracted rays in the orders other than the design order causes the production of flare and leads to lowering the resolving power of the optical system. In FIG. 23, there is shown the MTF (Modulation Transfer Function) characteristic with respect to the spatial frequency when the actual example described above is made up in the grating shape shown in FIG.  21 . In this graph, it is understandable that the MTF characteristic drops from the desired value in the low frequency region. So, as another actual example, a laminated type of diffraction grating is shown in FIG. 24 as usable in the diffractive optical element embodying one form of the invention. FIG. 25 is the wavelength-dependent characteristics of the diffraction efficiency in the first order of the diffractive optical element in this form. To actually produce the laminated type of diffraction grating, a first diffraction grating  104  of an ultraviolet setting resin (Nd=1.499, νd=54) is formed on the substrate  102 . As stacked on the first diffraction grating  104 , a second diffraction grating  105  of another ultraviolet setting resin (Nd=1.598, νd=28) is formed. In such a combination of the materials, the thickness d 1  of the first diffraction grating  104  is determined to be d 1 =13.8 μm and the thickness d 2  of the second diffraction grating  105  is determined to be d 2 =10.5 μm. As is understandable from FIG. 25, the diffraction efficiency in the design order can be increased to higher than 95% over the entire range of useful wavelengths. The MTF characteristics with respect to the spatial frequency in this case is shown in FIG.  26 . The use of the diffractive grating of the laminated type improves the MTF characteristics in the low frequency region. The desired MTF characteristics are thus obtained. It will be appreciated from the foregoing that, if, as the diffractive optical element, the laminated structure is used, further improvements of the optical performance can be achieved. 
     Incidentally, for the diffractive optical element of the laminated structure described above, the materials are not limited to the ultraviolet setting resin. Other materials, such as plastics, also may be used instead. In some cases of the substrates, the first diffraction grating  104  may be formed directly on the substrate. Furthermore, there is no need to make the thicknesses of the two gratings different from each other. In some combinations of materials, the thicknesses of the two gratings may be made equal to each other as shown in FIG.  27 . Since, in this case, no grooves are exposed to the outside from the surface of the diffractive optical element, the dust proof characteristic is excellent, contributing to an increase of the productivity on the assembling line in manufacturing the diffractive optical elements. Accordingly, more inexpensive optical systems can be produced.