Chromatic aberration correcting element and its application

A chromatic aberration correcting element that is a simple lens having at least one aspheric surface the radius of curvature of which increases from the optical axis toward the periphery, at least either one of the surfaces being formed as a diffraction lens surface that consists of annular segments in steps that are shifted discretely in a direction in which the lens thickness increases as a function of the distance from the optical axis. Also, a chromatic aberration correcting device having annular segments formed in steps on either a light entrance face or a light exit face or both, the annular segments being composed of planes perpendicular to and concentric with the optical axis.

BACKGROUND OF THE INVENTION 
The present invention relates to a lens that is capable of correcting 
chromatic aberration by itself. Also, the present invention relates to a 
device for correcting the chromatic aberration inherent in optical system. 
More particularly, the present invention relates to a chromatic aberration 
correcting device that is intended for use in combination with a single 
aspheric lens that is corrected for aberrations other than chromatic ones. 
The use of a simple objective lens having an aspheric surface on both sides 
has expanded these days in the art of optical disks and one of the 
principal reasons for this use is its contribution to weight reduction. 
However, the single lens in conventional use has been incapable of 
effective correction of chromatic aberration. 
A laser diode which is used as a light source for optical disks has the 
disadvantage that its emission wavelength is shifted on account of the 
change either in the output power of the laser or in the temperature. 
Hence, if the objective lens is not corrected for chromatic aberration, 
the focusing position of light rays will change in response to the shift 
in wavelength and this can cause errors when reading or writing 
information. 
To solve this problem, the present inventors previously proposed chromatic 
aberration correcting devices that had two or three glass lens elements 
cemented together (see Japanese Patent Public Disclosure Nos. Hei 3-155514 
and 3-155515). By combining either one of these chromatic correcting 
devices with a single aspheric lens, one could offer a lens system that 
was immune to the effect of wavelength variations, requiring less lens 
elements than the conventional system that is effectively corrected for 
chromatic aberration. 
However, the techniques proposed in the two patents cited above suffer from 
the disadvantage that in order to correct chromatic aberration, it is 
necessary to provide a device that is not directly concerned with the 
focusing action inherent in the objective lens. Therefore, optical system 
that is properly corrected for chromatic aberration weighs more and 
requires more parts than optical system that is not corrected. 
The conventional chromatic aberration correcting device has had the problem 
that its manufacturing cost is so high as to cancel the advantage of lower 
cost that results from the use of a single aspheric lens, whereby the net 
benefit is reduced to nil. 
The present invention has been accomplished under these circumstances and 
has as an object providing a lens that utilizes diffraction effect so as 
to correct chromatic aberration effectively without unduly increasing the 
number of lens elements. 
The present invention has been accomplished under these circumstances and 
has as an object providing a chromatic aberration correcting device that 
can be manufactured at a lower cost than devices that consist of two or 
three glass plates cemented together. 
SUMMARY OF THE INVENTION 
In order to meet the above-described requirement, according to the present 
invention, there is provided a single chromatic aberration correcting lens 
that is a single lens having at least one aspheric surface the radius of 
curvature of which increases from the optical axis toward the periphery, 
at least either one of the surfaces being formed as a diffractive lens 
surface that consists of annular segments in steps that are shifted 
discretely in a direction in which the lens thickness increases as a 
function of the distance from the optical axis. 
The single chromatic aberration correcting lens satisfies the following 
condition: 
EQU 0.8.ltoreq.t(n-1)/.lambda..sub.0 .ltoreq.10 
where 
.lambda..sub.0 : arbitrary wavelength in the operating wavelength 
t: the amount of axial shift of each annular segment (difference in height 
between adjacent steps); 
n: the refractive index of the medium of which the lens is made. 
The diffractive lens surface is provided by the surface closer to the far 
conjugate point whereas a continuous aspheric surface is provided by the 
surface closer to the near conjugate point, the diffractive lens surface 
being formed in steps as annular segments that are shifted discretely on a 
pitch that is substantially in inverse proportion to the square of the 
height from the optical axis. 
The correcting lens according may be provided in the optical system of an 
optical information recording and reproducing apparatus and which 
functions as an objective lens that causes incident parallel rays of light 
coming from the side closer to the far conjugate point to be focused on an 
optical recording medium. 
The diffractive lens surface is provided by the surface closer to the near 
conjugate point whereas a continuous aspheric surface is provided by the 
surface closer to the far conjugate point, the diffractive lens surface 
being formed in steps as annular segments that are shifted discretely on a 
pitch that is substantially in inverse proportion to the square of the 
height from the optical axis. 
According to another aspect of the invention, there is provided a chromatic 
aberration correcting device having annular segments formed in steps on 
either a light entrance face or a light exit face or both, the annular 
segments being composed of planes perpendicular to and concentric with the 
optical axis. 
The shift amount in the optical direction of adjacent annular zone t of the 
planes defined by the following condition: 
EQU t=m.lambda.0/(n-1) 
where m is an integer, n is the refractive index, and .lambda..sub.0 is an 
arbitrary wavelength in the operating wavelength range. 
The surface on which the step-like annular segments are formed is 
macroscopically a concave surface. 
The surface on which the step-like annular segments are formed is 
macroscopically a convex surface. 
According to the invention, in an optical information recording and 
reproducing apparatus that allows beams of light from a light source to be 
focused on an information recording medium by means of an objective lens 
so as to record or reproduce information, the improvement wherein a 
chromatic aberration correcting device is provided in the optical path 
between the light source and the objective lens, the chromatic aberration 
correcting device having annular segments formed in steps on either a 
light entrance surface or a light exit surface or both, the annular 
segments being composed of planes perpendicular to and concentric with the 
optical axis. 
According to another aspect of the invention, in a chromatic aberration 
correcting device of a diffraction type that has annular segments formed 
in steps on either a light entrance surface or a light exit surface or 
both, the annular segments being composed of planes perpendicular and 
concentric with the optical axis, the improvement wherein the base curve 
which is a macroscopic curvature of the planes formed in steps is an 
aspheric surface the radius of curvature of which decreases in absolute 
value with the increasing distance from the optical axis and, when the 
axial displacement of the base curve at a point having distance h from the 
optical axis is written as .DELTA.X(h), the displacement .DELTA.X'(h) of 
the planes formed in steps at a point having distance h from the optical 
axis is given by equation (3B): 
EQU .DELTA.X'(h)=(m.lambda..sub.0 /(n-1))Int((.DELTA.X(h)/(m.lambda..sub.0 
/(n-1)))+0.5) (3B) 
where m is an integer; n is the refractive index; .lambda..sub.0 is the 
wavelength at which the chromatic aberration correcting device is used or 
an arbitrary wavelength within the operating wavelength range of the 
device; and Int(X) is a function giving an integer not greater than x. 
The base curve is an aspheric surface resembling a spheroidal surface 
having a positive conic constant and, when the departure .epsilon.(h) from 
the spheroidal surface at a point having distance h from the optical axis 
is expressed by equation (1B), the base curve satisfies condition (4B) at 
all values of distance h within the effective maximum radius of passing 
beams of light: 
##EQU1## 
where C is the paraxial curvature; K is the conic constant; and .lambda. 
is the maximum operating wavelength. 
Optical system for an optical information recording and reproducing 
apparatus comprises: 
a light source; 
an objective lens that causes beams of light from the light source to be 
focused on an optical recording medium; and 
a beam splitter by means of which the reflected light from the optical 
recording medium is isolated from the optical path of incident light 
beams; 
the beam splitter having a surface that generates chromatic aberration 
which at least cancels the chromatic aberration that develops in the 
objective lens. 
According to the present invention, optics for an optical information 
recording and reproducing apparatus at least comprises: 
a light source; 
an optical path deflecting means that causes beams of light from the light 
source to be deflected toward an optical recording medium; 
an objective lens that causes the deflected light beams to be focused on 
the optical recording medium; 
a beam splitter by means of which the reflected light from the optical 
recording medium is isolated from the optical path of incident light 
beams; 
the optical path deflecting means having a surface that generates chromatic 
aberration which at least cancels the chromatic aberration that develops 
in the objective lens. 
According to the present invention, a chromatic aberration correcting 
device having at least one prism an annular planes concentric with the 
optical axis being formed in steps on at least one of the beam passing 
surfaces of the prism in such a way that the annular planes produce a 
macroscopically concave shape, chromatic aberration being generated by the 
step-like planes. 
According to another aspect of the invention, a hybrid lens that comprises: 
a glass lens having a refractive action; and 
a plastic diffraction element one surface of which is joined to the glass 
lens and the other surface of which is provided with a plurality of 
annular planes that are concentric with the optical axis and which are 
formed in steps in such a way that the lens thickness increases as a 
function of the distance from the optical axis. 
The hybrid lens may further satisfy the following condition: 
EQU 0.8.ltoreq.t(n-1)/.lambda..sub.0 .ltoreq.10 
where 
.lambda..sub.0 : arbitrary wavelength in the operating wavelength 
t: the axial difference in the thickness of the diffraction element between 
individual annular segments; and 
n: the refractive index of the medium of which the diffraction element is 
made. 
According to still another aspect of the invention, there is provided a 
chromatic aberration correcting device of a reflective and diffraction 
type that has a reflecting surface comprising the central reflecting face 
and a plurality of annular reflecting surfaces that are concentric with 
the central reflecting face, the reflecting surfaces being such that the 
shapes of their orthogonal projections onto a plane perpendicular to the 
optical axis are characterized by rotation symmetry with respect to the 
optical axis serving as the center of rotation, the central reflecting 
face, an annular reflecting face just outward of the central reflecting 
face and an adjacent annular reflecting surface being offset in position 
by the same step distance t in a direction perpendicular to those 
reflecting surfaces, so that when seen macroscopically, those reflecting 
surfaces provide a concave or a convex surface as a whole, the step 
distance t being specified in such a way that light entering as a plane 
wave at a reference wavelength will also emerge as a plane wave whereas 
light entering as a plane wave at a wavelength different from the 
reference wavelength will emerge as either a divergent or a convergent 
wavefront.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Embodiments of the single chromatic aberration correcting lens according to 
the present invention are described below. First, let us describe the 
operating theory of the invention. 
Suppose a thin lens having a focal length of f that is made from a material 
having a refractive index n which varies by .DELTA.n in response to the 
change in wavelength. The change in the power of this lens .DELTA.R in 
response to the change in wavelength is expressed by the following 
equation (1): 
EQU .DELTA.R=.DELTA.n/(f(n-1)) (1) 
In the absence of a material that has a sufficient refractive index n to 
make a lens and which yet experiences only a small index change .DELTA.n, 
no ordinary single lens having power is capable of suppressing the power 
change .DELTA.R that occurs as a result of change in wavelength. 
Under the circumstances, the single chromatic aberration correcting lens of 
the present invention is adapted to form a diffractive lens surface on 
either one of the surfaces of a single lens in such a way that the 
diffractive action of that surface is effectively used to cancel the 
chromatic aberration that will develop on account of the refractive action 
of the single lens. 
A diffractive lens may be available as either an amplitude diffractive or a 
phase diffraction lens depending upon the type of diffraction that occurs. 
From the viewpoint of efficient light utilization, a phase diffractive 
lens is desirably used. The phase diffractive lens is formed by providing 
a series of annular segments in steps that are planes perpendicular to and 
concentric with the optical axis. 
If the refractive power of a lens is written as .phi.R and if the power of 
a diffractive lens surface formed on one surface of that lens is written 
as .phi.D, the composite power .phi.T is expressed by the following 
equation (2): 
EQU .phi.T=(HR/Hl).phi.R+(HD/Hl).phi.D (2) 
where 
Hl: the height of a paraxial ray at which it enters the lens system; 
HR: the height of the Hl incident paraxial ray at which it enters the 
refractive lens on the front principal point; 
HD: the height of the Hl incident paraxial ray at which it enters the 
diffractive lens on the front principal point. 
For the sake of simplicity, let each lens be assumed as a thin lens. Then, 
equation (2) can be rewritten as follows: 
EQU .phi.T=.phi.R+.phi.D (3) 
With an ordinary refractive lens, the change in lens power .DELTA.R that is 
caused by the index change .DELTA.n due to a variation in wavelength is 
expressed by equation (4): 
EQU .DELTA.R=.phi.R(.DELTA.n/(n-1)) (4) 
where .phi.R is the refractive power of the lens. 
The power of a diffractive lens surface .phi.D is calculated by taking the 
differential coefficient of second order of the optical pathlength 
difference (as caused by diffraction) with respect to the distance from 
the optical axis. Since the optical pathlength difference is proportional 
to wavelength, the power change .DELTA.D due to the diffraction that 
occurs when the wavelength is shifted by .DELTA..lambda. from the design 
reference value .lambda..sub.0 is expressed by the following equation (5): 
EQU .DELTA.D=(.DELTA..lambda./.lambda..sub.0).phi.D (5) 
Suppose here that a lens having a focal length of 10 mm that is to be 
operated with a laser diode emitting light at a reference wavelength 
(.lambda..sub.0) of 780 nm with a shift (.DELTA..lambda.) of .+-.10 nm is 
fabricated from LAL 13 (trade name of Ohara Co., Ltd.; n780=1.68468; 
.DELTA.n=-0.000032). Equations (4) and (5) give the following values: 
EQU .DELTA.R=.phi.R(.DELTA.n/(n-1))=-4.67.times.10.sup.-4 .multidot..phi.R 
EQU .DELTA.D=.phi.D(.DELTA..lambda./.lambda.0)=1.28.times.10.sup.-2 
.multidot..phi.D 
In order to suppress the variation in composite power due to the difference 
in wavelength, .DELTA.R and .DELTA.D may be so set that their sum in zero 
(.DELTA.R+.DELTA.D=0). In other words, a lens that is free from chromatic 
aberration at wavelengths near the reference value 780 nm can be 
fabricated by satisfying the following condition (7): 
EQU .phi.R:.phi.D=1:0.0364 (7) 
Further, in order to insure the focal length 10 mm, the following equation 
(8) must hold: 
EQU .phi.R+.phi.D=0.100 (8) 
Equations (7) and (8) show that the refractive and diffractive powers are 
respectively expressed by the following equations (9) and (10): 
EQU .phi.R=0.09649 (9) 
EQU .phi.D=0.00351 (10) 
By the second integration of equation (10) with respect to the distance 
from the optical axis, the optical pathlength difference OPD(h) at the 
point on the diffractive lens surface that departs from the optical axis 
by height h is determined as follows: 
##EQU2## 
It should be noted here that in order to develop diffraction, the optical 
pathlength difference must be varied not continuously but intermittently 
or discretely in steps. Stated more specifically, the optical pathlength 
difference that occurs between light passing through a medium with the 
thickness t along the optical path and light passing through air is given 
by (n -1)t and, hence, the difference in height between adjacent steps on 
the diffractive lens must be t which is given by the following equation 
(12), or an integral multiple of the same: 
EQU t(h)=0.780.times.10.sup.-3 /(n-1) =0.780.times.10.sup.-3 
/0.68468=1.14.times.10.sup.-3 *h.sup.2 (12) 
Therefore, macroscopically, the diffractive lens is shaped like a concave 
lens the thickness of which increases in proportion to the square of the 
distance from the optical axis but, microscopically, annular segments are 
formed in steps concentric with the optical axis in the manner already 
defined hereinabove. By meeting these requirements, the diffractive lens 
can provide a desired power. 
The foregoing discussion assumes that the single chromatic aberration 
correcting lens of the present invention is a thin lens and that, 
therefore, the height of ray incidence does not change on the two surfaces 
of the lens. In practice, however, the height of ray incidence differs 
between the front and rear faces of the lens and, hence, the change in h 
must also be taken into consideration. 
It should also be noted that the ratio between the optical pathlength 
difference t(n-1) and the wavelength .lambda..sub.0 desirably satisfies 
the following condition (A): 
EQU 0.8.ltoreq.t(n-1)/.lambda..sub.0 .ltoreq.10 (A) 
It is generally held that if a diffractive lens surface is formed in such a 
way that the difference in height between adjacent steps is equal to the 
wavelength .lambda..sub.0 one will use light of first-order diffraction 
and, hence, is capable of suppressing the deterioration in wavefront 
aberration due to the change in wavelength, thereby preventing the drop in 
diffraction efficiency and imaging performance which would otherwise occur 
on account of the wavelength change. 
If the operating wavelength range is narrow in a case like that where the 
width of each annular segment is small enough to present difficulty in 
lens manufacture, the difference in height between adjacent steps may be 
increased to twice the wavelength or an integral multiple (.gtoreq.3) of 
the same and, yet, it is possible to perform the correction of chromatic 
aberration. However, if the difference in height between steps exceeds the 
upper limit of condition (A) and becomes greater than ten times the 
wavelength .lambda., the lens geometry will be no different from the 
conventional Fresnel lens and the following two problems will occur: due 
to a possible manufacturing error in the difference in height between 
steps, there is high likelihood of increased phase mismatching and, 
secondly, the efficiency of the diffractive lens decreases if the incident 
light has a wavelength departing from the design value. 
If, on the other hand, the lower limit of condition (A) is not reached, the 
phase matching necessary for the diffractive lens cannot be accomplished 
and it is substantially incapable of working as a "diffractive" lens. 
If the diffractive lens and the refractive lens are to be combined in an 
integral unit for the purpose of correcting chromatic aberration, almost 
all the power that develops is created by the refractive lens as equation 
(7) shows. Therefore, it is necessary that the refractive lens be adapted 
to be capable of substantial correction of aberrations by itself. On the 
other hand, the power of the diffractive lens is almost nil since its sole 
function is to correct the chromatic aberration that develops in the 
refractive lens. Therefore, the single chromatic aberration correcting 
lens as an integral unit has no marked difference from the conventional 
single aspheric lens as far as the macroscopic geometry is concerned. 
Example 1 
FIG. 1 shows optics that uses a single chromatic aberration correcting lens 
according to Example 1 of the present invention, in which the lens is used 
as an objective lens in an optical disk system. Beams of parallel light 
entering the lens 1 from the left are focused to from a spot on the 
recording surface located on the inner (right) side of the cover glass D 
of the optical disk. The lens 1 is an objective lens both surfaces of 
which are macroscopically convex. 
FIGS. 2(a) and 2(b) are a cross section and a plan view, respectively, that 
show the objective lens 1 as it is exaggerated to clarify the geometry of 
the annular segments formed on it. The left side of lens 1 (as seen in 
FIG. 2(a)) on which the parallel light is to be incident provides a 
discontinuous surface that is the combination of an aspheric surface of a 
refractive lens with annular segments that are formed on it to create a 
surface working as a diffractive lens surface. The annular segments are 
formed concentrically in steps that are shifted discretely in a direction 
in which the lens thickness increases as a function of the distance from 
the optical axis. The side of the lens 1 that faces the cover glass D 
forms an ordinary continuous aspheric surface. 
In order to correct spherical aberration and coma at the same time in the 
case where a high NA (numerical aperture) lens like the objective lens in 
an optical disk system is composed of a single lens, the surface on the 
side where parallel beams of light are incident, namely, on the side at 
the far conjugate point, must be formed as a convex aspheric surface the 
radius of curvature of which increases for the optical axis toward the 
periphery. 
In order for a lens to be bright, the sine condition for coma correction 
must be substantially satisfied. Hence, when combining a high NA lens with 
the diffractive lens, the optical pathlength that should be provided by 
the latter is not proportional to the square of the height of ray 
incidence h, but proportional to the square of the sine of the incident or 
emerging angle. Therefore, except in the case where the diffractive lens 
surface is on the sides where the parallel light enters and emerges, the 
geometry of the diffractive lens surface must be such that its curvature 
is not strictly proportional to the square of distance h from the optical 
axis but decreases gradually toward the periphery. It should also be noted 
that if the incident ray enters the diffractive lens at an angle 
(obliquely), the effective lens thickness will increase; therefore, in the 
case where the diffractive lens is located on the side of the high NA lens 
that is closer to the exit face, the amount of shift must also be 
considered as a function of h. 
If the diffractive lens to be combined in a unitary assembly is located at 
the far conjugate point as in the case of Example 1, the incident rays are 
subjected to the angle varying action on the diffractive lens surface in 
the axial direction and, hence, the difference in height between angular 
steps on the diffractive lens surface will increase from the optical axis 
toward the periphery. However, it is difficult to manufacture a system in 
which the lens surface is shifted along travelling rays; therefore, in the 
actual manufacturing operation, the lens surface may be shifted in the 
axial direction. 
The specific numerical data for Example 1 are listed in Tables 1 to 3 
below. FIG. 3 shows the three aberrations that develop in the system 
composed in accordance with those data: coma, chromatic aberration 
expressed in terms of spherical aberrations at 770 nm, 780 nm and 790 nm, 
and astigmatism (S, sagittal; M, meridional). 
TABLE 1 
______________________________________ 
Reference wavelength 
.lambda..sub.0 
780 nm 
Focal length f 3.30 mm 
Numerical aperture 
NA 0.55 
Lens quality n780 1.53677 
.DELTA.n 0.000025 /nm 
Lens thickness t 2.21 mm 
Disk thickness tD 1.20 mm 
Refractive indes of disk 
nD 1.57346 
______________________________________ 
The shape of the first surface of the single chromatic aberration 
correcting lens is given by the coefficients listed in Table 2 (see below) 
if the sag X(h) of the aspheric surface at the point that is departed from 
the optical axis by distance h is defined by the following equation (13) 
which has the term .DELTA.N added to the common expression of aspheric 
surface. Symbol INT(x) in Table 2 denotes a function for separating out 
the integral part of x: 
##EQU3## 
where r is the radius of curvature of the vertex of the aspheric surface; 
N is the number for the annular segment to which the point at height h 
belongs; K is the conic constant; and A4, A6, A8 and A10 are the aspheric 
coefficients of the fourth, sixth, eighth and tenth orders, respectively. 
TABLE 2 
______________________________________ 
N = INT(4.71 * h.sup.2 + 0.5) 
rN = 2.126 + 5.09 .times. 10.sup.-4 * N 
KN = -0.3689 
A4N = -1.470 .times. 10.sup.-3 + 1.45 .times. 10.sup.-6 * N 
A6N = -2.180 .times. 10.sup.-4 + 8.72 .times. 10.sup.-8 * N 
A8N = -1.000 .times. 10.sup.-5 + 4.36 .times. 10.sup.-8 * N 
A10N = -1.400 .times. 10.sup.-5 + 3.49 .times. 10.sup.-8 * N 
.DELTA.N = -0.001453 * N 
______________________________________ 
The shape of the second surface of the single chromatic aberration 
correcting lens 1 is given by the coefficients listed in Table 3 (see 
below) if the aspheric surface is defined by equation (14): 
##EQU4## 
TABLE 3 
______________________________________ 
r = -6.763 
K = 0.000 
A4 = 1.777 .times. 10.sup.-2 
A6 = -3.950 .times. 10.sup.-3 
A8 = 5.770 .times. 10.sup.-4 
A10 = -2.960 .times. 10.sup.-5 
______________________________________ 
Example 2 
FIG. 4 shows the case where the single chromatic aberration correcting lens 
according to Example 2 of the present invention is used as a collimator 
lens which collimates the divergent light from a laser diode. The 
collimator lens indicated by 2 has a meniscus shape which, as seen 
macroscopically, is convex on the left side from which beams of the 
collimated light emerge. 
FIGS. 5(a) and 5(b) are a cross section and a plan view, respectively, that 
show the collimator lens 2 as it is exaggerated to clarify the geometry of 
the annular segments formed on it. The right side of lens 2 (as seen in 
FIG. 5(a)) which faces the cover glass 3 of the laser diode provides a 
discontinuous surface that has annular segments formed on it to create a 
surface working as a substantially powerless diffractive lens surface. The 
annular segments are formed concentrically in steps that are shifted 
discretely in a direction in which the lens thickness increases as a 
function of the distance from the optical axis. The left side of the lens 
2 from which beams of collimated light emerge forms an ordinary continuous 
aspheric surface. 
In a case like that of Example 2 where a diffractive lens surface is formed 
on the side closer to the near conjugate point, one may employ an optical 
material having a refractive index ranging from 1.65 to 1.80. With such 
material, both spherical aberration and coma can be corrected by rendering 
only one surface aspheric whereas the other surface is left powerless. 
Thus, the diffractive lens surface can be formed on the basis of a plane 
and this facilitates the preparation of a lens forming mold. 
If the refractive index is not within the range 1.65 to 1.80, it is 
difficult to correct both spherical aberration and coma by means of a 
plane diffraction lens surface and some part of coma will remain 
uncorrected. Hence, the lens having an index outside the above-specified 
range is not suitable for use as a high NA lens. 
The specific numerical data for Example 2 are listed in Tables 4 and 5 
below. The shape of the first surface of collimator lens 2 which is on the 
left side as seen in FIG. 4 is given by equation (14) (see Example 1) into 
which the values listed in Table 5 are substituted. FIG. 6 shows the three 
aberrations that develop in the system composed in accordance with the 
data listed in Tables 4 and 5: coma, chromatic aberration expressed in 
terms of spherical aberrations, and astigmatism. 
TABLE 4 
______________________________________ 
Reference wavelength 
.lambda..sub.0 
780 nm 
Focal length f 10.8 mm 
Numerical aperture NA 0.20 
Lens quality n780 1.66959 
.DELTA.n 0.000030 /nm 
Lens thickness t 2.50 mm 
Cover glass thickness 
tC 0.25 mm 
Refractive index of cover glass 
nC 1.51072 
______________________________________ 
TABLE 5 
______________________________________ 
r = 7.231 
K = -0.5933 
A4 = 0.000 
A6 = -3.440 .times. 10.sup.-7 
A8 = -4.370 .times. 10.sup.-9 
A10 = 0.000 
______________________________________ 
The shape of the second surface of the single chromatic aberration 
correcting lens is given by the following equation (15) in terms of X(h), 
or the sag at the point that is departed from the optical axis by distance 
h: 
EQU X(h)=.DELTA.N (15) 
where N is the number for the annular segment to which the point at height 
h belongs and the asphericity-describing coefficient is the following 
function of N: 
EQU N=INT(2.70*h.sup.2 -0.0318*h.sup.4 +0.5) 
EQU .DELTA.N=0.001165*N 
Example 3 
FIG. 7 shows optics in which the single chromatic aberration correcting 
lens according to Example 3 of the present invention is used as an 
objective lens of a finite system for an optical disk. A laser beam form a 
laser light source (not shown) passes through a substrate 4 from the left 
and enters an objective lens 5 as divergent light, which is focused by 
that objective lens 5 to form a spot on the back side of the cover glass D 
of the optical disk. An optical decoupling hologram or the like is formed 
on the substrate 3. 
The left side of objective lens 5 comprises an aspheric surface having 
annular segments formed in steps to provide a diffractive lens surface, 
and the right side of the objective lens 3 provides a continuous aspheric 
surface. 
A bright objective lens of the finite system that is shown in Example 3 has 
a strong power or it must handle light at varying wavelengths that are not 
close to each other. In these cases, the refractive lens alone will 
experience wavelength-dependent changes not only in focal position but 
also in the amount of spherical aberration; however, the diffractive lens 
can be used to produce spherical aberrations that are sufficient to cancel 
those changes in spherical aberration. 
In a wavelength range near visible light, it can generally be the that the 
spherical aberration in a positive lens that is properly corrected at the 
reference wavelength will be under-corrected with respect to 
shorter-wavelength light which experiences high refractive idex whereas it 
is overcorrected with respect to longer-wavelength light which experiences 
lower refractive idex. 
Therefore, in order to cancel the change that occurs in spherical 
aberration on account of such variations in wavelength, the geometry of 
the diffractive lens may be so set that its power will increase gradually 
toward the periphery. The change in a lower-order spherical aberration can 
be expressed in a biquadratic function in terms of wavefront aberration; 
therefore, one can also suppress the variations in spherical aberration 
due to wavelength changes by defining the shape of the diffractive lens in 
terms of a function of two parts, one being proportional to the square of 
h and the other being proportional to the fourth power of h. 
The specific numerical data for Example 3 are listed in Tables 6 to 8 
below. The shape of the first surface of the objective lens 4 which is on 
the left side as seen in FIG. 7 is given by equation (13) (see Example 1) 
into which the values listed in Table 8 are substituted. FIG. 8 shows the 
three aberrations that develop in the system composed in accordance with 
the data listed in Tables 6 to 8: coma, chromatic aberration expressed in 
terms of spherical aberrations, and astigmatism. 
TABLE 6 
______________________________________ 
Refence wavelength .lambda..sub.0 
780 nm 
Magnification m -0.250 
Focal length f 2.64 mm 
Object-to-image distance 
IO 17.76 mm 
Numerical aperture NA 0.55 
Lens quality n780 1.53677 
.DELTA.n 0.000025 /nm 
Lens thickness t 2.00 mm 
Cover glass thickness 
tC 1.00 mm 
Refractive index of cover glass 
nC 1.51072 
Disk thickness tD 1.20 mm 
Refractive index of disk 
nD 1.57346 
______________________________________ 
TABLE 7 
______________________________________ 
N = INT(7.54 * h.sup.2 + 0.161 * h.sup.4 + 0.5) 
rN = 1.939 + 1.95 .times. 10.sup.-4 * N 
KN = -0.4290 + 6.90 .times. 10.sup.-5 * N 
A4N = -8.120 .times. 10.sup.-3 + 6.90 .times. 10.sup.-7 * N 
A6N = -3.900 .times. 10.sup.-4 - 2.07 .times. 10.sup.-7 * N 
A8N = -8.260 .times. 10.sup.-5 + 1.45 .times. 10.sup.-7 * N 
A10N = -1.910 .times. 10.sup.-5 - 1.03 .times. 10.sup.-8 * N 
.DELTA.N = -0.001453 * N 
______________________________________ 
TABLE 8 
______________________________________ 
r = -3.377 
K = 0.000 
A4 = 2.768 .times. 10.sup.-2 
A6 = -4.261 .times. 10.sup.-3 
A8 = 5.157 .times. 10.sup.-4 
A10 = -1.940 .times. 10.sup.-5 
______________________________________ 
As described on the foregoing pages, the present invention enables a single 
aspheric lens to correct chromatic aberration while suppressing other 
aberrations such as spherical aberration and coma. Therefore, if this lens 
is used as an objective lens, it offers the advantage that its size and 
weight are not much different from those of the prior art aspheric 
objective lens and that it yet is capable of correcting chromatic 
aberration to suppress defocusing that will occur on account of variations 
in the wavelength of the light source used. 
If a diffractive lens surface is formed on the side closer to the far 
conjugate point, namely, on the side where beams of parallel light enter 
when the lens of the invention is used as an objective lens for an optical 
disk, one can avoid the deposition of dirt or dust that is carried by an 
air stream generated by the revolving optical disk. Conversely, if a 
diffractive lens surface is to be formed on the side closer to the near 
conjugate point when the lens of the invention is used as a collimator 
lens, the diffractive lens surface can be formed on a substantially 
powerless side by properly selecting the refractive index of the optical 
material used. In this case, the diffractive lens surface may assume a 
simple shape that is just shifted from a plane surface and, hence, it can 
be manufactured easily. 
Various examples of the present invention are described below. 
A chromatic aberration correcting device according to an example of the 
present invention is shown in FIG. 9. A chromatic correction element is 
provided with a central surface having a revolution center about the 
optical axis and a plurality of annular zone surfaces which are coaxial 
with the central surface. The positions of the central surface, the zonal 
surfaces outside of the central surface and the adjacent annular zonal 
surfaces are displaced by a constant step distance t, so that these 
surfaces constitute a convex surface or a concave surface is a macroscopic 
manner. The step distance t is determined so that rays of light which are 
introduced as planar waves relative to a reference wave length light are 
emitted as planar waves, and when rays of light which are different from 
the reference wave length light in wavelength, the rays of light which 
have been introduced as planar waves are emitted as divergent or 
convergent wave surfaces. The width of each annular zone is preferably set 
to a value which is in reverse proportion to the square of the distance 
from the optical axis. With this dimension, in the case of the wavelength 
variation, it is possible to make the generated wave surface substantially 
spherical. The device is generally indicated by 101 and has a plurality of 
step-like planes formed on the light entrance face 101a which in on the 
left side whereas the exit face 101b is composed of a single plane. The 
planes at the entrance face 101a are formed as annular segments that are 
concentric with the optical axis as shown in FIG. 10. In FIGS. 9 and 10, 
the width of each annular segment and the difference in height between 
annular segments are shown enlarged to provide better understanding. 
The shift amount in the optical direction of adjacent annular zone t of 
individual planes is defined by the following condition: 
EQU t=m.lambda.0/(n-1) 
where m is an integer, n is the refractive index, and .lambda.0 is an 
arbitrary wavelength in the operating wavelength range. 
As shown in FIG. 11, the optical pathlength of rays of light at the 
wavelength .lambda..sub.0 is offset by m.lambda..sub.0 as they pass 
through adjacent planes and, after emerging from the exit face, they will 
form a plane wave again. 
If the wavelength changes to .lambda..sub.0 +.DELTA..lambda., the wavefront 
is offset by about m.DELTA..lambda. between adjacent planes (ignoring the 
change that occurs in the refractive index of the constituent material of 
the chromatic aberration correcting device on account of the change in 
wavelength) and the optical pathlength difference will not be an integral 
multiple of the wavelength. Hence, the emerging wavefront is not a plane 
wave but a generally spherical wave having power as shown in FIG. 12. 
If the chromatic aberration correcting device 101 is of a shape that 
resembles macroscopically a concavo-plane lens, it is capable of canceling 
the chromatic aberration that develops in an ordinary refraction using 
positive lens; hence, by using this device in combination with an 
objective lens for optical disk as shown in FIG. 13 where the objective 
lens is indicated by 102, correction of chromatic aberration can be 
accomplished. Shown by 103 in FIG. 13 is an optical disk cover glass. 
We then describe the effect of the chromatic aberration correcting device 
when it is positioned a certain distance away from the objective lens. 
Consider optics in which two lens groups A and B are spaced by a distance 
of L. If parallel light enters this optical system, the distance from the 
last lens surface to the imaging plane, which is generally called the back 
focus fB, is expressed by the following equation (1A) in which .phi.A and 
.phi.B represent the powers of the respective lens groups. By 
differentiating equation (1) with respect to .phi.B, L and .phi.A, we get 
equations (2A), (3A) and 4(A), respectively: 
EQU fB=(1-.phi.AL)/(.phi.A+.phi.B-.phi.A.phi.BL) (1A) 
EQU dfB/d.phi.B=-(1-.phi.AL).sup.2 /(.phi.A+.phi.B-.phi.A.phi.BL).sup.2 (2A) 
EQU dfB/dL=-.phi.A.sup.2 /(.phi.A+.phi.B-.phi.A.phi.BL).sup.2 (3A) 
EQU dfB/d.phi.A=-1/(.phi.A+.phi.B-.phi.A.phi.BL).sup.2 (4A) 
If the lens group A is assumed to be a chromatic aberration correcting 
device having no power, differential equations (2A), (3A) and (4A) can be 
simplified as follows: 
EQU dfB/d.phi.B=-1.phi.B.sup.2 (5A) 
EQU dfB/dL=0 (6A) 
EQU dfB/d.phi.A=-1/.phi.B.sup.2 (7A) 
Hence, the following conclusion is reached: if lens group A has a very weak 
power, a change in distance L will cause no change in the focusing 
position; if the power of lens group B changes, there occurs a shift in 
the focus position as represented by equation (5A); and if the power of 
lens group A changes, there occurs a change in the focus position as 
represented by equation (7A). 
Thus, in order to insure that there will be no shift in the focusing 
position even if a change in wavelength causes corresponding changes in 
the powers of lens groups A and B, one may set the respective lens groups 
so that the amount of change in the power of one lens group will cancel 
the amount of change in the power of the other lens group, namely, the 
coefficients of differentiation of the powers of the respective lens 
groups with respect to wavelength .lambda. will satisfy the relationship 
expressed by the following equation (8A): 
EQU d.phi.A/d.lambda.=-d.phi.B/d.lambda. (8A) 
The change in the power of lens group B in response to the change in 
wavelength is expressed by equation (9A) in relation to the change in back 
focus. If lens group B is assumed to be a diffractive lens, its power 
which is proportional to wavelength is expressed by the following equation 
(10A): 
EQU d.phi.B/d.lambda.=-(dfB/d.lambda.).phi.B.sup.2 (9A) 
EQU d.phi.A/d.lambda.=.phi.A/.lambda. (10A) 
Substituting equations (9A) and (10A) into equation (8A), the power of the 
chromatic aberration correcting device which is composed as a diffractive 
lens is given by: 
EQU .phi.A=-(dfB/d.lambda.).lambda..phi.B.sup.2 (11A) 
Take, for example, the case where lens group B is composed of an objective 
lens that has a focal length of 3 mm, that is to handle light from a laser 
operating at a wavelength of 780 mm and that has dfB/d.lambda.=0.060 
.mu.m/nm. The chromatic aberration correcting device may be set to have 
power .phi.A that is expressed by: 
EQU .phi.A=0.06.times.10.sup.-3 .multidot.780.multidot.(1/3).sup.2 =1/192.3 
(12A) 
Thus, the chromatic aberration that occurs in the objective lens can be 
corrected by using a positive diffractive lens having the focal length 192 
nm. It should, however, be noted that in order to adjust the overall power 
of the chromatic aberration correcting device to zero, a negative 
refractive lens having a focal length of -192 mm must be positioned in 
contact with this diffractive lens. If the negative lens is composed of a 
diffractive lens, dispersion will contribute a slight improvement in the 
chromatic aberration correcting effect. 
If the negative lens under discussion is made of BSL7 (trade name of Ohara 
Co., Ltd.; refractive index=1.51072 at wavelength .lambda..sub.0 =780 nm), 
the result is a concavo-plane lens that has a spherical entrance face with 
a curvature radius of -98.058 mm and a plane exit face. 
However, if the positive diffractive lens and the negative refractive lens 
are provided as separate members, the number of devices involved cannot be 
reduced to realize a lower manufacturing cost. To this end, the positive 
diffractive lens is desirably combined with the negative refractive lens 
into an integral unit. 
To realize an integral unit, the concave surface of the negative lens may 
be composed of step-like planes that are arranged in such a way that the 
axial pitch P will satisfy the equation: .lambda..sub.0 /(n-1)=1.5273 
.mu.m. This design helps provide a chromatic aberration correcting device 
that is capable of correcting chromatic aberration by working as a 
diffractive lens having the focal length 192 mm and which has no power at 
the operating center wavelength 780 nm since the light of first-order 
diffraction will travel straight. 
Assume a coordinate system that extends in the axial direction along the 
path of travelling light; if the coordinate of the point at the 
intersection with the optical axis is assumed to be zero, the coordinate 
X(h) of the area that departs from the optical axis by distance h is 
expressed by equation (13A) if the area is a curved plane and by equation 
(14A) if the area Is composed of step-like planes: 
##EQU5## 
where Int(x) is a function that gives the integral portion of x, and C is 
any constant that satisfies 0.ltoreq.C&lt;1. 
When using the chromatic aberration correcting device in combination with 
the aforementioned objective lens, the specific geometry of the device is 
as shown below in Table 9. 
TABLE 9 
______________________________________ 
h (mm) X (.mu.m) 
n: 1.51072 
______________________________________ 
0.000 .about. 0.387 0.00 
.about. 0.670 -1.53 
.about. 0.865 -3.05 
.about. 1.024 -4.58 
.about. 1.161 -6.11 
.about. 1.284 -7.64 
.about. 1.395 -9.16 
.about. 1.499 -10.69 
.about. 1.596 -12.22 
.about. 1.687 -13.75 
.about. 1.773 -15.27 
.about. 1.856 -16.80 
.about. 1.935 -18.33 
.about. 2.011 -19.85 
.about. 2.084 -21.38 
.about. 2.155 -22.91 
______________________________________ 
In the example described above, the axial pitch is adjusted to 
.lambda..sub.0 /(n-1); if the operating wavelength is within a narrow 
range, the axial pitch may be adjusted to m.lambda..sub.0 /(n-1) (m: 
integer) and the light of mth-order diffraction may safely be used without 
lowering the diffraction efficiency. 
It should be particularly noted here that the peripheral portion of the 
chromatic aberration correcting device is usually characterized by the 
smaller width of annular segments than those in the central portion. 
Hence, by gradually increasing the value of m starting from unity so as to 
give different pitches, one can prevent the width of annular segments in 
the peripheral portion from becoming unduly narrow. Equation (14A) may be 
modified as follows with m being taken into account: 
##EQU6## 
In the example described above, the chromatic aberration correcting device 
is composed in such a manner that its shape is macroscopically like a 
concavo-plane lens, whereby it is capable of correcting the chromatic 
aberration that has developed in a convex lens. It should be noted that 
the device may be turned around to produce a plano-concave lens which will 
function in entirely the same manner as the concavo-plane lens. 
Alternatively, both sides of the chromatic aberration correcting device 
may be rendered to have macroscopically curved surfaces as shown in FIG. 
14. The curved surface serving as a reference is not limited to the 
spherical surface used in the example and it may be an aspheric surface. 
Further, the chromatic aberration correcting device may be formed as a 
macroscopically convexo-plane lens of the type shown in FIG. 15 or as a 
biconvex lens of the type shown in FIG. 16; devices of these types can be 
used to correct the chromatic aberration that has developed in the 
negative refractive lens. 
FIG. 17 shows optical system in a magnetooptical information recording and 
reproducing apparatus that contains the chromatic aberration correcting 
device described hereinabove. Divergent light issuing from a laser diode 
10 serving as a light source is collimated by a collimator lens 11 and 
thereafter shaped to have a circular cross section by means of a beam 
shaping prism 12. The shaped laser beam is reflected by a prism 13 to pass 
through the chromatic aberration correcting device 101; the beam is 
thereafter reflected by a mirror 14 and focused by an objective lens 102 
to form a spot on disk D. 
Both the objective lens 102 and the mirror 14 are mounted on a carriage 15, 
which is slidable along guide rails 16 in the radial direction of disk D 
indicated by the two-head arrow in FIG. 17. 
The reflected light from disk D makes the second passage through objective 
lens 102, mirror 14 and chromatic aberration correcting lens 101 and is 
reflected by the prism 13; part of the reflected light passes through a 
condenser lens 17 to be collected on a light-receiving element 18 for 
signal reproduction and the remainder passes through a condenser lens 19 
to be collected on a light-receiving element 20 for error signal 
detection. In accordance with the reflected light received, the element 18 
outputs the information recorded on the disk whereas the element 19 
outputs an error signal such as a tracking error or a focusing error 
signal. 
A modification of the optical system described above is shown in FIG. 18. 
In this modified example, the chromatic aberration correcting device 101 
is attached to the prism 13. 
The laser diode 10 will produce an output which, in a recording mode, 
increases intermittently in a region where it changes the direction of 
magnetization on the disk and which is small and constant in a 
reproduction mode. This change in power causes a corresponding change in 
oscillation wavelength. However, as described above, the chromatic 
aberration correcting device 101 is inserted between the light source and 
the objective lens in accordance with the present invention, whereby the 
convergence of light beams can be varied slightly as there occurs a change 
in wavelength so as to suppress the undesired shift in the position where 
the condenser lens 102 collects light beams. 
As described on the foregoing pages, the present invention permits a single 
optical element to correct the chromatic aberration that develops in a 
positive or a negative lens, thereby producing a lens system that uses a 
smaller number of optical elements and which yet is free from chromatic 
aberration. Therefore, the present invention will contribute to the 
manufacture of a lighter lens system at a lower cost. 
If the chromatic aberration correcting device of the present invention is 
used in optical system for an optical information recording and 
reproducing apparatus, the position where the condenser lens collects 
light beams can be prevented from shifting on account of variations in the 
wavelength of light source and this insures the apparatus to be operated 
consistently even if the operating wavelength is switched from one value 
to another. 
The following embodiments relate to a device for correcting the chromatic 
aberration inherent in optical system. More particularly, the present 
invention relates to a chromatic aberration correcting device that is 
intended for use in combination with a single aspheric surface that is 
corrected for aberrations other than chromatic aberration. 
The conventional chromatic aberration correcting device is positioned in a 
substantially afocal portion of optical system and, depending upon of the 
wavelength of incident parallel light, transforms it to either divergent 
or convergent light so as to cancel the axial chromatic aberration that 
develops in an objective lens. 
The lens to be corrected for chromatic aberration is typically a positive 
lens that is corrected for spherical aberration at a single wavelength. 
The focal length of a positive lens decreases at shorter wavelengths and 
increases at longer wavelengths (assuming that the lens is used at 
wavelengths near visible light). Therefore, in order to cancel the axial 
chromatic aberration and prevent the shifting of focus position, the rays 
of light entering the positive lens may be transformed to divergent light 
if the incident light has short wavelength and to convergent light if it 
has long wavelength. 
Optical system using this conventional chromatic aberration correcting 
device is capable of correcting axial chromatic aberration; however, it 
experiences varying spherical aberrations in response to changes in 
wavelength and, hence, under those conditions which cause a wide range of 
changes in wavelength, it has been impossible for the optical system to 
maintain good performance both at the wavelength before change and at the 
wavelength after change. 
Even if a positive lens is corrected for spherical aberration at a 
reference wavelength, the spherical aberration is undercorrected with 
respect to shorter-wavelength light that experiences a higher refractive 
index and it is overcorrected with respect to longer-wavelength light that 
experiences a lower refractive index. This is the change that occurs to 
spherical aberration depending upon wavelength. 
If parallel light is transformed to either divergent or convergent light 
under the action of the conventional chromatic aberration correcting 
device, this transformation, which is equivalent to the change from an 
object at infinity from a positive lens to an object at finite distance, 
will cause a change in spherical aberration. As a result of this changes 
the spherical aberration is undercorrected if divergent light enters the 
positive lens and it is overcorrected if convergent light enters the 
positive lens. This is the change that develops in spherical aberration 
under the action of the chromatic aberration correcting device. 
The changes in spherical aberration due to these two factors take place in 
the same direction and, hence, it has been impossible to correct them by 
optical system that uses the conventional chromatic aberration correcting 
device. 
If the operating wavelength band is as narrow as the expected range of 
change in the oscillation wavelength of a laser diode, the change in 
spherical aberration is very small and causes no great problems. However, 
if the operating wavelength is expected to change over a wider range as in 
the case where two light sources emitting at wavelengths that are not 
close to each other are selectively operated, as exemplified by the use of 
a near infrared laser diode (780 nm) and a visible red laser diode (680 
nm) or the use of a He--Ne laser (633 nm) and the SHG wave from a YAG 
laser (532 nm), or if a plurality of wavelengths are used simultaneously, 
a greater change in spherical aberration is also expected and must be 
dealt with by some method. 
The present invention has been accomplished under these circumstances and 
has an object providing a chromatic aberration correcting device that not 
only corrects the axial chromatic aberration developing in a positive lens 
but which also is capable of suppressing the change in spherical 
aberration even if it is used on two light sources that emit light beams 
at wavelengths that are not close to each other and which are selectively 
operated at those wavelengths. 
Examples 
Several examples of the chromatic aberration correcting device according to 
the present invention are described below. 
In order to insure that both the change in spherical aberration that 
develops in a positive lens depending upon wavelength and the spherical 
aberration that occurs in response to the incidence of divergent or 
convergent light on the positive lens are corrected by the chromatic 
aberration correcting device, the surface of the device that has a 
chromatic aberration correcting action need be adjusted have to a geometry 
that generates spherical aberration. Hence, the chromatic aberration 
correcting device of the present invention is so adapted that it generates 
a divergent wavefront having an overcorrected spherical aberration in 
response to the incidence of parallel beams of light at a wavelength 
shorter than a reference wavelength and that it generates a concentrating 
wavefront having an undercorrected spherical aberration in response to the 
incidence of parallel beams of light at a wavelength longer than the 
reference wavelength. 
The chromatic aberration correcting device is available in two specific 
types: a refractive type that is composed by cementing a positive and a 
negative lens that are formed of materials having substantially no 
difference in refractive index but having different dispersion values at 
the reference wavelength; and a diffraction type that has annular segments 
formed in steps on either a light entrance face or a light exit face or 
both, the annular segments being composed of planes perpendicular to and 
concentric with the optical axis. The above-described spherical aberration 
can be generated by insuring that the cemented surface (in the case of a 
refractive type) or the base curve which is a macroscopic curvature of the 
radius of curvature of the planes formed in steps (in the case of 
diffraction type) is an aspheric surface the radius of curvature of which 
decreases in absolute value with the increasing distance from the optical 
axis. 
Lower-order spherical aberrations can generally be expressed by a 
biquadratic function of the height of ray incidence; therefore, most of 
the changes in spherical aberration can be effectively corrected by 
providing the chromatic aberration correcting device with a surface having 
fourth-order asphericity. It should, however, be noted that if a single 
aspheric lens is to be used as the positive lens to be corrected, the 
aspheric surface of the chromatic aberration correcting device is 
preferably designed as an aspheric surface that resembles a spheroidal 
surface having a positive conic constant and this enables more effective 
correction in that it can handle the component of a change in higher-order 
aberrations. 
When the departure .epsilon.(h) from the spheroidal surface at a point 
having distance h from the optical axis is expressed by the following 
equation (1B), the aspheric surface of interest which resembles the 
spheroidal surface desirably satisfies the following condition (2B) (in 
the case of a refractive type) or (4B) (in the case of a diffraction type) 
at all values of distance h within the effective maximum radius of passing 
beams of light: 
##EQU7## 
where .DELTA.X(h) is the sag of the aspheric surface; C is the paraxial 
curvature; K is theconic constant; .lambda. is the maximum operating 
wavelength; and .DELTA.nMAX is the absolute value of difference in 
refractive index in the case where the difference between the refractive 
indices of the media on both sides of the cemented surface is the greatest 
in the operating wavelength band; and n is the refractive index. 
In the case of a diffraction-type chromatic aberration correcting device, 
when the axial displacement of the base curve at a point having distance h 
from the optical axis is written as .DELTA.X(h), the displacement 
.DELTA.X' (h) of the planes formed in steps at a point having distance h 
from the optical axis is given by the following equation (3B): 
EQU .DELTA.X'(h)=(m.lambda..sub.0 /(n-1))Int((.DELTA.X(h)/(m.lambda..sub.0 
/(n-1)))+0.5) (3B) 
where m is an integer; n is the refractive index; .lambda..sub.0 is the 
wavelength at which the chromatic aberration correcting device is used or 
an arbitrary wavelength within the operating wavelength range of the 
device; and Int(x) is a function giving an integer not greater then x. 
Condition (2B) must be satisfied in order to produce an optical pathlength 
difference of 1.lambda. or less when a chromatic aberration correcting 
device of a refractive type is used. Similarly, condition (4B) must be 
satisfied in order to produce an optical pathlength difference of 
1.lambda. or less when a chromatic aberration correcting device of a 
diffraction type is used. If these conditions are not met, the rms (root 
mean square) value of wavefront aberrations will exceed 0.1.lambda. and 
the device is no longer suitable for use in the recording or reproduction 
of optical information. 
FIG. 19 is a simplified diagram showing schematically a positive objective 
lens to be corrected by the chromatic aberration correcting devices used 
in Examples 1B to 3B that follow. The specific numerical data for this 
lens are listed in Table 1B, in which NA denotes the numerical aperture, f 
the focal length, .omega. the half view angle, fb the back focus, r the 
radius of curvature, d the lens thickness or the aerial distance between 
adjacent lenses, ni the refractive index at wavelength i nm, and .nu. the 
Abbe number. The first and second surfaces in FIG. 19 define the objective 
lens having an aspheric surface on both sides, and the third and fourth 
surfaces define the cover glass of an optical disk. 
The aspheric surface is expressed by the following equation: 
##EQU8## 
where X is the distance by which the coordinates at the point on the 
aspheric surface where the height from the optical axis is Y are departed 
from the plane tangent to the vertex of the aspheric surface; C is the 
curvature (l/r) of the vertex of the aspheric surface; K is the conic 
constant; and A4, A6, A8 and A10 are the aspheric coefficients of the 
fourth, sixth, eighth and tenth orders, respectively. 
The conic constants and aspheric coefficients for the first and second 
surfaces are listed in Table 2B. FIG. 20 shows the spherical aberration 
SA, sine condition SC, and the chromatic aberration that is expressed in 
terms of spherical aberrations at wavelengths of 780 nm and 680 nm. 
TABLE 1B 
______________________________________ 
NA = 0.55 f = 3.00 .omega. = 1.4.degree. fb = 1.088 
Surface 
No. r d n588 .nu. n780 n680 
______________________________________ 
1 1.894 2.200 1.49700 
81.6 1.49282 
1.49461 
2 -4.186 1.088 
3 .infin. 1.200 1.58547 
29.9 1.57346 
1.57834 
4 .infin. 
______________________________________ 
TABLE 2B 
______________________________________ 
1st surface 2nd surface 
______________________________________ 
K = -0.5800 K = 0.000 
A4 = 0.7540 .times. 10.sup.-3 
A4 = 0.3250 .times. 10.sup.-1 
A6 = -0.3670 .times. 10.sup.-4 
A6 = -0.1000 .times. 10.sup.-1 
A8 = 0.2800 .times. 10.sup.-4 
A8 = 0.2000 .times. 10.sup.-2 
A10 = -0.3600 .times. 10.sup.-4 
A10 = -0.1820 .times. 10.sup.-3 
______________________________________ 
Example 1B 
FIG. 21 shows optical system in which the refractive-type chromatic 
aberration correcting device according to Example 1B of the present 
invention is combined with the objective lens shown in FIG. 19. The 
cemented surface r2 of the correcting device is ellipsoidal and 
.epsilon.(h) is zero within the effective radius. The specific numerical 
data for the optics are listed in Table 3B. The first to third surfaces 
define the chromatic aberration correcting device, the fourth and fifth 
surfaces define the objective lens, and the sixth and seventh surfaces 
define the cover glass of an optical disk. In Example 1B, the second, 
fourth and fifth surfaces are aspheric and the associated aspheric 
coefficients are listed in Table 4B. FIG. 22 shows the aspheric and 
chromatic aberrations that develop in the optics composed in accordance 
with the data listed in Table 3B. 
TABLE 3B 
______________________________________ 
FNO = 1:0.9 f = 3.00 .omega. = 1.4.degree. fb = 0.00 
Surface 
No. r d n588 .nu. n780 n680 
______________________________________ 
1 .infin. 2.000 1.75500 
52.3 1.74523 
1.74940 
2 -4.400 1.000 1.76182 
26.5 1.74404 
1.75132 
3 .infin. any 
distance 
4 1.894 2.200 1.49700 
81.6 1.49282 
1.49461 
5 -4.186 1.088 
6 .infin. 1.200 1.58547 
29.9 1.57346 
1.57834 
7 .infin. 
______________________________________ 
TABLE 4B 
__________________________________________________________________________ 
4th surface 5th surface 2nd surface 
__________________________________________________________________________ 
K = -0.5800 K = 0.0000 K = 0.2500 .times. 10 
A4 = 0.7540 .times. 10.sup.-3 
A4 = 0.3250 .times. 10.sup.-1 
A6 = -0.3670 .times. 10.sup.-4 
A6 = -0.1000 .times. 10.sup.-1 
A8 = 0.2800 .times. 10.sup.-4 
A8 = 0.2000 .times. 10.sup.-2 
A10 = -0.3600 .times. 10.sup.-4 
A10 = -0.1820 .times. 10.sup.-3 
__________________________________________________________________________ 
FIG. 23 shows optical system that has the same configuration as in Example 
1B except that the cemented surface r2 is spherical. FIG. 24 shows the 
aspheric and chromatic aberrations that develop in the optical system 
shown in FIG. 23. Comparing FIGS. 22 and 24, one can see that the amount 
of change in spherical aberration due to variations in wavelength is 
reduced if the geometry of the cemented surface is changed from spherical 
to ellipsoidal. 
Example 2B 
FIG. 25 shows optical system in which a chromatic aberration correcting 
device of a diffraction type is combined with the objective lens shown in 
FIG. 19. As shown in FIGS. 26A and 26B, a diffraction-type chromatic 
aberration correcting device has annular segments formed in steps as they 
are perpendicular to and concentric with the optical axis. 
Table 5B lists numerical data for the optical system in which the 
diffraction-type chromatic aberration correcting device of Example 2B is 
combined with the objective lens shown in FIG. 19. The correcting device 
is such that the base curve which is a macroscopic curvature of surface r1 
formed in steps provides a fourth-order aspheric surface. FIG. 27 shows 
the spherical and chromatic aberrations that develop in the optical system 
composed in accordance with the data shown in Table 5B. 
In Example 2B, the first, third and fourth surfaces are aspheric and the 
associated aspheric coefficients are listed in Table 6B. 
TABLE 5B 
______________________________________ 
FNO = 1:0.9 f = 3.00 .omega. = 1.4.degree. fb = 0.00 
Surface 
No. r d n588 .nu. n780 n680 
______________________________________ 
1 -104.400 1.000 1.51633 
64.1 1.51072 
1.51315 
2 .infin. any 
distance 
3 1.894 2.200 1.49700 
81.6 1.49282 
1.49461 
4 -4.186 1.090 
5 .infin. 1.200 1.58547 
29.9 1.57346 
1.57834 
6 .infin. 
______________________________________ 
TABLE 6B 
__________________________________________________________________________ 
3rd surface 4th surface 1st surface 
__________________________________________________________________________ 
K = -0.5800 K = 0.0000 K = 0.0000 
A4 = 0.7540 .times. 10.sup.-3 
A4 = 0.3250 .times. 10.sup.-1 
A4 = -0.3400 .times. 10.sup.-3 
A6 = -0.3670 .times. 10.sup.-4 
A6 = -0.1000 .times. 10.sup.-1 
A8 = 0.2800 .times. 10.sup.-4 
A8 = 0.2000 .times. 10.sup.-2 
A10 = -0.3600 .times. 10.sup.-4 
A10 = -0.1820 .times. 10.sup.-3 
__________________________________________________________________________ 
Example 3B 
Table 7B lists numerical data for optical system in which the chromatic 
aberration correcting device of Example 3B is combined with the objective 
lens shown in FIG. 19. The correcting device is such that the base curve 
which is a macroscopic curvature of surface r1 formed in steps provides an 
ellipsoidal surface and .epsilon.(h) is zero within the effective radius. 
FIG. 28 shows the spherical and chromatic aberrations that develop in the 
optical system composed in accordance with the data listed in Table 7B. In 
Example 3B, the first, third and fourth surfaces are aspheric and the 
associated coefficients are listed in Table 8B. 
TABLE 7B 
______________________________________ 
FNO = 1:0.9 f = 3.00 .omega. = 1.4.degree. fb = 0.00 
Surface 
No. r d n588 .nu. n780 n680 
______________________________________ 
1 -104.400 1.000 1.51633 
64.1 1.51072 
1.51315 
2 .infin. any 
distance 
3 1.894 2.200 1.49700 
81.6 1.49282 
1.49461 
4 -4.186 
5 .infin. 1.200 1.58547 
29.9 1.57346 
1.57834 
6 .infin. 
______________________________________ 
TABLE 8B 
__________________________________________________________________________ 
3rd surface 4th surface 1st surface 
__________________________________________________________________________ 
K = -0.5800 K = 0.0000 K = 0.2000 .times. 10.sup.+4 
A4 = 0.7540 .times. 10.sup.-3 
A4 = 0.3250 .times. 10.sup.-1 
A6 = -0.3670 .times. 10.sup.-4 
A6 = -0.1000 .times. 10.sup.-1 
A8 = 0.2800 .times. 10.sup.-4 
A8 = 0.2000 .times. 10.sup.-2 
A10 = -0.3600 .times. 10.sup.-4 
A10 = -0.1820 .times. 10.sup.-3 
__________________________________________________________________________ 
FIG. 29 shows the spherical and chromatic aberrations that develop in 
optical system that has the same configuration as in Examples 2B and 3B 
except that the base curve for the surface formed in steps provides a 
spherical surface. Comparing FIGS. 27 and 28, one can see that the amount 
of change in spherical aberration due to variations in wavelength is 
reduced if the geometry of the base curve provides either a fourth-order 
aspheric or an ellipsoidal surface rather than a spherical surface. 
FIG. 30 is a simplified diagram showing schematically the single positive 
lens having an aspheric surface on both sides that is to be corrected by 
the chromatic aberration correcting devices according to Examples 4B an 
5B. The specific numerical data for this lens are listed in Tables 9B an 
10B. The spherical aberration that develops in this lens alone, as well as 
the chromatic aberration that is expressed in terms of spherical 
aberrations at wavelengths of 633 nm and 532 nm are shown in FIG. 31. 
TABLE 9B 
______________________________________ 
NA = 0.55 f = 3.29 .omega. = 1.7.degree. fb = 1.332 
Surface 
No. r d n588 .nu. n633 
______________________________________ 
1 2.180 2.250 1.54358 55.6 1.54151 
2 -6.250 1.332 
3 .infin. 1.200 1.58547 29.9 1.58156 
4 .infin. 
______________________________________ 
TABLE 10B 
______________________________________ 
1st surface 2nd surface 
______________________________________ 
K = -0.3265 K = 0.0000 
A4 = -0.2265 .times. 10.sup.-2 
A4 = 0.1670 .times. 10.sup.-1 
A6 = -0.5014 .times. 10.sup.-3 
A6 = -0.5080 .times. 10.sup.-2 
A8 = -0.7162 .times. 10.sup.-5 
A8 = 0.8000 .times. 10.sup.-3 
A10 = -0.3194 .times. 10.sup.-4 
A10 = -0.4848 .times. 10.sup.-4 
______________________________________ 
Example 4B 
FIG. 32 is a simplified diagram showing schematically optical system in 
which the refractive-type chromatic aberration correcting device according 
to Example 4B of the present invention is combined with the objective lens 
shown in FIG. 30. The specific numerical data for the optical system are 
listed in Tables 11B and 12B. The cemented surface r2 of the correcting 
device is ellipsoidal and .epsilon.(h) is zero within the effective 
radius. FIG. 33 shows the spherical and chromatic aberrations that develop 
in the optical system composed in accordance with the data listed in 
Tables 11b and 12B. 
TABLE 11B 
______________________________________ 
FNO = 1:0.9 f = 3.29 .omega. = 1.7.degree. fb = 0.00 
Surface 
No. r d n588 .nu. n633 n532 
______________________________________ 
1 .infin. 0.800 1.74077 
27.8 1.73541 
1.74959 
2 2.280 2.000 1.74100 
52.7 1.73804 
1.74567 
3 .infin. any 
distance 
4 2.180 2.250 1.54358 
55.6 1.54151 
1.54680 
5 -6.250 1.332 
6 .infin. 1.200 1.58547 
29.9 1.58156 
1.59194 
7 .infin. 
______________________________________ 
TABLE 12B 
______________________________________ 
4th surface 5th surface 2nd surface 
______________________________________ 
K = -0.3265 K = 0.0000 K = 0.6000 
A4 = -0.2263 .times. 10.sup.-2 
A4 = 0.1670 .times. 10.sup.-1 
A6 = -0.5014 .times. 10.sup.-3 
A6 = -0.5080 .times. 10.sup.-2 
A8 = -0.7162 .times. 10.sup.-5 
A8 = 0.8000 .times. 10.sup.-3 
A10 = -0.3194 .times. 10.sup.-4 
A10 = -0.4848 .times. 10.sup.-4 
______________________________________ 
FIG. 34 shows optical system having the same configuration as described 
above except that the cemented surface r2 of the chromatic aberration 
correcting device is spherical, and FIG. 35 shows the spherical and 
chromatic aberrations that develop in the optical system under 
consideration. Obviously, the use of an ellipsoidal cemented surface is 
effective not only in bringing the profiles of spherical aberration curves 
close to each other at the two wavelengths but also in reducing the 
overall amount of spherical aberrations. 
Example 5B 
FIG. 36 in a simplified diagram showing schematically optical system in 
which the diffraction-type chromatic aberration correcting device 
according to Example 5B of the present invention is combined with the 
objective lens shown in FIG. 30. The specific numerical data for the 
optical system are listed in Tables 13b and 14B. In the correcting device 
of Example 5B, the base curve for the planes formed in steps is 
ellipsoidal and .epsilon.(h) is zero within the effective radius. The 
spherical and chromatic aberrations that develop in the optical system 
composed in accordance with the data listed in Tables 13B and 14B shown in 
FIG. 37. 
TABLE 13B 
______________________________________ 
f = 3.29 .omega. = 1.7.degree. fb = 0.00 
Surface 
No. r d n588 .nu. n633 n532 
______________________________________ 
1 .infin. 2.000 1.51633 
64.1 1.51462 
1.51900 
2 41.000 any 
distance 
3 2.180 2.250 1.54358 
55.6 1.54151 
1.54680 
4 -6.250 1.341 
5 .infin. 1.200 1.58547 
29.9 1.58156 
1.59194 
6 .infin. 
______________________________________ 
TABLE 14B 
__________________________________________________________________________ 
3rd surface 4th surface 1st surface 
__________________________________________________________________________ 
K = -0.3265 K = 0.0000 K = 0.2450 .times. 10.sup.+3 
A4 = -0.2263 .times. 10.sup.-2 
A4 = 0.1670 .times. 10.sup.-1 
A6 = -0.5014 .times. 10.sup.-3 
A6 = -0.5080 .times. 10.sup.-2 
A8 = -0.7162 .times. 10.sup.-5 
A8 = 0.8000 .times. 10.sup.-3 
A10 = -0.3194 .times. 10.sup.-4 
A10 = -0.4848 .times. 10.sup.-4 
__________________________________________________________________________ 
FIG. 38 shows the spherical and chromatic aberrations that develop in 
optical system having the same configuration as in Example 5B except that 
the base curve for the planes formed in steps in the chromatic aberration 
correcting device is spherical. Comparing FIGS. 37 and 38, one can see 
that the variation in spherical aberration is reduced if the base curve is 
made ellipsoidal. 
As described on the foregoing pages, the present invention not only 
corrects the axial chromatic aberration that develops in a condenser lens 
on account of variations in wavelength but it also is capable of 
suppressing the variations in spherical aberration. Hence, it has the 
advantage of expanding the range over which the fluctuation in the 
performance of optical system due to variations in wavelength can be 
suppressed. 
Because of these advantages, the present invention offers a practical 
benefit in that even a lens that is yet to be corrected for chromatic 
aberration can be used on an optical information recording apparatus that 
employs two wavelengths fairly remote from each other or on an information 
reading apparatus that employs a light-emitting diode and a white light 
source, and this helps realize a compact unit of optical system. 
The following embodiments relate to optical system for an optical 
information recording and reproducing apparatus which records or 
reproduces information on a medium such as an optical disk. The 
embodiments of the present invention also relate to a chromatic aberration 
correcting device that is to be installed in the optical system. 
The present invention has been accomplished under these circumstances and 
has as an object providing optical system for an optical information 
recording and reproducing apparatus that is effectively corrected for 
chromatic aberration without using more optical elements than in the case 
where chromatic aberration is not corrected. Another object of the present 
invention is to provide a chromatic aberration correcting device that is 
to be used in the optical system. 
Examples of the optical system for optical information recording and 
reproducing apparatus according to the present invention, as well as the 
chromatic aberration correcting device of the same invention are described 
below. 
Example 1C 
FIG. 39 shows the optical system for optical information recording and 
reproducing apparatus according to Example 1C of the present invention. 
Divergent light issuing from a laser diode 110 serving as a light source 
is collimated by a collimator lens 120; the collimated light then passes 
through a beam splitter 130 and is focused by an objective lens 140 to 
form a spot on an optical disk 150. The reflected light from the optical 
disk 150 makes reentry into the beam splitter 130 and part of it is 
reflected and passes through a condenser lens 160 to be collected by a 
light-receiving element 170. Depending upon the reflected light it 
receives, the element 170 outputs either the information recorded on the 
optical disk or a signal such as a tracking error or focusing error 
signal. 
The beam splitter 130 is composed of two prisms 131 and 132 joined together 
by a beam splitting surface 130a, and a concavo-plane lens 133 that is 
cemented to prism 132 which faces the objective lens 140. Prism 132 and 
lens 133 are typically made of two materials that have substantially the 
same refractive index but which have different Abbe numbers as shown in 
Table 1C below. This arrangement offers the advantage that the cemented 
surface which is substantially powerless is capable of generating 
chromatic aberration that is at least sufficient to cancel the chromatic 
aberration that develops in objective lens 140. 
TABLE 1C 
______________________________________ 
Material 
nA' nd .nu.d 
______________________________________ 
Prism 132 YGH51 1.74566 1.75500 
52.33 
Lens 133 TIH14 1.74475 1.76182 
26.55 
______________________________________ 
(Names under "Material" are trade names of Ohara Co., Ltd.) 
If desired, as concave surface may be formed on the side facing the prisms 
using a high-dispersion material whereas a plano-convex lens may be formed 
of a low-dispersion material. This arrangement also produces equally good 
chromatic aberration correcting effects. 
Whichever arrangement is adopted, the only difference from the case where 
chromatic aberration is not corrected is that the shape of beam splitter 
130 is modified; hence, optical system that is effectively corrected for 
chromatic aberration can be offered without using any additional elements. 
In Example 1C, one surface of prism 132 is made convex. If desired, this 
surface may be rendered planar and a plano-convex lens may be combined 
with a convexo-plane lens to constitute a chromatic aberration correcting 
device, which is attached to the beam splitter 130. 
FIG. 40 shows a modification of Example 1C. In this modified example, laser 
light issues from laser diode 110 in a direction parallel to the surface 
of optical disk 150; it then passes through collimator lens 120 and beam 
splitter 130. A mirror 190 serving as an optical path deflecting means 
reflects the laser light toward the optical disk 150 and the reflected 
light is focused by objective lens 140 to form a spot on the optical disk 
150. As shown, the beam splitter 130 is composed of prisms 131 and 132', 
as well as a convexo-plane lens 133'. 
Example 2C 
FIG. 41 shows the optics for optical information recording and reproducing 
apparatus according to Example 2C of the present invention. In this 
example, beam splitter 130 is composed of two prisms 131 and 134 joined 
together by the beam splitting surface 130a, and planes perpendicular to 
the optical axis are formed in steps on one beam passing surface 134a of 
prism 134 as annular segments concentric with the optical axis in such a 
way that they produce a macroscopically concave shape. 
The axial pitch P of annular planes is expressed by the following equation: 
EQU P=.lambda./(n-1) 
where n is the refractive index of prism 134 and .lambda. is the reference 
wavelength at which there is no change in wavefront, or at which no 
chromatic aberration will develop. 
The surface 134a on which annular planes are formed in steps works as a 
diffraction grating; if incident light has a wavelength equal to the 
reference wavelength, the surface 134a will transmit the incident light 
without causing any change in the wavefront but if the wavelength of the 
incident light is different from the reference wavelength, the surface 
will generate a predetermined chromatic aberration that is sufficient to 
cancel the chromatic aberration that develops in the objective lens 140. 
Example 3C 
FIGS. 42 and 43 show the optical system for optical information recording 
and reproducing apparatus according to Example 3C of the present 
invention. In this example, beams of light issuing from laser diode 110 
pass through collimator lens 120 and the resulting parallel light passes 
through a beam splitter 180 that has a beam shaping capability. The light 
is then reflected by mirror 190 and is focused by objective lens 140 to 
form a spot on optical disk 150. 
The beam splitter 180 is composed of two prisms 181 and 182 joined together 
by a beam splitting surface 180a, and a convexo-plane lens 183 cemented to 
the prism 182. The prisms and the lens are formed of the materials listed 
in Table 2C below. 
TABLE 2C 
______________________________________ 
Material 
nA' nd .nu.d 
______________________________________ 
Prism 181 LAM54 1.74688 1.75700 
47.82 
Prism 182 TIH14 1.74475 1.76182 
26.5 
Lens 183 YGH51 1.74566 1.75500 
52.33 
______________________________________ 
Since prisms 181 and 182 are made of two materials that have substantially 
the same refractive index but which have different dispersion values, the 
bend in the optical path across the cemented surface 180a is small and the 
desired beam shaping and chromatic aberration correcting effects can be 
exhibited without unduly increasing the size of beam splitter 180. 
As in the case shown in FIG. 39, the beams of light that has been isolated 
by the beam splitter 180 from the light reflected from the optical disk 
150 pass through a condenser lens (not shown) to be collected on the 
light-receiving element 170. 
Example 4C 
FIG. 44 shows the optical system for optical information recording and 
reproducing apparatus according to Example 4C of the present invention. 
Beams of light issuing from laser diode 110 pass through collimator lens 
120 and beam splitter 130. The light emerging from the beam splitter 130 
enters an optical path deflector 190 which deflects the light towards 
optical disk 150. In Example 4C, the optical path deflector 190 is adapted 
to have a chromatic aberration correcting action. 
The optical path deflector 190 is composed of two prisms 191 and 192 joined 
together by a mirror surface 191a, as well as a concavo-plane lens 193 
cemented to the prism 192. Prism 192 and lens 193 are made of two 
materials that have substantially the same refractive index but which have 
different dispersion values, and this arrangement enables the deflector 
190 to correct the chromatic aberration that develops in the objective 
lens 140. In this example, the optical path deflector 190 is so positioned 
that the chromatic aberration correcting surface faces the objective lens; 
if desired, the deflector 190 may be reversed so that the chromatic 
aberration correcting surface will be positioned closer to the collimator 
lens. 
The light reflected from the optical disk 150 is then reflected by the beam 
splitter 130 and passes through a condenser lens (not shown) to be 
collected on the light-receiving element. 
Example 5C 
FIG. 45 shows the optical system for optical information recording and 
reproducing apparatus according to Example 5C of the present invention. In 
this example, a prism 194 is provided as an optical path deflecting member 
and annular planes concentric with the optical axis are formed in steps on 
the light-transmitting surface 194a in such a way that those annular 
planes will produce a macroscopically concave shape, and those step-like 
planes on the surface 194a exhibit the ability to correct the chromatic 
aberration that develops in the objective lens 140. 
The pitch of the annular planes and the function of the light-transmitting 
surface 194a are the same as described in Example 2C. In the actual 
system, a beam splitter, a condenser lens and a light-receiving element 
are provided between the collimator lens 120 and the prism 194 but they 
are not shown in FIG. 45. 
As in Example 4C, the prism 194 may be so positioned that the surface 
having step-like planes faces either the objective lens or the collimator 
lens. 
As described on the foregoing pages, the present invention depends on a 
beam splitter or an optical path deflector to provide a chromatic 
aberration correcting action and this helps provide improved optical 
system that is effectively corrected for chromatic aberration without 
increasing the number of elements that compose the optical system. 
According to still another aspect, the present invention relates to the 
correction of chromatic aberration in a lens, more particularly, to a 
hybrid lens that uses a diffraction element to correct the chromatic 
aberration that develops in a single lens. 
The degree of chromatic aberration that develops in a lens is determined by 
the characteristics, in particular, the dispersion value, of the 
constituent material of that lens. In the presence of dispersion, the 
power of a lens varies with wavelength and, hence, the chromatic 
aberration that develops in a single lens cannot be effectively corrected 
by itself. Therefore, when designing optical system that requires the 
correction of chromatic aberration, the common practice is to combine two 
or more lens elements so that the lens powers which differ with wavelength 
on account of dispersion cancel each other to accomplish the intended 
correction of chromatic aberration. 
A different approach was proposed in "Applications of Diffractive Optics", 
SPIE Vol. 1354, international Lens Design Conference (1990). According to 
this technique, annular planes that are concentric with the optical axis 
are formed in steps on one surface of a glass lens to provide a 
diffractive action so that it is used to correct the chromatic aberration 
that develops in the glass lens. Annular planes may be formed in steps on 
the surface of glass lens by etching but this method of working is not 
suitable for large-scale production and must be replaced by a glass 
molding technique. Theoretically, this technique is capable of producing 
single glass lenses that are corrected for chromatic aberration. 
In practice, however, glass is so viscous that a structure as fine as the 
diffraction surface cannot be exactly transferred from the mold to the 
glass. If the diffraction surface cannot be transferred correctly and if 
portions that should have differences in height come out smooth, light 
other than the diffracted light of the desired order will leak out; 
therefore, if the molded lens is used on an optical information recording 
and reproducing apparatus, the diameter of a beam spot formed on the 
medium will increases to such an extent that the bit error rate in the 
writing or reading of optical information will increase. If the lens is 
used as a photographic lens, the flare will increase or the resolution 
will decrease. 
Compared to glass lenses, plastic lenses have the advantage that a fine 
structure can be easily transferred from the mold; therefore, plastic 
lenses are suitable for the making of a diffraction element. However, 
there is high likelihood that plastic lenses already become nonuniform in 
refractive index in the molding process; furthermore, the performance of 
plastic lenses is apt to vary with the humidity of a use environment or in 
response to the change in humidity. 
If a plastic lens whose refractive index is not uniform in its interior is 
used as a focusing lens, the spot diameter will increase. If that plastic 
lens is used as a large-aperture lens like photographic lens, marked image 
deterioration will take place. Therefore, plastic lenses having uneven 
index distribution are not suitable for use in either application. 
The present invention has been accomplished under these circumstances and 
has as an object providing a chromatic-aberration corrected hybrid lens to 
which the pattern of a diffraction element can be transferred precisely 
and which will not experience uneven distribution of internal refractive 
indices even in the face of environmental changes, etc., thereby 
exhibiting consistent lens performance. 
Examples of the hybrid lens according to the present invention are 
described below with reference to the accompanying drawings. As shown 
schematically in FIG. 46A, the hybrid lens of the examples comprises a 
glass lens 201 having a refractive action and a plastic diffraction 
element 202 that is joined to one surface of the glass lens 201. 
Depending on the type of diffraction, diffraction elements are available 
either as an amplitude type or as a phase type, the latter being divided 
into an index modulation type and a relief type. In the examples, a phase- 
and a relief-type diffraction element is used in view of the high 
utilization of light and the ease of manufacture. 
As shown in FIG. 46B, the side of the phase- and relief-type diffraction 
element 202 that is not joined to the glass lens 201 is provided with a 
plurality of annular surfaces 203 that are concentric with the optical 
axis Ax and which are formed in steps in such a way that the lens 
thickness increases as a function of the distance from the optical axis 
Ax. 
An optical pathlength difference occurs between light that passes through a 
medium having a thickness of t and light that passes through air, and this 
pathlength difference is given by (n-1)t, with n being the refractive 
index of the medium. Therefore, the axial difference in the thickness of 
the diffraction element 202 between adjacent annular segments must be 
equal to t that is given by the following equation (1D), or an integral 
multiple of t: 
EQU t(h)=.lambda./(n-1) (1D) 
where .lambda. is the operating wavelength. 
Furthermore, the ratio between t(n-1), or the optical pathlength difference 
due to t(i.e., the axial difference in the thickness of the diffraction 
element between individual annular segments), and wavelength 
.lambda..sub.0 desirably satisfies the following condition (A): 
EQU 0.8.ltoreq.t(n-1)/.lambda..sub.0 .ltoreq.10 (A) 
If the compound lens of the examples is to be used as a bright (high NA) 
lens such as one that is to be used on an optical information recording 
and reproducing apparatus or in the case where the lens is to be used as a 
wide-angle lens, the ratio between t(n-1) and .lambda..sub.0 desirably 
satisfies the following condition (2D): 
EQU 0.8.ltoreq.t(n-1)/.lambda..sub.0 .ltoreq.1 (2D) 
Suppose here that t(n-1)/.lambda..sub.0 is unity. If a lens that uses a 
laser diode as a light source that operates at varying wavelengths with 
the reference value (.lambda..sub.0) lying at 780 nm is to be manufactured 
from LAL 13 (trade name of Ohara Co, Ltd.; n780=1.68468), the axial 
difference (t) in the thickness of the diffraction element between 
individual annular surfaces is calculated as follows: 
EQU t=0.780.times.10.sup.-3 /(n-1) =0.780.times.10.sup.-3 
/0.68468=1.14.times.10.sup.-3 (3D) 
The 1.14-.mu.m difference in thickness is so fine that it is impossible for 
the glass molding technique to have the pattern of the mold transferred 
precisely to the highly viscous glass. It is for solving this problem that 
the plastic diffraction element 202 is used in the present invention. 
Example 1D 
FIG. 47 shows optical system that uses the hybrid lens according to Example 
1D of the present invention, in which the hybrid lens is used as an 
objective lens in an optical disk system. Beams of parallel light entering 
the optical system from the left are focused by the objective lens 
composed of glass lens 201 and diffraction element 202, so as to form a 
spot on the recording surface located on the inner (right) side of the 
cover glass of the optical disk D. 
The surface that is on the left side, or the side the closest to the 
object, is a discontinuous surface on which annular segments are formed 
and which serves as a diffracting surface. The base curve which is a 
macroscopic shape of that discontinuous surface is aspheric. Glass lens 
201 has a spherical surface on both sides. 
The specific numerical data for Example 1D are listed in Table 1D, in which 
symbol .lambda..sub.0 denotes the operating wavelength, f the focal 
length, NA the numerical aperture, r the radius of curvature, d the lens 
thickness or the aerial distance between individual lenses, and the 
refractive index at the d-line, .nu.d the Abbe number, and n780 the 
refractive index at the wavelength 780 nm. FIG. 48 shows the two 
aberrations that develop in the system composed in accordance with the 
data listed in Table 1D: chromatic aberration expressed in terms of 
spherical aberrations at 770 nm, 780 nm and 790 nm, as well as astigmatism 
(S, sagittal; M, meridional). 
TABLE D1 
______________________________________ 
.lambda..sub.0 = 780 nm f = 3.30 mm NA = 0.55 
Surface 
No. r d nd .nu.d n780 
______________________________________ 
1 Diffracting 
0.40 1.51653 
surface 
2 2.900 2.110 1.89799 
34.0 1.88115 
3 42.460 1.339 
4 .infin. 1.200 1.58547 
29.9 1.57346 
5 .infin. 
______________________________________ 
The shape of the first surface of the hybrid lens is given by the 
coefficients listed in Table 2D (see below) if the sag X(h) of the 
aspheric surface at the point that is departed from the optical axis by 
distance h is defined by the following equation (4D) which has the term 
.DELTA.N added to the common expression of aspheric surface. Symbol N 
denotes the number for the annular segment to which the point at height h 
belongs, and each of the coefficients that define the aspheric surface is 
a function of N. Symbol INT(x) denotes a function for separating out the 
integral part of x: 
##EQU9## 
where r is the radius of curvature of the vertex of the aspheric surface; 
K is the conic constant; and A4, A6, A8 and A10 are the aspheric 
coefficients of the fourth, sixth, eighth and tenth orders, respectively. 
TABLE 2D 
______________________________________ 
N = INT(7.20 .times. h.sup.2 + 0.33 .times. h.sup.4 + 0.5) 
rN = 2.700 + 5.13 .times. 10.sup.-4 .times. N 
KN = -0.5000 
A4N = -1.570 .times. 10.sup.-3 + 1.00 .times. 10.sup.-6 .times. N 
A6N = -1.900 .times. 10.sup.-4 + 3.02 .times. 10.sup.-7 .times. N 
A8N = -1.900 .times. 10.sup.-5 + 1.51 .times. 10.sup.-8 .times. N 
A10N = -9.000 .times. 10.sup.-7 
.DELTA.N = -0.001510 .times. N 
______________________________________ 
In the case where an objective lens is manufactured from a high-index 
glass, lens performance satisfactory as a high-NA objective lens can be 
achieved without using an aspheric surface and, therefore, a spherical 
lens can effectively be used as in Example 1D discussed above. 
Example 2D 
FIG. 49 shows optical system that uses the hybrid lens according to Example 
2D of the present invention. In this example, too, the hybrid lens is used 
as an objective lens in an optical disk system. The specific numerical 
data for Example 2D are listed in Table 3D. The first surface of the 
hybrid lens under consideration is a diffraction surface whereas the third 
surface is an ordinary smooth aspheric surface. FIG. 50 shows the 
aberrations that develop in the system composed in accordance with the 
data listed in Table 3D. 
TABLE 3D 
______________________________________ 
.lambda..sub.0 = 780 nm f = 3.30 mm NA = 0.55 
Surface 
No. r d nd .nu.d n780 
______________________________________ 
1 Diffracting 
0.040 1.51653 
surface 
2 2.400 2.110 1.58913 
61.2 1.58252 
3 Aspheric 1.355 
surface 
4 .infin. 1.200 1.58547 
29.9 1.57346 
5 .infin. 
______________________________________ 
The shape of the first surface is given by the coefficients listed in Table 
4D (see below) if the sag X(h) of the aspheric surface at the point that 
is departed from the optical axis by distance h is defined by the 
aforementioned equation (4D). 
TABLE 4D 
______________________________________ 
N = INT(4.41 .times. h.sup.2 + 0.20 .times. h.sup.4 + 0.5) 
rN = 2.182 + 5.14 .times. 10.sup.-4 .times. N 
KN = -0.3610 
A4N = -1.731 .times. 10.sup.-3 + 1.27 .times. 10.sup.-6 .times. N 
A6N = -2.010 .times. 10.sup.-4 + 4.23 .times. 10.sup.-7 .times. N 
A8N = -3.170 .times. 10.sup.-5 - 6.04 .times. 10.sup.-9 .times. N 
A10N = 6.000 .times. 10.sup.-7 + 6.04 .times. 10.sup.-9 .times. N 
.DELTA.N = -0.001510 .times. N 
______________________________________ 
The asphericity of the third surface is given by the coefficients listed in 
Table 5D (see below) if the sag X(h) of the aspheric surface at the point 
that is departed from the optical axis by distance h is defined by the 
following equation (5D), in which the respective symbols have the same 
meanings as in equation (4D). 
The lower the refractive index, the lower the temperature at which optical 
materials can be molded to fabricate glass molded lenses. Therefore, using 
a low-index optical material is desired when making a glass lens by the 
molding method. In that case, the surface of the lens on the side that is 
opposite the side where the cemented surface lies may be rendered aspheric 
as in Example 2D and this lens design is effective in correcting chromatic 
aberration by a sufficient degree to make it satisfactory as a high-NA 
objective lens. 
##EQU10## 
TABLE 5D 
______________________________________ 
r = -9.585 
K = 0.000 
A4 = 1.320 .times. 10.sup.-2 
A6 = -2.520 .times. 10.sup.-3 
A8 = 5.580 .times. 10.sup.-4 
A10 = -5.340 .times. 10.sup.-5 
______________________________________ 
FIG. 51 shows a prior art single lens that has an aspheric surface on both 
sides and which performs as well as the lens of Example 2D except in 
chromatic aberration. The specific numerical data for that prior art lens 
are listed in Table 6D (see below) and the associated aspheric 
coefficients are as listed in Table 7D (also see below). The aberrations 
that develop in the system composed to those data are shown in FIG. 52. 
Comparing FIGS. 50 and 52, one can clearly see the chromatic aberration 
correcting effect of the diffraction element. 
TABLE 6D 
______________________________________ 
.lambda..sub.0 = 780 nm f = 3.30 mm NA = 0.55 
Surface 
No. r d nd .nu.d 
n780 
______________________________________ 
1 Aspheric 2.145 1.58913 61.2 1.58252 
surface 
2 Aspheric 1.355 
surface 
3 .infin. 1.200 1.58547 29.9 1.57346 
4 .infin. 
______________________________________ 
TABLE 7D 
______________________________________ 
1st Surface 2nd Surface 
______________________________________ 
r = 2.206 r = -9.585 
K = -0.328 K = 0.000 
A4 = -0.150 .times. 10.sup.-2 
A4 = 0.132 .times. 10.sup.-1 
A6 = -0.167 .times. 10.sup.-3 
A6 = -0.252 .times. 10.sup.-2 
A8 = -0.305 .times. 10.sup.-4 
A8 = 0.558 .times. 10.sup.-3 
A10 = 0.800 .times. 10.sup.-6 
A10 = -0.534 .times. 10.sup.-4 
______________________________________ 
According to Examples 1D and 2D, objective lenses can be provided that are 
of substantially the same size and weight as the prior art aspheric lens 
and which yet are effectively corrected for chromatic aberration. As a 
further advantage, the portion of those lenses that has a refractive power 
is a glass lens and, hence, the imaging performance of the lenses is 
completely immune to the effect of humidity changes and substantially 
immune to temperature changes. 
Example 3D 
FIG. 53 shows optical system that uses the compound lens according to 
Example 3D of the present invention. In this example, the hybrid lens is 
used as a collimator lens in an optical disk apparatus. Plane parallel 
plate C shown on the right side of FIG. 53 is a cover glass for the laser 
diode. The specific numerical data for Example 3D are shown in Table 8D. 
In the example under consideration, the first surface is an ordinary 
aspheric surface and the third surface is a diffraction surface. FIG. 54 
shows the aberrations that develop in the system composed in accordance 
with the data listed in Table 8D. 
TABLE 8D 
______________________________________ 
.lambda..sub.0 = 780 nm f = 10.8 mm NA = 0.20 
Surface 
No. r d nd .nu.d n780 
______________________________________ 
1 Aspheric 2.460 1.67790 
55.3 1.66959 
surface 
2 .infin. 0.040 1.51653 
3 Diffracting 
9.000 -- 
surface 
4 .infin. 0.250 1.51633 
64.1 1.51072 
5 .infin. -- -- 
______________________________________ 
The asphericity of the first surface is given by the coefficients listed in 
Table 9D (see below) if the sag X(h) of the aspheric surface at the point 
that is departed from the optical axis by distance h is defined by the 
aforementioned equation (5D). 
TABLE 9D 
______________________________________ 
r = 7.231 
K = -0.5933 
A4 = 0.000 
A6 = -3.440 .times. 10.sup.-7 
A8 = -4.370 .times. 10.sup.-9 
A10 = 0.000 
______________________________________ 
The shape of the third surface is given by the coefficients listed in Table 
10D (see below) if the sag X(h) at the point that is departed from the 
optical axis by distance h is expressed by the following equation (6D): 
EQU X(h)=.DELTA.N (6D) 
TABLE 10D 
______________________________________ 
N = INT(2.61 .times. h.sup.2 - 0.0212 .times. h.sup.4 + 0.5) 
.DELTA.N = 0.001510 .times. N 
______________________________________ 
With a high-NA lens, beams of light enter the diffraction element obliquely 
in the peripheral portion of the lens and, therefore, compared to the 
central portion where almost normal incidence occurs, the peripheral 
portion of the lens provides a longer optical path even if the two areas 
have the same thickness. Hence, in order to insure that the phase 
difference for each annular segment is the same in both the central and 
peripheral portions, the difference in the thickness of the diffraction 
element between individual annular segments must be rendered to decrease 
from the center outward. 
Consider, for example, a lens having a comparable NA to that employed in 
Example 3D; in such a lens, continuity in phase can be assured by making 
the difference in thickness between annular segments in the outermost area 
smaller than the difference in the central area by about 1%. However, the 
discontinuity in phase that occurs if the difference in thickness between 
annular segments is made equal in the whole part of the lens will cause no 
problem in practical applications. Therefore, in Example 3D under 
discussion, .DELTA.N is expressed as a linear function of N and the 
difference in thickness between individual annular segments is set to be 
equal in both the central and peripheral parts of the lens. 
It should also be mentioned that in the case of a lens like that of Example 
3D which does not have a very large NA, forming the diffraction surface of 
a plane surface alone is desired in view of the ease with which mold 
working and shape measurement can be accomplished. 
Example 4D 
FIG. 55 shows optical system in which the hybrid lens of Example 4D of the 
present invention is used as part of a telephoto lens system. The specific 
numerical data for Example 4D are listed in Table 11D (see below), in 
which symbol .omega. denotes the half view angle and fb the back focus. 
A diffraction element formed of a thermosetting plastic material is joined 
to the object side (which is on the left as seen in FIG. 55) of the first 
lens of this telephoto lens system which is positioned the closest to the 
object. However, because of the small thickness of the diffraction 
element, the first and second surfaces are shown to overlap each other in 
FIG. 55. 
The telephoto lens system under consideration is intended to be used in a 
wavelength band of 435 to 656 nm and the reference wavelength 
.lambda..sub.0 for the diffraction element at the time of its design is 
546.07 nm. FIG. 56 shows the aberrations that develop in the system 
composed in accordance with the data listed in Table 11D. 
TABLE 11D 
______________________________________ 
f = 293.1 mm (at 588 nm) 
NA = 2.8 .omega. = 4.2.degree. fb = 72.40 
Surface 
No. r d nd .nu.d 
______________________________________ 
1 Diffracting 
0.04 1.52249 
59.8 
surface 
2 134.989 14.76 1.51633 
64.1 
3 -1430.844 2.20 -- 
4 113.600 11.80 1.51633 
64.1 
5 525.000 8.98 -- 
6 .infin. 5.50 1.80610 
33.3 
7 178.352 50.0 -- 
8 86.700 3.00 1.79952 
42.2 
9 42.660 14.80 1.62041 
60.3 
10 496.238 10.42 -- 
11 -585.886 5.00 1.80518 
25.4 
12 -97.810 3.20 1.58875 
51.2 
13 50.630 60.09 -- 
14 96.200 6.60 1.69680 
55.5 
15 -80.000 2.70 1.53172 
48.9 
16 113.576 7.00 -- 
17 .infin. 2.00 1.51633 
64.1 
18 .infin. -- -- 
______________________________________ 
The shape of the first surface is given by the coefficients listed in Table 
12D (see below) if the sag X(h) at the point that is departed from the 
optical axis by distance h is expressed by the following equation (7D). 
The effective radius of the first lens is 52.3 mm and its first surface is 
a diffracting surface composed of 133 annular surfaces: 
##EQU11## 
TABLE 12D 
______________________________________ 
N = INT(4.43 .times. 10.sup.-2 .times. h.sup.2 + 1.54 
.times. 10.sup.-6 .times. h.sup.4 + 0.5) 
rN = 135.029 + 3.58 .times. 10.sup.-4 .times. N 
.DELTA.N = 
-0.001041 .times. N 
______________________________________ 
FIG. 57 shows a modification of the telephoto lens of Example 4D, in which 
the hybrid lens positioned the closest to the object is replaced by a 
single lens having no diffraction element and in which a chromatic 
aberration correcting filter joined with a diffraction element is 
positioned closer to the object than the single lens. The diffraction 
element is joined to the image side of the filter. In this case, too, the 
diffraction element is so thin that the second and third surfaces are 
shown to overlap each other in FIG. 57. 
The specific numerical data for this modified lens system are as listed in 
Table 13D. The fifth and subsequent surfaces have the same data as the 
third and subsequent surfaces in the lens system of Example 4D and the 
aberration and other performance characteristics of the two lens systems 
are also the same. 
TABLE 13D 
______________________________________ 
Surface 
No. r d nd .nu.d 
______________________________________ 
1 .infin. 8.00 1.51633 
64.1 
2 .infin. 0.04 1.52249 
59.8 
3 Diffracting 
2.00 -- 
surface 
4 135.029 14.80 1.51633 
64.1 
5 -1430.844 2.00 -- 
6 113.600 11.80 1.51633 
64.1 
7 525.000 8.98 -- 
8 .infin. 5.50 1.80610 
33.3 
9 178.352 50.00 -- 
10 86.700 3.00 1.79952 
42.2 
11 42.660 14.80 1.62041 
60.3 
12 496.238 10.42 -- 
13 -585.886 5.00 1.80518 
25.4 
14 -97.810 3.20 1.58875 
51.2 
15 50.630 60.09 -- 
16 96.200 6.60 1.69680 
55.5 
17 -80.000 2.70 1.53172 
48.9 
18 113.576 7.00 -- 
19 .infin. 2.00 1.51633 
64.1 
20 .infin. -- -- 
______________________________________ 
The shape of the third surface is given by the coefficients listed in Table 
14D (see below) if the sag X(h) at the point that is departed from the 
optical axis by distance h is expressed by the aforementioned equation 
(6D). 
TABLE 14D 
______________________________________ 
N = INT(4.43 .times. 10.sup.-2 .times. h.sup.2 + 1.51 
.times. 10.sup.-6 .times. h.sup.4 + 0.5) 
.DELTA.N = 
0.001041 .times. N 
______________________________________ 
FIG. 58 shows a telephoto lens system that has comparable performance to 
the system of Example 4D, except that chromatic aberration is corrected by 
a particular combination of optical materials without using a diffraction 
element. The specific numerical data for this lens system are as listed in 
Table 15D. The aberrations that develop in the system composed in 
accordance with those data are as shown in FIG. 59. Comparing FIGS. 56 and 
59, one can see that if a diffraction element is used, chromatic 
aberration can selectively be corrected in a very efficient manner without 
affecting other performance characteristics. 
TABLE 15D 
______________________________________ 
f = 293.1 mm (at 588 nm) 
NA = 2.9 .omega. = 4.2.degree. fb = 72.00 
Surface 
No. r d nd .nu.d 
______________________________________ 
1 140.152 14.80 1.49700 
81.6 
2 -1148.125 2.00 -- 
3 111.252 11.80 1.49700 
81.6 
4 440.000 10.33 -- 
5 .infin. 5.50 1.72047 
34.7 
6 180.590 49.79 -- 
7 86.700 3.00 1.79952 
42.2 
8 42.690 14.50 1.62041 
60.3 
9 496.238 9.73 -- 
10 -585.886 5.00 1.80518 
25.4 
11 -97.810 3.20 1.58875 
51.2 
12 50.630 60.11 -- 
13 96.200 6.60 1.69680 
55.5 
14 -80.000 2.70 1.53172 
48.9 
15 113.576 8.67 -- 
16 .infin. 2.00 1.51633 
64.1 
17 .infin. -- -- 
______________________________________ 
The foregoing description in Examples 1D to 4D is limited to the case where 
the hybrid lens of the present invention is used either as an objective or 
collimator lens for optical disk or as part of a telephoto lens system. It 
should, however, be noted that the hybrid lens is also applicable to other 
types of optical system unless the view angle is very wide. 
As described above, the present invention combines a glass lens with a 
plastic diffraction element so as to provide a chromatic aberration 
corrected compound lens whose performance is less susceptible to 
environmental changes and to which a diffraction pattern can be 
transferred in an exact manner. 
The following embodiments of the present invention relate to an optical 
device for correcting chromatic aberration by making use of the reflective 
diffraction of light. 
According to yet another aspect of the present invention, there is provided 
an optical device that is capable of correcting the chromatic aberration 
that develops in a single lens when the operating wavelength is offset 
from the reference value. Stated more specifically, if a wavefront 
aberration (chromatic aberration) occurs in a single lens when the 
operating wavelength is offset from the reference value, the chromatic 
aberration correcting device of a reflection and diffraction type 
according to the present invention cancels that aberration by creating at 
a reflecting surface a divergent or convergent wavefront of opposite 
nature. 
The chromatic aberration correcting device of a reflective refractive type 
according to the present invention may be used not only for correcting the 
chromatic aberration that develops in a single lens but also for 
correcting the chromatic aberration that develops in a compound lens. A 
plurality of lens elements sometimes fails to correct chromatic aberration 
for various reasons associated with refractive index, transmittance, etc. 
and, especially at short wavelengths near .lambda.=300 nm, only one type 
of optical material is available and the correction of chromatic 
aberration is difficult to accomplish. The chromatic aberration correcting 
device of a reflection and diffraction type according to the present 
invention is capable of correcting chromatic aberration even in such short 
wavelength range. 
In one embodiment of the invention, the contours of the central reflecting 
surface and the annular reflecting surfaces in the chromatic aberration 
correcting device are made circular as seen in a direction perpendicular 
to those reflecting surfaces and the step distance t between adjacent 
reflecting surfaces is set to be as follows: 
EQU t=.lambda.m/2n (m is an integer) 
where .lambda. is the reference wavelength within the operating wavelength 
band, and n is the refractive index of the reflecting surface on the 
incident side. 
If the correcting device is to be inserted in the optical path obliquely, 
the contours of the central reflecting face and the annular reflecting 
surfaces may be rendered elliptical as seen in a direction perpendicular 
to those reflecting surfaces and the step distance t is set to be as 
follows: 
EQU t=A.lambda.m/2n (m is an integer) 
where .lambda. is the reference wavelength within the operating wavelength 
band, n is the refractive index of the reflecting surface on the incident 
side, and A is the ratio between the major and minor axes of the ellipse. 
The value of m desirably satisfies the condition 
1.ltoreq..vertline.m.vertline..ltoreq.10. The zero value of m means a 
reflecting mirror the surface of which is planar as a whole; therefore, a 
chromatic aberration correcting device of a reflective diffraction type 
cannot be fabricated unless m is 1 or more. On the other hand, if m 
exceeds 10, a serious disadvantage will occur under great variations in 
wavelength in that the proportion of light of higher-order diffraction 
increases to lower the efficiency of light utilization. The sign of the 
value m determines whether the reflecting surface, taken as a whole, is 
macroscopically convex or concave. 
If the width of each annular reflecting surface is set to be in inverse 
proportion to the square of the distance from the optical axis, the 
wavefront generated upon variation in the wavelength of incident light can 
be made generally spherical. If the lens to be combined is expected to 
experience a large change in spherical aberration on account of the 
variation in wavelength, it may be corrected by properly adjusting the 
width of annular segments on the reflecting surface in design stage; 
however, from the viewpoint of wide applicability, it suffices that the 
width of each annular reflecting surface is set to be in inverse 
proportion to the square of the distance from the optical axis. 
The central reflecting surface and the annular reflecting faces may 
comprise planes that are parallel to one another; alternatively, those 
surfaces may be curved. 
The chromatic aberration correcting device of a reflective diffraction type 
according to the present invention is to be combined with a lens to 
correct the chromatic aberration that will occur in that lens. Stated more 
specifically, when light having a wavelength different from a reference 
wavelength enters the lens, it will develop chromatic aberration and in 
order to correct this aberration, the device of the present invention 
changes the wavefront of the incident light by means of reflection. 
The present invention also provides a chromatic aberration correcting 
apparatus, in which the chromatic aberration correcting device of a 
reflective diffraction type described above is inserted in the optical 
path between a collimator for collimating the light entering a lens and 
the lens. An exemplary application of this apparatus is to correct the 
aberration that develops in a single lens used for focusing laser light to 
form a spot on an optical disk in an optical information recording and 
reproducing apparatus. 
Examples 
The present invention is described below with reference to the examples 
shown in the accompanying drawings. FIGS. 60 and 61 show the operating 
theory of the chromatic aberration correcting device of the present 
invention. 
Reference is first made to FIG. 60. The chromatic aberration correcting 
device of a reflective diffraction type which is generally indicated by 
311 comprises a circular central reflecting surface 311ac on the optical 
axis O and three coaxial circular annular reflecting faces 311bc, 311cc 
and 311dc that are located around the central reflecting surface 311ac. 
Only three annular reflecting surfaces are shown in FIG. 60 but in 
practice the correcting device of the present invention will be provided 
with from 10 to about 100 annular reflecting surfaces. The prior art 
diffractive lens has as many as several hundred annular segments and this 
is one of the factors by which the chromatic aberration correcting device 
of a reflective diffraction type according to the present invention can be 
distinguished from the conventional diffractive lens. 
The circular central reflecting surface 311ac and the circular annular 
reflecting surfaces 311bc, 311cc and 311dc comprise planes that are 
parallel to one another and which are offset in position along the optical 
axis O by step distance t; taken as a whole, those reflecting faces 
produce a macroscopically convex shape. For the sake of clarity, let the 
correcting device 311 be assumed to be in air (n=1). Also assume that the 
reference wavelength of light entering the reflecting surface is .lambda.. 
Then, the step distance t is given by t=.lambda./2 and this corresponds to 
the case where m=1 and n=1 in the equation t=.lambda.m/2n. 
Consider here the case where plane-wave light (beams of parallel light) 
having the reference wavelength .lambda. enter the correcting device 311. 
Adjacent lines 312 indicate the positions taken along the optical path by 
the travelling plane-wave light of a specified phase (e.g. 0.degree.) 
having the reference wavelength .lambda.. Since the light having the 
reference wavelength satisfies the condition t=.lambda./2, it will remain 
as a plane wave even after it has been reflected by the circular central 
reflecting face 311ac or the circular annular reflecting surfaces 
311bc-311dc. 
Stated in general terms, the optical pathlength difference that occurs upon 
reflection in a medium (refractive index, n; thickness, t) along the 
optical path is given by 2nt. Therefore, if the correcting device 311 has 
step-like reflecting surfaces whose step distance is t as expressed by 
t(h)=.lambda./2n (h is the distance from the optical axis O), or mt (m is 
an integer), the wavefront of the light having the reference wavelength 
will in no way change in shape after reflection since if it is reflected 
by adjacent reflecting areas, the only change that occurs to its wavefront 
is a phase shift of m.lambda. and the reflected light will keep on 
travelling without changing its wavefront. 
FIG. 61 shows the case where a plane wave having a wavelength .lambda.' 
slightly longer than the reference wavelength .lambda. enters the 
correcting device 311 which is the same as shown in FIG. 60. The distance 
between adjacent lines 312' is longer than the distance between adjacent 
lines 312 (see FIG. 60) by the shift in wavelength. In the case of 
reflection by the correcting device 311, the light that is reflected by 
the circular central reflecting face 311ac travels the shortest distance 
through the medium whereas the light that is reflected by the circular 
annular reflecting face 311dc will travel the longest distance. It should 
also be noted that light having a wavelength longer than the reference 
wavelength has such a nature that the longer the distance it travels, the 
more advanced its wavefront is. As a result, the phase of the wavefront of 
light that has been reflected by the circular central reflecting surface 
311ac and the circular annular reflecting surfaces 311bc-311dc will lead 
as a function of the distance from the optical axis O and the wavefronts 
of the reflected light beams will, taken as a whole, be curved to create a 
single convergent wavefront. In other words, the correcting device 311 
having step-like reflecting faces that provide macroscopically a shape 
convex to the ray entrance side will cause incident plane-wave light to be 
reflected as a convergent wavefront if it has a longer wavelength than the 
reference wavelength. This is equivalent to saying that the light 
reflection by the correcting device 311 will produce a chromatic 
aberration that cancels off the chromatic aberration that develops in a 
positive lens having a refractive action and the device can accordingly 
accomplish the necessary correction of chromatic aberration. 
Conversely, the wavefront of light having a shorter wavelength than the 
reference wavelength will lag as it travels a longer distance through the 
medium and, hence, it is rendered divergent by the action of the 
correcting device 311. In other words, the correcting device 311 which has 
step-like reflecting surfaces that provide macroscopically a shape convex 
to the ray entrance side will cause incident plane-wave light to be 
reflected as a divergent wavefront if it has a shorter wavelength than the 
reference wavelength. This is equivalent to saying that the light 
reflection by the correcting device 311 will produce a chromatic 
aberration that cancels off the chromatic aberration that develops in a 
negative lens having a refractive action and the device can accordingly 
accomplish the necessary correction of chromatic aberration. 
Whether the step-like reflecting surfaces to be formed on the correcting 
device 311 produce a macroscopically convex or concave shape depends on 
various factors such as whether the chromatic aberration to be corrected 
develops in a positive lens or a negative lens. 
The widths s1, s2 and s3 of the circular annular reflecting surfaces 311bc, 
311cc and 311dc, respectively, are each set to be in inverse proportion to 
the square of the distance from the optical axis O. 
FIGS. 62 and 63 show an example of the present invention in which the 
correcting device generally indicated by 311A is positioned at an angle of 
45.degree. with respect to the optical axis O. The reflecting surface of 
this correcting device comprises an elliptical reflecting surface 311ae 
which, as seen in a direction perpendicular to that reflecting surface, is 
positioned at the center of the optical axis O, and coaxial elliptical 
annular reflecting surfaces 311be, 311ce and 311de that are positioned 
around the central reflecting surface 311ae. 
The ratio A between the major and minor axes of the ellipse is determined 
in such a way that each of the orthogonal projections of the reflecting 
surfaces 311ae-311de onto a plane perpendicular to the optical axis O will 
be a circle. In other words, A is 2.sup.1/2. 
If the ellipse defined by the elliptical reflecting surface 311ae is 
expressed by (X.sup.2 /A.sup.2)+(Y.sup.2 /1)=r.sup.2 (r is a constant) in 
an XY coordinate system, then the step distance t between the reflecting 
surface 311ae and the adjacent annular reflecting surface 311be and 
between individual annular reflecting surfaces 311be, 311ce and 311de is 
given by t=.lambda..multidot.2.sup.-1/2. As in the example shown in FIGS. 
60 and 61, this corresponds to the case where n=1 and m=1 in the equation 
t=A.lambda.m/2n (m is an integer). Hence, the example under consideration 
provides entirely the same advantage as is obtained in the previous 
example. 
The two examples discussed above concern the case where m=1; if the 
operating wavelength range is not very wide, the value of m may be 
adjusted to 2 or more when determining the step distance t and the light 
of mth-order diffraction may safely be used without lowering the 
diffraction efficiency. Particularly in the case where the width of 
annular segments decreases from the center outward, one may gradually 
increase the value of m starting from unity within a single device. In 
this case, the axial distance .DELTA.X(h) of a particular annular 
reflecting face from the central reflecting surface may be determined as a 
function of the distance h from the optical axis O by the following 
equation: 
EQU .DELTA.X(h)=(m.lambda./2n)Int{[r-(1-(1-h.sup.2 
/r.sup.2).sup.1/2)/(m.lambda./2n)]+0.5} 
where Int(x) is a function giving an integer not greater than x. 
FIG. 64 shows an embodiment of the present invention in which the chromatic 
aberration correcting device 311A of a reflection and diffraction type is 
applied to an optical information recording and reproducing apparatus. 
Laser light issuing from a laser light source 321 is collimated by a 
collimator lens 322, shaped by a beam shaping prism 323 to have a circular 
cross section and enters a beam splitter 324. Part of the separated laser 
light is reflected by the correcting device 311A fixed on a carriage 334 
to enter an objective lens 326. The carriage 334 is slidable along guide 
rails 335 in the radial direction of an optical disk 327 indicated by the 
two-head arrow in FIG. 64. The laser light incident on the objective lens 
326 is focused on the optical disk 327 and the reflected light from the 
disk makes reentry into the correcting device 311A which returns it to the 
beam splitter 324. Part of the return light passes through a lens 330 in 
signal reproducing optics 328 to be supplied into a sensor 332 and the 
remainder passes through a lens 331 in servo optics 329 to be supplied 
into a sensor 333. 
Various types are known for the optical information recording and 
reproducing apparatus that operates in this manner and by combining the 
objective lens 326 (which is a single lens) with the correcting device 
311A, the chromatic aberration that develops in the objective lens 326 can 
be effectively corrected. 
On the pages that follow, the present invention is described in greater 
detail with reference to specific examples, all of which are intended to 
correct the chromatic aberration that developed in a positive objective 
lens. 
Example 1E 
FIG. 65 shows a chromatic aberration correcting device that has a 
reflecting surface perpendicular to the optical axis O and which is 
generally indicated by 311. The device 311 is adapted to correct chromatic 
aberration that occurs in an objective lens having the geometry shown in 
FIG. 70 and the characteristics shown in FIG. 71. In FIG. 70, the 
objective lens is indicated by 341 and the reference numeral 342 denotes 
an optical disk. Parallel beams of laser light coming from a collimator 
lens are focused by the objective lens 341 to form a spot on the inner 
recording surface of the optical disk 342; hence, the objective lens 341 
is equivalent to the objective lens 326 in the apparatus shown in FIG. 64. 
The objective lens 341 has the following specifications: 
Focal length 3.3 mm 
Operating wavelength, (reference wavelength) 780 nm 
Shift in back focus in response to a change in wavelength by unit amount, 
df.sub.B /d.lambda. 11 .mu.m/nm 
The numerical data for the objective lens 341 are listed in Table 1E. 
The symbols used in FIG. 71 have the following meanings: SA, spherical 
aberration; SC, sine condition; S, sagittal; M, meridional. In Table 1E, 
r.sub.i denotes the radius of curvature of an individual lens surface; 
d.sub.i, the lens thickness or the aerial distance between individual 
lenses; N, refractive index. 
TABLE 1E 
______________________________________ 
NA = 0.55 F = 3.30 .omega. -1.7 
Surface 
No. r d N 
______________________________________ 
1* 2.168 2.230 1.53677 
2* -6.205 1.363 
3 .infin. 1.200 1.57346 
4 .infin. 
______________________________________ 
*denotes asphericity. 
No. 1; K = -0.3265, A4 = -0.2263 .times. 10.sup.-2, A6 = -0.5014 .times. 
10.sup.-3, A8 = -0.7162 .times. 10.sup.-5, A10 = -0.3194 .times. 10.sup.- 
No. 2; K = -0.9120, A4 = 0.1648 .times. 10.sup.-1, A6 = -0.5064 .times. 
10.sup.-2, A8 = 0.7995 .times. 10.sup.-3, A10 = -0.4848 .times. 10.sup.-4 
The correcting device 311 of Example 1E is intended for normal incidence 
and reflection by the obverse surface; if it is assumed that the 
correcting device 311 corresponds to a positive lens having a focal length 
of 126 mm, the power of the diffractive lens is proportional to wavelength 
and the chromatic aberration that develops in the objective lens 341 can 
be corrected. However, if the objective lens and the correcting devices 
are used as two separate elements, a change in their distance will cause a 
corresponding change in the height of ray incidence on the objective lens; 
to avoid this problem, the objective lens and the correcting device must 
be combined, in a unitary assembly. Hence, the correcting device of the 
present invention is designed to have a macroscopic shape that is 
equivalent to a negative lens having a focal length (f) of -126 mm and its 
reflecting surface is made planar in order to insure that first-order 
light will not be subjected to the refractive action of diffraction. 
If reflection is obverse face reflection in air, n=1.0 and to make a 
negative lens of f=-126 mm on the reflecting surface, the radius of 
curvature must be r=252.0 mm. If a surface having this curvature is made 
planar by providing planes with the axial step distance t being adjusted 
to .lambda./2=390 nm=0.390 .mu.m, one can attain both the action of a 
diffractive lens having f=126 mm and the action of a refractive lens 
having f=-126 mm, thereby insuring that first-order light will travel in a 
straight path. 
Stated more specifically, X(h), or the axial distance of each of the 
annular reflecting surfaces 311bc, 311cc and 311dc from the central 
reflecting surface 311ac, is expressed in a function of the distance h 
from the optical axis as follows: 
EQU .DELTA.X(h)=(.lambda./2n)Int{[r-(1-(1-h.sup.2 
/r.sup.2).sup.1/2)/(.lambda./2n)]+0.5} 
where Int(x) is a function giving an integer not exceeding x. If those 
reflecting surfaces are arranged to provide a macroscopic shape expressed 
by that equation, one can correct the chromatic aberration that develops 
in the objective lens 341. Table 2E below gives data for describing the 
overall shape of the correcting device 311 shown in FIG. 65. 
TABLE 2E 
______________________________________ 
h (mm) .DELTA.X (.mu.m) 
______________________________________ 
0.000 .about. 0.313 
0.0 
.about. 0.542 0.39 
.about. 0.700 0.78 
.about. 0.829 1.17 
.about. 0.940 1.56 
.about. 1.039 1.95 
.about. 1.130 2.34 
.about. 1.214 2.73 
.about. 1.292 3.12 
.about. 1.366 3.51 
.about. 1.436 3.90 
.about. 1.503 4.29 
.about. 1.567 4.68 
.about. 1.628 5.07 
.about. 1.688 5.46 
.about. 1.745 5.85 
.about. 1.800 6.24 
.about. 1.854 6.63 
.about. 1.906 7.02 
.about. 1.957 7.41 
.about. 2.007 7.80 
______________________________________ 
If the correcting device 311 having this geometry is inserted in the beams 
of parallel light between the collimator lens and the objective lens 314 
and if the reflected light from the device 311 is separated by the beam 
splitter, defocusing (chromatic aberration) due to the variation in the 
operating wavelength of the semiconductor laser can be canceled. In other 
words, the chromatic aberration shown in FIG. 71 that developed in the 
single objective lens 314 can be effectively corrected. 
FIG. 69 shows schematically the chromatic aberration that develops in the 
objective lens 341 and how it is corrected by the correcting device 311. 
If the incoming laser light has the reference wavelength .lambda.=780 nm, 
the optical system works properly in that the desired image is picked up 
by the sensor 322 (see FIG. 64) as a result of processing through the 
objective lens 341 and the correcting device 311. In order words, no 
defocusing will occur. 
However, if the wavelength of the incoming laser light changes to 
.lambda.'=770 nm, chromatic aberration (wavefront aberration) as shown by 
curve B in FIG. 69 will develop in the objective lens 341. This wavefront 
aberration is more or less undercorrected in the peripheral portion of the 
lens. On the other hand, in response to the wavelength shift toward the 
shorter range, the correcting device 311 will transform the incident 
plane-wave light to produce a divergent wavefront. This divergent 
wavefront is more or less overcorrected as shown by curve C in FIG. 69. 
Hence, the two wavefronts cancel each other and the composite wavefront is 
such as to produce a desired image in focus. In other words, the chromatic 
aberration that develops in the objective lens 341 as a result of 
wavelength shift can be corrected by the correcting device 311 of the 
present invention. 
Example 2E 
In system of Example 1E, the reflected light from the correcting device 311 
is separated by the beam splitter and a loss is prone to occur in the beam 
splitter. To solve this problem, it is preferred to position the 
correcting device as it is included by 45.degree. with the optical axis as 
shown in FIG. 64, where the correcting device is indicated by 311A. In 
this case, as already described with reference to FIGS. 62 an 63, the 
reflecting surface of the correcting device 311A is composed of elliptical 
central reflecting surface 311ae and three elliptical annular reflecting 
surfaces 311be-311de. Considering that the effective phase difference that 
is given to the wavefront by one step is sin 
45.degree..perspectiveto.0.707, the step distance t is about 1.41 times as 
great as the step distance adopted in Example 1E (1/sin 
45.degree..perspectiveto.1.41). Therefore, the 45.degree. incidence 
correcting device 311A which performs as effectively as the device 311 of 
Example 1E has a geometry that is shown physically in FIG. 66 and 
numerically in Table 3E below. 
TABLE 3E 
______________________________________ 
along minor axis along major axis 
h (mm) h (mm) .DELTA.X (.mu.m) 
______________________________________ 
0.000 .about. 0.313 
0.000 .about. 0.443 
0.0 
.about. 0.542 .about. 0.767 
0.55 
.about. 0.700 .about. 0.991 
1.10 
.about. 0.829 .about. 1.172 
1.65 
.about. 0.940 .about. 1.330 
2.20 
.about. 1.039 .about. 1.470 
2.75 
.about. 1.130 .about. 1.598 
3.30 
.about. 1.214 .about. 1.717 
3.86 
.about. 1.292 .about. 1.827 
4.41 
.about. 1.366 .about. 1.932 
4.96 
.about. 1.436 .about. 2.031 
5.51 
.about. 1.503 .about. 2.126 
6.06 
.about. 1.567 .about. 2.216 
6.61 
.about. 1.628 .about. 2.303 
7.17 
.about. 1.688 .about. 2.387 
7.72 
.about. 1.745 .about. 2.468 
8.27 
.about. 1.800 .about. 2.548 
8.82 
.about. 1.854 .about. 2.622 
9.37 
.about. 1.906 .about. 2.698 
9.92 
.about. 1.957 .about. 2.768 
10.47 
.about. 2.007 .about. 2.838 
11.03 
______________________________________ 
If the correcting device 311A having this geometry is inserted in the beams 
of parallel light between the collimator lens and the objective lens 314 
(between collimator lens 322 and objective lens 326 in the case shown in 
FIG. 64), defocusing (chromatic aberration) due to the variation in the 
operating wavelength of the laser diode can be effectively canceled. 
Example 3E 
In Examples 1E and 2E, the reflecting surface is provided on the obverse 
surface of the chromatic aberration correcting device. However, the 
chromatic aberration correcting device of the present invention may also 
be constructed as a reverse surface reflection type. FIG. 67 shows an 
example of the correcting device adapted for such reverse surface 
reflection, which is generally indicated by 311B in FIG. 67. The 
correcting device of this reverse surface reflection type has the 
advantage that its performance is in no way affected if dust or dirt is 
deposited on the steps formed on the reflecting surface on the reverse 
side. In the case of reverse surface reflection, the ratio of operating 
wavelength to refractive index decreases in the medium (n&gt;1) and, hence, 
the step distance t becomes shorter than in Examples 1E and 2E (because 
n&gt;1 in the equation t=.lambda.m/2n). Table 4E below shows the geometry of 
the reflecting surface of the 45.degree. incidence aberration correcting 
device 311B that was fabricated from an optical material having n=1.51072. 
TABLE 4E 
______________________________________ 
along minor axis along major axis 
h (mm) h (mm) .DELTA.X (.mu.m) 
______________________________________ 
0.000 .about. 0.313 
0.000 .about. 0.443 
0.0 
.about. 0.542 .about. 0.767 
0.36 
.about. 0.700 .about. 0.991 
0.73 
.about. 0.829 .about. 1.172 
1.09 
.about. 0.940 .about. 1.330 
1.46 
.about. 1.039 .about. 1.470 
1.82 
.about. 1.130 .about. 1.598 
2.19 
.about. 1.214 .about. 1.717 
2.55 
.about. 1.292 .about. 1.827 
2.92 
.about. 1.366 .about. 1.932 
3.28 
.about. 1.436 .about. 2.031 
3.65 
.about. 1.503 .about. 2.126 
4.01 
.about. 1.567 .about. 2.216 
4.38 
.about. 1.628 .about. 2.303 
4.74 
.about. 1.688 .about. 2.387 
5.11 
.about. 1.745 .about. 2.468 
5.47 
.about. 1.800 .about. 2.548 
5.84 
.about. 1.854 .about. 2.622 
6.20 
.about. 1.906 .about. 2.696 
6.57 
.about. 1.957 .about. 2.768 
6.93 
.about. 2.007 .about. 2.838 
7.30 
______________________________________ 
Example 4E 
The angle of incidence on the chromatic aberration correcting device of a 
reflective diffraction type according to the present invention is in no 
way limited to 0.degree. or 45.degree.. All that is required is that the 
orthogonal projections of the central reflecting surface and the annular 
reflecting surfaces onto a plane perpendicular to the optical axis 
describe shapes that are of a rotation symmetry with respect to the 
optical axis which is the center of rotation. FIG. 68 and Table 5E show an 
example of the geometry of a chromatic aberration correcting device (which 
is indicated by 311C) that performs as effectively as the device of 
Examples 1E to 3E when the angle of incidence is 30.degree.. Since 1/sin 
30.degree.=2, the step distance t adopted in Example 4E is longer than 
those selected in Examples 1E to 3E; therefore, the correcting device of 
Example 4E has the advantage of greater ease in fabrication. 
TABLE 5E 
______________________________________ 
along minor axis along major axis 
h (mm) h (mm) .DELTA.X (.mu.m) 
______________________________________ 
0.000 .about. 0.313 
0.000 .about. 0.626 
0.0 
.about. 0.542 .about. 1.085 
0.78 
.about. 0.700 .about. 1.401 
1.56 
.about. 0.829 .about. 1.658 
2.34 
.about. 0.940 .about. 1.880 
3.12 
.about. 1.039 .about. 2.079 
3.90 
.about. 1.130 .about. 2.260 
4.68 
.about. 1.214 .about. 2.428 
5.46 
.about. 1.592 .about. 2.585 
6.24 
.about. 1.366 .about. 2.733 
7.02 
.about. 1.436 .about. 2.873 
7.80 
.about. 1.503 .about. 3.006 
8.58 
.about. 1.567 .about. 3.134 
9.36 
.about. 1.628 .about. 3.257 
10.14 
.about. 1.688 .about. 3.376 
10.92 
.about. 1.745 .about. 3.490 
11.70 
.about. 1.800 .about. 3.601 
12.48 
.about. 1.854 .about. 3.709 
13.26 
.about. 1.906 .about. 3.813 
14.04 
.about. 1.957 .about. 3.915 
14.82 
.about. 2.007 .about. 4.014 
15.60 
______________________________________ 
Example 5E 
The chromatic aberration correcting device of a reflective and diffraction 
type according to the present invention may be provided in portions other 
than where beams of parallel light travel. In this Example 5E, the present 
invention is applied to the reflecting surface of a catadioptric lens as 
shown in FIG. 72, in which the catadioptric lens and the reflecting 
surface are indicated by 343 and 344, respectively. Numerical data for the 
catadioptric lens 343 are listed in Table 6E below and the various 
aberrations that are caused in that lens are shown in FIG. 73, in which 
d-, g-, C-, F- and e-lines refer to the chromatic aberrations as expressed 
in terms of spherical aberration, as well as the lateral chromatic 
aberrations that develop at the respective wavelengths. In Table 6E, .nu. 
denotes the Abbe number. 
TABLE 6E 
______________________________________ 
F.sub.NO = 1:5.6 f = 44.68 
Surface 
No. r d N .nu. 
______________________________________ 
1 25.000 3.00 1.77250 
49.6 
2 252.451 1.00 
3 -26.100 2.00 1.49176 
57.4 
4 -800.000 
______________________________________ 
The fourth surface of this lens provides the reflecting surface 344. 
The catadioptric lens 343 forms an image at a magnification of 1/6 and with 
this lens, the image of an abject lying above the optical axis can be 
focused below the axis. However, the lens is unable to achieve 
satisfactory correction of axial chromatic aberration and at wavelengths 
near 588 nm, df.sub.B /d.lambda. is 7.0 .mu.m/nm. In accordance with the 
theory of the present invention, the reflecting surface 344 of the lens 
343 is formed of annular segments and the thus formed surface is capable 
of correcting the axial chromatic aberration that develops in the lens 
343. In other words, the reflecting surface 344 is adapted for normal 
incidence and reflection by the rear surface (which is equivalent to the 
device shown in FIG. 65 except that the reflecting surface is adapted for 
reverse surface reflection as in the device shown in FIG. 67). Table 7E 
below shows the geometry of the reflecting surface 344 of the lens 343 
that was fabricated from an optical material having n=1.49176. 
TABLE 7E 
______________________________________ 
h (mm) .DELTA.X (.mu.m) 
______________________________________ 
0.000 .about. 0.59 
0.19 
.about. 1.02 0.39 
.about. 1.32 0.59 
.about. 1.56 0.78 
.about. 1.77 0.98 
.about. 1.96 1.18 
.about. 2.13 1.37 
.about. 2.29 1.57 
.about. 2.44 1.77 
.about. 2.58 1.96 
.about. 2.71 2.16 
.about. 2.84 2.36 
.about. 2.96 4.56 
.about. 3.07 2.75 
.about. 3.18 2.95 
.about. 3.29 3.15 
.about. 3.40 3.34 
.about. 3.50 3.54 
.about. 3.60 3.74 
.about. 3.69 3.98 
.about. 3.79 4.13 
.about. 3.88 4.33 
.about. 3.97 4.52 
.about. 4.06 4.72 
.about. 4.14 4.92 
.about. 4.22 5.12 
.about. 4.31 5.31 
______________________________________ 
The reflecting surface having this geometry is capable of correcting the 
chromatic aberrations shown in FIG. 73. 
As described on the foregoing pages, the chromatic aberration correcting 
device of a reflective diffraction type according to the present invention 
is fabricated from a single reflecting element and it yet is capable of 
effective correction of the chromatic aberration that develops in a lens 
being used in combination with that device. Since the reflecting element 
is used extensively in optical system, one only need process this 
reflecting element to fabricate the chromating aberration correcting 
device of the present invention and, hence, the desired correction of 
chromatic aberration can be achieved without adding any special optical 
elements. Furthermore, if the correcting device is used on an optical 
information recording and reproducing apparatus, defocusing due to the 
variation in the wavelength of laser light can be corrected by a low-cost 
system layout.