Zoom lens of retrofocus type

A zoom lens of the retrofocus type includes, in order from a longer-distance conjugate point side to a shorter-distance conjugate point side, a front lens unit of negative refractive power, and a rear lens unit of positive refractive power, wherein a separation between the front lens unit and the rear lens unit varies according to variation of magnification, and at least one of the front lens unit and the rear lens unit is provided with a diffractive optical element.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to zoom lenses and, more particularly, to 
zoom lenses of the retrofocus type. 
2. Description of Related Art 
For a camera using an image-pickup element, such as a video camera or 
digital still camera, a certain long back focal distance is prerequisite 
to the photographic lens, for the single-lens reflex camera, to a 
wide-angle lens, and for an liquid crystal projector, to the projection 
lens. It has, therefore, been the common practice in the art that a lens 
unit of negative refractive power takes the lead as viewed from the 
long-distance conjugate point side (in the camera, from the object side, 
or in the projector, from the screen side). That is, the retrofocus type 
has been used in such lenses. 
Zoom lenses of the retrofocus type for such cameras are known in Japanese 
Laid-Open Patent Applications No. Hei 1-191820, No. Hei 3-203709 and No. 
Hei 3-240011. Each of these comprises, in order from the object side, a 
first lens unit of negative refractive power, a second lens unit of 
positive refractive power and a third lens unit of positive refractive 
power, the second lens unit axially moving to vary the focal length, while 
simultaneously moving the first lens unit to compensate for the shift of 
an image plane. 
A projection lens of the retrofocus type for the liquid crystal projector 
in Japanese Laid-Open Patent Application No. Sho 62-291613 comprises a 
first lens unit of negative refractive power followed by a number of lens 
units whose overall refractive power is positive. Japanese Laid-Open 
Patent Application No. Hei 3-145613 discloses another projection lens 
which comprises, in order from the screen side, a first lens unit of 
negative refractive power, a second lens unit of positive refractive power 
and a third lens unit of positive refractive power. 
To simplify the aberrational problems, it has been well known to use 
aspheric surfaces in the lens system. The aspheric surface is very 
effective for correcting spherical aberration, curvature of field and 
coma, but has a little effect on chromathc aberrations. To correct 
chromatic aberrations, a diffractive optical element can be used as 
disclosed in Japanese Laid-Open Patent Application No. Hei 4-213421 (U.S. 
Pat. No. 5,044,706), Japanese Laid-Open Patent Application No. Hei 
6-324262 and U.S. Pat. No. 5,268,790 and No. 5,493,441. 
However, the lens systems disclosed in Japanese Laid-Open Patent 
Applications No. Hei 4-213421 and No. 
Hei 6-324262 are monofocal. Therefore, no consideration is made on the 
chromatic aberrations of the zoom lens, in which their variation is very 
peculiar. Meanwhile, U.S. Pat. No. 5,268,790 and U.S. Pat. No. 5,493,441, 
although disclosing examples of application of the diffractive optical 
element to zoom lenses, both do not relate to the retrofocus type. So far, 
there are not known any examples of application of diffractive optical 
elements to the retrofocus type zoom lens. 
BRIEF SUMMARY OF THE INVENTION 
An object of the present invention is to provide a zoom lens of heretofore 
unknown configuration, as obtained by using a diffractive optical element 
in the retrofocus type of zoom lens. 
To achieve the above object, in accordance with an aspect of the invention, 
there is provided a zoom lens of retrofocus type, which comprises, in 
order from a longer-distance conjugate point side to a shorter-distance 
conjugate point side, a front lens unit of negative refractive power, and 
a rear lens unit of positive refractive power, wherein a separation 
between the front lens unit and the rear lens unit varies according to 
variation of magnification, and at least one of the front lens unit and 
the rear lens unit is provided with a diffractive optical element. 
The above and other objects and features of the invention will become 
apparent from the following detailed description of preferred embodiments 
thereof taken in conjunction with the accompanying drawings.

DETAILED DESCRIPTION OF THE INVENTION 
Hereinafter, preferred embodiments of the invention will be described in 
detail with reference to the drawings. 
FIG. 1 in lens block diagram shows a first embodiment 1 of a 2-unit zoom 
lens for the digital still camera in the wide-angle end. The zoom lens 
comprises, in order from the object side (the longer-distance conjugate 
point side), a first lens unit I that is the front lens unit and a second 
lens unit II that is the rear lens unit and a flat plane glass III such as 
color filters and a phase plate. The first lens unit I is constructed with 
two lenses L1 and L2 in minus-plus power arrangement, having a negative 
refractive power as a whole. The second lens unit II is constructed with 
two lenses L3 and L4 in plus-minus power arrangement, having a positive 
refractive power as a whole. During zooming from the wide-angle end to the 
telephoto (end, the first lens unit I axially moves toward the image side, 
while simultaneously the second lens unit II axially moves toward the 
object side, as shown by the arrows. In the embodiment 1, use is made of a 
diffractive optical surface on the front lens surface of the lens L3 in 
the second lens unit II, thus canceling chromatic aberrations in the first 
and second lens units I and II. Thus, in the embodiment 1, the lens L3 is 
a diffractive optical element. 
Further, the rear lens surface of the lens L1, the front lens surface of 
the lens L3 and the rear lens surface of the lens L4 are formed to 
aspheric shapes. 
On the premise that the diffractive optical element is to be used in the 
2-unit zoom lens, it is found that its unique merit is most effectively 
obtained when the diffractive optical element takes its place in the first 
surface of the second lens unit II as in the present embodiment. With this 
arrangement, concerning the longitudinal chromatic aberration, achromatism 
can be almost completed in the second lens unit II. Particularly, for the 
long focal lengths at or near the telephoto end, the achromatic effect is 
excellent. 
The lateral chromatic aberration, too, can be deprived of almost perfectly 
by introducing the diffractive optical element. It is to be noted that, 
particularly in the wide-angle region, the chromatic aberrations produced 
from the glass lenses of the second lens unit II are preliminarily 
corrected to an excess in the reverse direction by the diffractive optical 
element. When combined with the front lens unit, this residual is canceled 
out. The chromatic aberrations on the image plane are thus maintained 
stable at a minimum. 
The diffractive optical element may be made up with varying pitches in 
order to act as en aspheric surface. The terms in higher orders of the 
phase are then optimized so that the diffractive optical surface has an 
effect of correcting even coma and spherical aberration in the wide-angle 
end for improving the performance. 
The use of such a configuration as in the present embodiment 1 leads to 
provide a possibility of correcting well not only spherical aberration, 
coma and curvature of field but also longitudinal and lateral chromatic 
aberrations, thus correcting all aberrations well at once. Particularly, 
the variation with zooming of the chromatic aberrations, which becomes a 
serious problem in the zoom lens, is suppressed to a minimum. So, the 
optical system can be constructed with a smallest number of lens elements. 
It becomes possible to provide a zoom lens which is reduced to a compact 
size and amenable to low-cost production techniques, while still 
maintaining a high performance. 
The diffractive optical element is an optical element for bending light by 
the law of diffraction that gives the following equation: 
EQU n.multidot.sin .theta.-n'.multidot.sin .theta.'=m.lambda./d 
where n is the refractive index of the medium containing the incident 
light, n' is the refractive index containing the emergent light, .theta. 
is the angle of incidence, .theta.' is the angle of emergence, m is the 
order of diffraction, .lambda. is the wavelength and d is the grating 
space. 
For the refractive optical elements of ordinary glasses, the dispersion is 
expressed by .nu.=(n-1)/.DELTA.n. For the diffractive optical elements, on 
the other hand, the dispersion is expressed by 
.nu.=.lambda./.DELTA..lambda.. Whilst the Abbe numbers of the most optical 
glasses lie in a range between 20 and 95, the Abbe numbers of the 
diffractive optical elements take a constant value of -3.453. In other 
words, whilst the ordinary optical glasses are positive in the Abbe 
number, the diffractive optical element is negative. Even in the partial 
dispersion ratio, it has a far different value from those of the ordinary 
glasses. By utilizing such characteristics of the diffractive optical 
element, the chromatic correction can be done effectively. 
The diffractive optical surface can be expressed by the following phase 
equation: 
EQU .phi.(h)=(2.pi./.lambda.).multidot.(C.sub.1 h.sup.2 +C.sub.2 h.sup.4 + . . 
. +C.sub.i h.sup.2.multidot.i) (1) 
where .phi.(h) is the phase of the diffractive optical element, h is the 
radial distance from the optical axis of the lens system, and .lambda. is 
the reference wavelength. That is, the diffractive optical surface is 
expressed as derived from the substrate surface of the lens by adding the 
phase. 
The aspheric surface used in the embodiment 1 is of revolution symmetry and 
expressed in the coordinates with h in the radial distance from the lens 
axis and Z(h) in the axial direction by the following equation: 
##EQU1## 
where r is the radius of the reference curvature, and k, B, C, D and E are 
the aspheric coefficients. 
FIGS. 2 to 5 show the form and the construction and arrangement of the 
constituent lenses of the embodiments 2 to 5 in the wide-angle end. Of 
these, the embodiments 2 to 4 shown in FIGS. 2 to 4 each employ two 
diffractive optical surfaces which are coincident with the rear lens 
surface of the lens L1 and the front lens surface of the lens L3. The lens 
surfaces for which to provide with aspheres are the same as in the 
embodiment 1. 
The embodiment 5 shown in FIG. 5 has the rear lens surface of the lens L1 
in the form of a diffractive optical surface. The lens surfaces for which 
to provide with aspheres are the same as in the embodiments 1 to 4. 
Next, five numerical examples 1 to 5 corresponding to the embodiments 1 to 
5 are shown. In the numerical data for these examples, ri is the radius of 
curvature of the i-th lens surface, when counted from the object side, di 
is the i-th axial lens thickness or air separation, and ni and .nu.i are 
respectively the refractive index and Abbe number of the material of the 
i-th lens element. 
For the aspheric surfaces, the values of the coefficients in the equation 
(2) are tabulated. To define the diffractive optical surface, the phase 
coefficients in the equation (1) are evaluated. The first order of 
diffraction is used as the design order. The design wavelength is 587.6 nm 
(spectral d-line). 
______________________________________ 
Numerical Example 1: 
f = 3.75095.about.10.99 
Fno = 1:2.85.about.5.66 
2.omega. = 66.3.degree..about.25.2.degree. 
r1 = 21.087 
d1 = 0.81 n1 = 1.77250 
.nu. 1 = 49.6 
r2 = 2.828 d2 = 1.76 
r3 = 5.459 d3 = 1.81 n2 = 1.80518 
.nu. 2 = 25.4 
r4 = 9.662 d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 4.225 d6 = 2.88 n3 = 1.67790 
.nu. 3 = 55.3 
r7 = -8.330 
d7 = 0.12 
r8 = -8.807 
d8 = 2.20 n4 = 1.80518 
.nu. 4 = 25.4 
r9 = 34.023 
d9 = Variable 
r10 = .infin. 
d10 = 3.10 n5 = 1.51633 
.nu. 5 = 64.2 
r11 = .infin. 
d11 = 1.22 
r12 = .infin. 
Focal Length 
3.75 3.88 10.99 
d4 5.87 5.28 1.00 
d5 4.40 4.58 1.00 
d9 3.82 3.95 10.98 
Aspheric Coefficients: 
r2 q: 
r = 2.82839 .multidot. 10.sup.0 
k = -1.59475 .multidot. 10.sup.-1 
B = -2.14175 .multidot. 10.sup.-3 
C = -2.76791 .multidot. 10.sup.-4 
D = 1.51140 .multidot. 10.sup.-5 
E = -5.24174 .multidot. 10.sup.-6 
r6 bq: 
r = 4.22466 .multidot. 10.sup.0 
k = -2.42500 .multidot. 10.sup.-1 
B = -2.73790 .multidot. 10.sup.-5 
C = 3.88250 .multidot. 10.sup.-5 
D = -2.91830 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.0 
r9 q: 
r = 3.40225 .multidot. 10.sup.-1 
k = 8.17051 .multidot. 10.sup.0 
B = 4.16531 .multidot. 10.sup.-3 
C = 4.46491 .multidot. 10.sup.-4 
D = -2.84128 .multidot. 10.sup.-5 
E = 9.74972 .multidot. 10.sup.-6 
Phase Coefficients: 
r6: C.sub.1 = -1.32450 .multidot. 10.sup.-3 
C.sub.2 = -5.48090 .multidot. 10.sup.-5 
C.sub.3 = 4.38270 .multidot. 10.sup.-5 
C.sub.4 = -5.69600 .multidot. 10.sup.-6 
C.sub.5 = 2.99310 .multidot. 10.sup.-7 
______________________________________ 
______________________________________ 
Numerical Example 2: 
f = 3.75096.about.10.99 
Fno = 1:2.85.about.5.65 
2.omega. = 66.3.degree..about.25.2.degree. 
r1 = 21.132 
d1 = 0.81 n1 = 1.77250 
.nu. 1 = 49.6 
r2 = 2.811 d2 = 1.71 
r3 = 5.419 d3 = 1.80 n2 = 1.80518 
.nu. 2 = 25.4 
r4 = 9.713 d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 4.227 d6 = 2.93 n3 = 1.67790 
.nu. 3 = 55.3 
r7 = -8.320 
d7 = 0.11 
r8 = -8.686 
d8 = 2.19 n4 = 1.80518 
.nu. 4 = 25.4 
r9 = 37.319 
d9 = Variable 
r10 = .infin. 
d10 = 3.10 n5 = 1.51633 
.nu. 5 = 64.2 
r11 = .infin. 
d11 = 1.23 
r12 = .infin. 
Focal Length 
3.75 3.97 10.99 
d4 5.83 5.11 1.00 
d5 4.49 4.52 1.00 
d9 3.79 4.00 10.91 
Aspheric Coefficients: 
r2:bq 
r = 2.81147 .multidot. 10.sup.0 
k = -6.47770 .multidot. 10.sup.-3 
B = -4.18270 .multidot. 10.sup.-3 
C = 2.67460 .multidot. 10.sup.-4 
D = -1.28850 .multidot. 10.sup.-4 
E = 0.00000 .multidot. 10.sup.0 
r6:bq 
r = 4.22466 .multidot. 10.sup.0 
k = -2.37130 .multidot. 10.sup.-1 
B = -3.12470 .multidot. 10.sup.-5 
C = 3.99250 .multidot. 10.sup.-5 
D = -2.57630 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.0 
r9:q r = 3.73194 .multidot. 10.sup.+1 
k = -1.51757 .multidot. 10.sup.+1 
B = 4.14203 .multidot. 10.sup.-3 
C = 4.80770 .multidot. 10.sup.-4 
D = -4.04006 .multidot. 10.sup.-5 
E = 1.12205 .multidot. 10.sup.-5 
Phase Coefficients: 
r2: C.sub.1 = -5.45840 .multidot. 10.sup.-4 
C.sub.2 = 9.41210 .multidot. 10.sup.-4 
C.sub.3 = 
C.sub.4 = 1.40270 .multidot. 10.sup.-4 
C.sub.5 = -1.09070 .multidot. 10.sup.-5 
-5.90030 .multidot. 10.sup.-4 
r6: C.sub.1 = -1.32220 .multidot. 10.sup.-3 
C.sub.2 = -5.11230 .multidot. 10.sup.-5 
C.sub.3 = 
C.sub.4 = -4.99700 .multidot. 10.sup.-6 
C.sub.5 = 2.64420 .multidot. 10.sup.-7 
4.00700 .multidot. 10.sup.-5 
______________________________________ 
______________________________________ 
Numerical Example 3: 
f = 3.75087.about.10.99 
Fno = 1:2.85.about.5.65 
2.omega. = 66.3.degree..about.25.1.degree. 
r1 = 25.926 
d1 = 0.81 n1 = 1.80100 
.nu. 1 = 35.0 
r2 = 2.711 d2 = 1.29 
r3 = 5.176 d3 = 1.91 n2 = 1.84666 
.nu. 2 = 23.8 
r4 = 11.618 
d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 3.679 d6 = 2.34 n3 = 1.72000 
.nu. 3 = 50.3 
r7 = -11.286 
d7 = 0.10 
r8 = -30.000 
d8 = 1.44 n4 = 1.84666 
.nu. 4 = 23.8 
r9 = 6.991 d9 = Variable 
r10 = .infin. 
d10 = 3.10 n5 = 1.51633 
.nu. 5 = 64.2 
r11 = .infin. 
d11 = 0.13 
r12 = .infin. 
Focal Length 
3.75 5.49 10.99 
d4 7.64 4.78 1.00 
d5 1.77 1.07 1.00 
d9 4.46 6.03 11.07 
Aspheric Coefficients: 
r2:bq 
r = 2.71055 .multidot. 10.sup.0 
k = -4.93830 .multidot. 10.sup.-1 
B = -6.60180 .multidot. 10.sup.-4 
C = -1.07380 .multidot. 10.sup.-4 
D = -2.89890 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.-0 
r6:bq 
r = 3.67860 .multidot. 10.sup.0 
k = -3.40360 .multidot. 10.sup.-2 
B = -2.42480 .multidot. 10.sup.-4 
C = -1.56120 .multidot. 10.sup.-4 
D = 6.57520 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.0 
r9:q r = 6.99105 .multidot. 10.sup.0 
k = -7.30229 .multidot. 10.sup.0 
B = 1.06598 .multidot. 10.sup.-2 
C = 8.81474 .multidot. 10.sup.-4 
D = 9.58382 .multidot. 10.sup.-6 
E = 3.62469 .multidot. 10.sup.-5 
Phase Coefficients: 
r2: C.sub.1 = 1.48350 .multidot. 10.sup.-3 
C.sub.2 = -2.10080 .multidot. 10.sup.-5 
C.sub.3 = 
C.sub.4 = -1.37710 .multidot. 10.sup.-5 
C.sub.5 = 3.44510 .multidot. 10.sup.-7 
1.07140 .multidot. 10.sup.-4 
1.68270 .multidot. 10.sup.-3 
C.sub.2 = 2.14430 .multidot. 10.sup.-4 
C.sub.3 = 
C.sub.4 = 2.64920 .multidot. 10.sup.-5 
C.sub.5 = -1.66460 .multidot. 10.sup.-6 
-1.28080 .multidot. 10.sup.-4 
______________________________________ 
______________________________________ 
Numerical Example 4: 
f = 3.75085.about.10.99 
Fno = 1:2.85.about.5.66.degree. 
2.omega. = 66.3.degree..about.25.18.degree. 
r1 = 29.871 
d1 = 0.90 n1 = 1.78590 
.nu. 1 = 44.2 
r2 = 3.216 d2 = 1.90 
r3 = 6.466 d3 = 1.86 n2 = 1.76182 
.nu. 2 = 26.5 
r4 = 14.947 
d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 4.385 d6 = 2.91 n3 = 1.71300 
.nu. 3 = 53.8 
r7 = -15.726 
d7 = 0.12 
r8 = -16.991 
d8 = 2.11 n4 = 1.84666 
.nu. 4 = 23.8 
r9 = 14.858 
d9 = Variable 
r10 = .infin. 
d10 = 3.10 n5 = 1.51633 
.nu. 5 = 64.2 
r11 = .infin. 
d11 = 3.02 
r12 = .infin. 
Focal Length 
3.75 5.75 10.99 
d4 7.83 3.12 1.00 
d5 5.31 4.49 1.65 
d9 2.24 4.09 9.00 
Aspheric Coefficients: 
r2:bq 
r = 3.21613 .multidot. 10.sup.0 
k = -1.06050 .multidot. 10.sup.0 
B = 1.29110 .multidot. 10.sup.-3 
C = 1.30560 .multidot. 10.sup.-4 
D = -1.16840 .multidot. 10.sup.-5 
E = 0.00000 .multidot. 10.sup.0 
r6:bq 
r = 4.38486 .multidot. 10.sup.0 
k = -5.12940 .multidot. 10.sup.-4 
B = 1.42920 .multidot. 10.sup.-4 
C = 1.68860 .multidot. 10.sup.-5 
D = -2.06550 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.0 
r9:q r = 1.48584 .multidot. 10.sup.+1 
k = -7.30229 .multidot. 10.sup.0 
B = 4.75557 .multidot. 10.sup.-3 
C = -2.28683 .multidot. 10.sup.-5 
D = -2.28683 .multidot. 10.sup.-5 
E = 1.31093 .multidot. 10.sup.-5 
Phase Coefficients: 
r2: C.sub.1 = 5.38670 .multidot. 10.sup.-4 
C.sub.2 = 3.02180 .multidot. 10.sup.-4 
C.sub.3 = 
C.sub.4 = 7.76268 .multidot. 10.sup.-6 
C.sub.5 = 2.86200 .multidot. 10.sup.-8 
-7.74490 .multidot. 10.sup.-5 
r6: C.sub.1 = -1.23700 .multidot. 10.sup.-3 
C.sub.2 = -3.27010 .multidot. 10.sup.-5 
C.sub.3 = 
C.sub.4 = -3.84740 .multidot. 10.sup.-6 
C.sub.5 = 1.78230 .multidot. 10.sup.-7 
3.18390 .multidot. 10.sup.-5 
______________________________________ 
______________________________________ 
Numeral Example 5: 
f = 3.75096.about.10.95 
Fno = 1:2.85.about.5.67 
2.omega. = 66.3.degree..about.25.29.degree. 
r1 = 67.347 
d1 = 0.81 n1 = 1.76200 
.nu. 1 = 40.1 
r2 = 3.564 d2 = 1.86 
r3 = 7.114 d3 = 1.46 n2 = 1.84666 
.nu. 2 = 23.8 
r4 = 16.975 
d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 3.947 d6 = 2.67 n3 = 1.73400 
.nu. 3 = 51.5 
r7 = -6.098 
d7 = 0.10 
r8 = -7.045 
d8 = 2.60 n4 = 1.84666 
.nu. 4 = 23.8 
r9 = 11.231 
d9 = Variable 
r10 = .infin. 
d10 = 3.10 n5 = 1.51633 
.nu. 5 = 64.2 
r11 = .infin. 
d11 = Variable 
r12 = .infin. 
Focal Length 
3.75 6.45 10.95 
d4 7.85 3.94 0.16 
d5 2.69 0.07 0.10 
d9 1.29 3.13 6.23 
d11 1.88 1.88 1.88 
Aspheric Coefficients: 
r2:bq 
r = 3.56368 .multidot. 10.sup.0 
k = -1.09130 .multidot. 10.sup.0 
B = 1.00420 .multidot. 10.sup.-3 
C = 3.20070 .multidot. 10.sup.-5 
D = -1.48110 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.0 
r6:q r = 3.94652 .multidot. 10.sup.0 
k = -1.85220 .multidot. 10.sup.-1 
B = -6.48580 .multidot. 10.sup.-4 
C = -1.74870 .multidot. 10.sup.-5 
D = -1.25600 .multidot. 10.sup.-5 
E = 0.00000 .multidot. 10.sup.0 
r9:q r = 1.12315 .multidot. 10.sup.+1 
k = -7.30229 .multidot. 10.sup.0 
B = 7.57468 .multidot. 10.sup.-3 
C = 7.85907 .multidot. 10.sup.-4 
D = -4.38603 .multidot. 10.sup.-6 
E = 4.77683 .multidot. 10.sup.-6 
Phase Coefficients: 
r2: C.sub.1 = -1.64750 .multidot. 10.sup.-4 
C.sub.2 = 1.45960 .multidot. 10.sup.-4 
C.sub.3 = 1.83520 .multidot. 10.sup.-5 
C.sub.4 = 4.95320 .multidot. 10.sup.-6 
C.sub.5 = 3.38260 .multidot. 10.sup.-7 
______________________________________ 
FIGS. 6A to 6D through FIGS. 15A to 15D show the aberrations of the zoom 
lenses of the embodiments 1 to 5, respectively. From these graphs, it is 
understood that any of the embodiments has been corrected well for all 
aberrations. 
The diffractive optical elements are usually manufactured by a similar 
technique to that of manufacturing holographic optical elements, but may 
otherwise be produced in the form of "binary optics" by the 
photo-lithographic technique. Also, using these methods, a mold may be 
made, from which they are produced. Yet another method is to take casts 
from a thin layer of plastic material and then deposit them as the 
diffractive optical layer on the leas surfaces. That is, the so called 
"replica" technique may be used. 
The grating grooves of the diffractive optical element in the embodiments 
described above have the kinoform as shown in FIG. 16. Further, the 
diffractive optical element of the present embodiments have their pitches 
and depths falling in the ranges chat sufficiently allow for 
manufacturing. For example, in the embodiment 1, when the diffractive 
optical element is formed in a single layer, the minimum pitch is 103.3 
.mu.m, and the depth is 0.867 .mu.m. These values lie at the level of 
manufacturing the diffractive optical element satisfactorily. 
To produce this diffraction grating, the surface of a substrate 1 is coated 
with an ultra-violet ray setting resin layer. In this layer 2, a 
diffraction grating 3 is then formed to a thickness d so that the 
diffraction efficiency in the first order for the wavelength of 530 .mu.m 
is 100%. This diffractive optical element has wavelength dependent 
characteristics of the first order diffraction efficiency, as shown in 
FIG. 17. The diffraction efficiency in the design order becomes 
progressively lower as the wavelength goes away from the optimized value 
of 530 .mu.m. Meanwhile, the diffracted rays of the next orders to the 
design one, or zero and second orders rise increasingly. This increase of 
the diffracted rays of the other orders than the design one causes 
production of flare and leads to lower the resolving power of the optical 
system. 
FIG. 18 shows the characteristics of Modulation Transfer Function (MTF) 
versus the spatial frequency of the grating form of FIG. 16 in the 
embodiment 1. It is understood that the MTF of the low frequency region is 
lower than the desired values. 
So, it is considered to form the grooves of the grating by using a 
laminated type shown in FIG. 19. On the substrate 1, a first diffraction 
grating 4 is made from an ultraviolet setting resin (Nd=1.499, .nu.d=54) 
and, as is stacked thereon, a second diffraction grating 5 is made from 
another ultraviolet setting resin (Nd=1.598, .nu.d=28). For this 
combination of the materials, the grating thickness dl of the first 
diffraction grating 4 is determined to be d1=13.8 .mu.m and the grating 
thickness d2 of the second diffraction grating 5 is determined to be 
d2=10.5 .mu.m. 
The diffractive optical element of this structure has a wavelength 
dependent characteristic of the diffraction efficiency in the first order, 
as shown in FIG. 20. As is apparent from FIG. 20, the making of the 
diffraction grating in the laminated structure increases the diffraction 
efficiency for the design order to higher than 95% over the entire useful 
range of wavelengths. FIG. 21 shows the spatial frequency response MTF 
characteristics for this case. By using the diffraction grating of the 
laminated structure, the resolving power in the low frequencies is 
improved. The desired MTF characteristic is thus obtained. It will be 
appreciated from the foregoing that the use of the diffraction grating of 
the laminated structure achieves further improvements of the optical 
performance. 
It should be noted that the diffraction grating of the laminated structure 
described above is not confined in material to the ultraviolet setting 
resin. Other materials such as plastics may be used instead. Although it 
depends on the kind of material to be used in the substrate, the first 
diffraction grating 4 may be formed directly in the substrate 1. 
Furthermore, there is no need to differentiate the thicknesses of the two 
grating layers from each other. In some combinations of materials, the 
thicknesses of the two layers may be made equal to each other as shown in 
FIG. 22. Since, in this case, no gratings are exposed out of the surface 
of the diffractive optical element, the dust proof is excellent, 
contributing to an increase of the productivity on the assembling line in 
manufacturing the diffractive optical elements. So, inexpensive optical 
systems can be obtained. 
Other embodiments are next described which are different from the 
embodiments 1 to 5 described above in that the rear lens unit is 
constructed with a plurality of lens units. 
FIG. 23 to FIG. 26 in lens block diagram show four embodiments 6 to 9, 
respectively, applied to zoom lenses for the video camera. In the 
embodiments 6 to 9, the optical system comprises, in order from the object 
side (the longer-distance conjugate point side), a first lens unit L1 of 
negative refractive power movable during zooming, a second lens unit L2 of 
positive refractive power movable for zooming as the variator, a third 
lens unit L3 of positive refractive power, and an optical filter or face 
plate F. In the embodiments 6 to 9, the first lens unit L1 corresponds to 
the front lens unit, and the second and third lens units L2 and L3 
correspond to the rear lens unit. The overall refractive power of the 
second and third lens units L2 and L3 is positive. In the embodiments 6 to 
9, during zooming from the wide-angle end to the telephoto end, the second 
lens unit L2 axially moves toward the object side, while simultaneously 
moving the first lens unit L1 to compensate for the shift of an image 
plane. The first lens unit L1, or the second lens unit L2, or the third 
lens unit L3, that is, at least one of these lens units, has at least one 
diffractive optical surface of revolution symmetry with respect to an 
optical axis. 
In particular, the third lens unit L3 is either stationary or movable 
during zooming. Focusing is possible also by using this third lens unit 
L3. Further, a stop S is positioned in the space between the first lens 
unit L1 and the second lens unit L2. It is preferred that the stop S is 
arranged particularly in the neighborhood of the second lens unit L2. 
In the embodiments 6 to 9, at least one of the three lens units is provided 
with a diffractive optical element to correct chromatic aberrations well. 
Suppose, for example, the first lens unit L1 is selected to use the 
diffractive optical element therein, and assuming that the diffractive 
optical element has an appropriate phase, then the lateral chromatic 
aberrations for two wavelengths, for example, d-line and g-line, produced 
in the first lens unit L1 are suppressed to a minimum for good stability 
of lateral chromatic aberration over the entire zooming range. Moreover, 
the width of longitudinal chromatic aberration (secondary spectrum) itself 
does not worsen in the telephoto end. 
Alternatively, suppose, for example, the second lens unit L2 is selected to 
use the diffractive optical element therein, and assuming that the 
diffractive optical element has an appropriate phase, then the lateral 
chromatic aberrations for two wavelengths, for example, d-line and g-line, 
produced in the second lens unit L2 are suppressed to a minimum for good 
stability of lateral chromatic aberration over the entire zooming range. 
Moreover, the width of longitudinal chromatic aberration (secondary 
spectrum) itself does not worsen in the telephoto end. 
According to the prior art, to achromatize the zoom lens, it is the common 
practice that the front or first lens unit L1 is constructed with one or 
two negative lens or lenses of high dispersion and one or two positive 
lens or lenses of low dispersion. In more elaborate cases, the negative 
and positive lenses are cemented together, or the achromatism is shared by 
a plurality of lenses. Unlike this, the present invention is to employ the 
diffractive optical element in the first lens unit. By this, the number of 
lens elements necessary to correct the chromatic aberrations is reduced. 
Thus, it is made possible to reduce the total number of constituent 
lenses. Also, according to the prior art, the rear or second lens unit L2, 
too, is constructed with a negative lens of low dispersion and a positive 
lens of high dispersion each being one or two in number. The negative and 
positive lenses have to be cemented together, or a plurality of lenses 
have to be used for sharing the achromatism. However, even in the second 
lens unit L2 as well, a diffractive optical element may be used to reduce 
the number of lens elements necessary to correct chromatic corrections. 
Thus, it becomes possible to reduce the total number of constituent 
lenses. 
This leads to provide a possibility that, even in a zoom lens that is to 
achieve higher level of correction of chromatic aberrations, the compact 
form is further improved, while still maintaining the high optical 
performance. 
Even in the embodiments 6 to 9, the phase of the diffractive optical 
surface is expressed by using the equation (1). 
From the equation (1), it is understandable that the phase can be adjusted 
in accordance with variation of the distance h from the optical axis. That 
is, the larger the lens diameter, the greater the influence of the 
coefficients in higher degrees. In the field of art of zoom lenses for 
home use, particularly the ones for video cameras, to which the 
embodiments 6 to 9 are assumed to be applied, efforts are being devoted to 
advance the compactness. The lens of too much large diameter, in other 
words, the lens that takes a very large value in the distance h, does not 
meet the trend of the art. On this account, the diameter has to decrease. 
Even in this case, if the phase coefficients are determined to be 
appropriate, advantageous correction of aberrations can be achieved. To 
this purpose, it is preferred that the diffractive optical surface 
satisfies the following conditions: 
EQU 1.multidot.10.sup.-4 &lt;.vertline.C.sub.2 /C.sub.1 .vertline.&lt;1(3) 
EQU 1.multidot.10.sup.-7 &lt;.vertline.C.sub.3 /C.sub.1 
.vertline.&lt;1.multidot.10.sup.-1 (4) 
These inequalities are, as described above, for assuring correction of 
aberrations to be done effectively at a small diameter. When these 
conditions are violated, it becomes difficult not only to correct 
aberrations but also to produce the diffractive optical surfaces. So, the 
violations are objectionable. 
Specifically speaking, the first lens unit L1 is constructed in the form 
of, for example, a positive lens and a negative lens, totally two lenses, 
or two negative lenses and one positive lens, totaling three lenses, with 
the diffractive optical surface in any one of these lenses. Such positive 
and negative lenses may be cemented together. If so, this cemented surface 
must be brought into cooperation with the diffractive optical surface in 
correcting the chromatic aberrations. With this arrangement, the 
diffractive optical element must be made stronger in the positive 
refractive power. 
The first lens unit L1 may otherwise be constructed with two negative 
lenses, before or after or between which a plate having at least one 
diffractive optical surface is arranged. 
Also, the second lens unit L2 is, constructed in a specific form of, for 
example, two positive lenses and one negative lens, totally three lenses, 
before or after which, or between adjacent two of which a plate having at 
least one diffractive optical surface lies. 
The second lens unit L2 may otherwise be constructed with two lenses of 
plus-minus or minus-plus power arrangement in total with a diffractive 
optical layer on any one of these lenses. 
In any case, the frontmost or exposed surface of the complete lens to the 
outside is not suited to be used as the diffractive optical surface, 
except for the particular situations such as that when the designer cannot 
but select this surface on aberration correction, because the diffractive 
optical surface is made of an array of annular grooves of very narrow 
widths of, for example, several microns, or on the submicron order. To 
protect this surface from dust or the like, it is, therefore, preferable 
not to make the arrangement on the frontmost lens surface. 
In the embodiments 6 to 8, the rear lens surface of the front lens in the 
first lens unit L1, the frontmost and rearmost lens surfaces in the second 
lens unit L2 are made aspherical. In the embodiment 9, the rear lens 
surface of the intermediate lens in the first lens unit L1 and the 
frontmost lens surface in the second lens unit L2 are made aspherical. 
The diffractive optical surface is used as well, for the embodiment 6, in 
coincidence with the frontmost lens surface of the second lens unit L2, 
for the embodiment 7, with the rear lens surface of the front lens of the 
first lens unit L1, for the embodiment 8, with the frontmost lens surface 
of the third lens unit L3, and, for the embodiment 9, with the frontmost 
lens surface of the second lens unit L2. 
In such a manner, the diffractive optical surface is arranged inside the 
lens system. As it lies in the first lens unit L1, or the second lens unit 
L2, or the third lens unit L3, the diffractive optical surface suppresses 
the chromatic aberrations (secondary spectrum) produced in that lens unit 
which contains it in cooperation with the other lens units. A good 
stability of chromatic correction is thus maintained against zooming of 
the second lens unit L2. If the refracting power of this diffractive 
optical surface is strengthened, the difference in saw tooth-shaped pitch 
between the paraxial and marginal zones increases largely, causing the 
production technique to become difficult. The diffraction efficiency of 
finished products also is not good. Therefore, for a case where the 
cemented contact or like achromatic means in the first lens unit L1, or 
the second lens unit L2, or the third lens unit L3 is replaced by the 
diffractive optical surface when the chromatic aberrations are corrected, 
this surface needs not to have so much refracting power. 
Nonetheless, in view of correcting some of the off-axial aberrations, 
especially field curvature and distortion, that surface may be given a 
refracting power. For this purpose, letting the focal lengths of the 
diffractive optical surfaces in the first, second and third lens units L1, 
L2 and L3 be denoted by Fbo1, Fbo2 and Fbo3, respectively, and the focal 
lengths of the first, second and third lens units L1, L2 and L3 be denoted 
by F1, F2 and F3, respectively, the following conditions are set forth. So 
long as the relevant one of these conditions is satisfied, no difficult 
problems arise in manufacturing, and the aberrational problems including 
the chromatic one, too, are affected well. 
EQU 0.05&lt;F1/Fbo1&lt;3.0 (5) 
EQU 0.05&lt;F2/Fbo2&lt;2.0 (5') 
EQU 0.05&lt;F3/Fbo3&lt;1.0 (5") 
Further, in the case where the first lens unit L1 has the diffractive 
optical surface, it is preferred to satisfy an additional condition as 
follows: 
EQU -2.0&lt;F1/.sqroot.Fw.multidot.Ft&lt;6.0 (6) 
where Fw and Ft are the shortest and longest focal lengths of the entire 
lens system, respectively. 
If the focal length F1 lies in this range, the diffractive optical element 
can behave effectively. When the lower limit of the condition (6) is 
exceeded, as this means that the refractive power of the first lens unit 
L1 is too strong, any attempt to correct the chromatic aberrations by the 
diffractive optical element results in failure. The way to manufacture 
becomes also difficult. When the upper limit is exceeded, the diffractive 
optical element is no longer necessary to use, because the chromatic 
aberrations become so much easy to remove. Also, to obtain the complete 
lens of desired focal lengths, particularly, the second lens urit L2 
becomes stronger in refractive power. So, the produced amount of 
aberrations by the second lens unit L2 increases to a value larger than is 
appropriate. In other words, the Petzval sum increases in the negative 
sense, and over-correction of field curvature results. 
In general, the diffractive optical element produces chromatic aberrations 
in the reverse sense to that for the ordinary refraction. For Example, the 
cemented surface used in the conventional way to achromatize is removed 
since the cemented lens is replaced by a lens to reduce the total number 
of lens elements. For this case, it is preferred that the diffractive 
optical surface coincides with that surface which would be used to 
contribute the reverse chromatic aberrations to those the cemented surface 
contributes. With this arrangement, it results that the reverse chromatic 
aberrations to those the ordinary refraction produces are produced by the 
diffractive optical surface and that their directions coincide with those 
when the cemented surface would otherwise be used. Thus, it is made 
possible for the single lens to do the same achromatism as the cemented 
lens does. 
From the point of view of what are so-called the "chromatic aberration 
coefficients" ("Lens Design Method" by Yoshiya Matsui at p. 98 issued from 
Kyoritsu Shuppan (Publishing Co. Ltd.)), it is preferred that, as the 
diffractive optical surface takes its place on the object side of the 
stop, the surface that contributes the longitudinal chromatic aberration 
coefficient L and the lateral chromatic aberration coefficient T, both of 
which have the same sign, is selected to use. On the image side of the 
stop, the surface of both contributions of opposite sign to each other is 
selected to use for the diffractive optical surface. 
Although not revealed in the embodiments 6 to 9, it is also possible that 
the first lens unit L1 or the second lens unit L2 is constructed with only 
one lens element by using the diffractive optical element. 
Next, four numerical examples 6 to 9 corresponding to the embodiments 6 to 
9 are shown. In the numerical data for the examples 6 to 9, ri is the 
radius of curvature of the i-th lens surface, when counted from the object 
side, di is the i-th axial lens thickness or air separation, and ni and 
.nu.i are respectively the refractive index and Abbe number of the 
material of the i-th lens element. 
The equation for the aspheric surface in the embodiments 6 to 9 is the same 
as the equation (2) described in connection with the embodiments 1 to 5, 
and is not mentioned here again. 
______________________________________ 
Numerical Example 6: 
f = 3.74977 Fno = 1:2.85 2.omega. = 63.0 
r1 = 18.838 
d1 = 1.00 n1 = 1.77250 
.nu. 1 = 49.6 
r2 = 2.842 d2 = 1.45 
r3 = 5.109 d3 = 1.70 n2 = 1.80518 
.nu. 2 = 25.4 
r4 = 10.190 
d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 4.339* 
d6 = 3.25 n3 = 1.67790 
.nu. 3 = 55.3 
r7 = -8.490 
d7 = 0.13 
r8 = -8.701 
d8 = 2.00 n4 = 1.80518 
.nu. 4 = 25.4 
r9 = 26.030 
d9 = Variable 
r10 = 31.840 
d10 = 1.10 n5 = 1.51633 
.nu. 5 = 64.1 
r11 = -24.514 
d11 = 1.00 
r12 = .infin. 
d12 = 3.10 n6 = 1.51633 
.nu. 6 = 64.2 
r13 = .infin. 
d13 = -32.57 
r14 = .infin. 
*) Diffractive Optical Surface 
Focal Length 
3.75 7.38 11.00 
d4 5.94 1.36 1.04 
d5 4.78 2.89 1.00 
d9 2.00 5.89 9.77 
Aspheric Coefficients: 
r2: r = 2.84235 .multidot. 10.sup.0 
k = -3.28517 .multidot. 10.sup.-1 
B = -2.63180 .multidot. 10.sup.-4 
C = 2.63180 .multidot. 10.sup.-4 
D = 3.67708 .multidot. 10.sup.-5 
E = -4.60653 .multidot. 10.sup.-6 
r6: r = 4.33890 .multidot. 10.sup.0 
k = -2.13355 .multidot. 10.sup.-1 
B = -8.90957 .multidot. 10.sup.-5 
C = 4.05938 .multidot. 10.sup.-5 
D = -2.74445 .multidot. 10.sup.-5 
E = 0.00000 .multidot. 10.sup.0 
r9: r = 2.60299 .multidot. 10.sup.1 
k = -2.32563 .multidot. 10.sup.1 
B = 4.09405 .multidot. 10.sup.-3 
C = 4.25310 .multidot. 10.sup.-4 
D = -3.66683 .multidot. 10.sup.-5 
E = 9.71881 .multidot. 10.sup.-6 
Phase Coefficients: 
r6: C.sub.1 = -1.38576 .multidot. 10.sup.-3 
C.sub.2 = -5.51769 .multidot. 10.sup.-5 
C.sub.3 = 4.66871 .multidot. 10.sup.-5 
C.sub.4 = -6.04382 .multidot. 10.sup.-6 
C.sub.5 = 2.92159 .multidot. 10.sup.-7 
______________________________________ 
______________________________________ 
Numerical Example 7: 
f = 3.74786 Fno = 1:2.85 2.omega. = 63.0 
r1 = 16.518 
d1 = 1.00 n1 = 1.77250 
.nu. 1 = 49.6 
r2 = 2.812* 
d2 = 1.52 
r3 = 5.072 d3 = 1.70 n2 = 1.80518 
.nu. 2 = 25.4 
r4 = 9.180 d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 4.374 d6 = 3.25 n3 = 1.67790 
.nu. 3 = 55.3 
r7 = -8.279 
d7 = 0.13 
r8 = -8.827 
d8 = 2.00 n4 = 1.80518 
.nu. 4 = 25.4 
r9 = 20.374 
d9 = Variable 
r10 = 18.507 
d10 = 1.10 n5 = 1.51633 
.nu. 5 = 64.1 
r11 = 1586.291 
d11 = 1.00 
r12 = .infin. 
d12 = 3.10 n6 = 1.51633 
.nu. 6 = 64.2 
r13 = .infin. 
*) Diffractive Optical Surface 
Focal Length 
3.75 7.37 11.00 
d4 7.64 2.55 2.10 
d5 4.88 2.94 1.00 
d9 2.43 6.37 10.32 
Aspheric Coefficients: 
r2: r = 2.81245 .multidot. 10.sup.0 
k = -2.82491 .multidot. 10.sup.-1 
B = -2.09075 .multidot. 10.sup.-3 
C = -2.58187 .multidot. 10.sup.-4 
D = 3.72765 .multidot. 10.sup.-5 
E = -4.99400 .multidot. 10.sup.-6 
r6: r = 4.37416 .multidot. 10.sup.0 
k = -2.03479 .multidot. 10.sup.-1 
B = -2.16103 .multidot. 10.sup.-4 
C = 2.32139 .multidot. 10.sup.-5 
D = -2.69331 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.0 
r9: r = 2.03739 .multidot. 10.sup.1 
k = -3.45356 .multidot. 10.sup.1 
B = 3.96398 .multidot. 10.sup.-3 
C = 4.44621 .multidot. 10.sup.-4 
D = -4.41524 .multidot. 10.sup.-5 
E = 8.49502 .multidot. 10.sup.-6 
Phase Coefficients: 
r2: C.sub.1 = -2.73173 .multidot. 10.sup.-3 
C.sub.2 = 4.79617 .multidot. 10.sup.-4 
C.sub.3 = 
C.sub.4 = 5.39271 .multidot. 10.sup.-7 
-3.11298 .multidot. 10.sup.-5 
______________________________________ 
______________________________________ 
Numerical Example 8: 
f = 3.75009 Fno = 1:2.8 2.omega. = 62.9.degree. 
______________________________________ 
r1 = 19.911 
d1 = 1.00 n1 = 1.77250 
.nu.1 = 49.6 
r2 = 2.924 d2 = 1.50 
r3 = 5.199 d3 = 1.70 n2 = 1.80518 
.nu.2 = 25.4 
r4 = 9.470 d4 = Variable 
r5 = .infin. (Stop) 
d5 = Variable 
r6 = 4.177 d6 = 3.25 n3 = 1.67790 
.nu.3 = 55.3 
r7 = -7.319 
d7 = 0.13 
r8 = -8.095 
d8 = 2.00 n4 = 1.84666 
.nu.4 = 23.8 
r9 = 23.672 
d9 = Variable 
r10 = -23.522* 
d10 = 1.10 n5 = 1.51633 
.nu.5 = 64.1 
r11 = -10.465 
d11 = 1.00 
r12 = .infin. 
d12 = 3.10 n6 = 1.51633 
.nu.6 = 64.2 
r13 = .infin. 
______________________________________ 
*) Diffractive Optical Surface 
Focal Length 
3.75 7.38 11.00 
______________________________________ 
d4 6.71 1.98 1.52 
d5 4.50 2.75 1.00 
d9 2.20 5.96 9.71 
______________________________________ 
Aspheric Coefficients: 
r2: r = 2.92356 .multidot. 10.sup.0 
k = -2.13294 .multidot. 10.sup.-1 
B = -1.66532 .multidot. 10.sup.-3 
C = -2.65729 .multidot. 10.sup.-4 
D = 2.78451 .multidot. 10.sup.-5 
E = -4.22498 .multidot. 10.sup.-6 
r6: r = 4.17748 .multidot. 10.sup.0 
k = -3.38936 .multidot. 10.sup.-1 
B = -1.38841 .multidot. 10.sup.-4 
C = 3.51215 .multidot. 10.sup.-5 
D = -4.26335 .multidot. 10.sup.-6 
E = 0.00000 .multidot. 10.sup.0 
r9: r = 2.36717 .multidot. 10.sup.1 
k = -3.79872 .multidot. 10.sup.1 
B = 4.11618 .multidot. 10.sup.-3 
C = 4.71814 .multidot. 10.sup.-4 
D = -2.22596 .multidot. 10.sup.-5 
E = 7.02493 .multidot. 10.sup.-6 
Phase Coefficients: 
r10: C.sub.1 = -4.96638 .multidot. 10.sup.-4 
C.sub.2 = 4.28021 .multidot. 10.sup.-4 
C.sub.3 = -2.67732 .multidot. 10.sup.-5 
C.sub.4 = -1.43091 .multidot. 10.sup.-6 
______________________________________ 
______________________________________ 
Numerical Example 9: 
f = 6.00006 Fno = 1:2.84 2.omega. = 54.9.degree. 
______________________________________ 
r1 = 13.483 
d1 = 1.20 n1 = 1.69680 
.nu.1 = 55.5 
r2 = 6.036 d2 = 2.00 
r3 = 36.212 
d3 = 1.20 n2 = 1.69350 
.nu.2 = 53.2 
r4 = 7.600 d4 = 1.72 
r5 = 9.515 d5 = 1.30 n3 = 1.80518 
.nu.3 = 25.4 
r6 = 20.705 
d6 = Variable 
r7 = .infin. (Stop) 
d7 = 1.50 
r8 = 6.489* 
d8 = 2.30 n4 = 1.58313 
.nu.4 = 59.4 
r9 = -2149.780 
d9 = 1.32 
r10 = 24.069 
d10 = 1.00 n5 = 1.69895 
.nu.5 = 30.1 
r11 = 5.466 
d11 = 0.32 
r12 = 11.081 
d12 = 1.40 n6 = 1.77250 
.nu.6 = 49.6 
r13 = -116.517 
d13 = Variable 
r14 = 55.036 
d14 = 1.50 n7 = 1.51633 
.nu.7 = 64.1 
r15 = -28.037 
d15 = 1.00 
r16 = .infin. 
d16 = 4.13 n8 = 1.51633 
.nu.8 = 64.2 
r17 = .infin. 
______________________________________ 
*) Diffractive Optical Surface 
Focal Length 
6.00 13.92 18.00 
______________________________________ 
d6 16.35 3.97 1.85 
d15 5.99 15.89 20.99 
______________________________________ 
Aspheric Coefficients: 
r4: r = 7.60014 .multidot. 10.sup.0 
k = -5.05839 .multidot. 10.sup.-1 
B = -9.16037 .multidot. 10.sup.-5 
C = -4.12196 .multidot. 10.sup.-6 
D = 0.00000 .multidot. 10.sup.0 
E = 0.00000 .multidot. 10.sup.0 
r8: r = 6.48883 .multidot. 10.sup.0 
k = -7.13274 .multidot. 10.sup.-1 
B = 1.19802 .multidot. 10.sup.-4 
C = -2.22194 .multidot. 10.sup.-6 
D = -5.49430 .multidot. 10.sup.-7 
E = 2.44790 .multidot. 10.sup.-8 
Phase Coefficients: 
r8: C.sub.1 = -1.26069 .multidot. 10.sup.-3 
C.sub.2 = 4.67730 .multidot. 10.sup.-5 
C.sub.3 = -3.98604 .multidot. 10.sup.-6 
C.sub.4 = 1.11279 .multidot. 10.sup.-5 
______________________________________ 
FIGS. 27A to 27D through FIGS. 38A to 38D show the aberrations of the 
embodiments 6 to 9, respectively, in the wide-angle end, a middle focal 
length position and the telephoto end. 
In the embodiments 6 to 9, the diffractive optical elements are 
manufactured in the same way as in the embodiments 1 to 5. 
FIG. 39 shows the characteristics of Modulation Transfer Function (MTF) 
versus spatial frequency of the numerical example 6 using the grating form 
of FIG. 16. It is appreciated that the MTF in the low frequency region has 
a lower value than desired. 
FIG. 40 shows the spatial frequency response MTF characteristics of the 
numerical example 6 using the laminated grating of FIG. 19. By altering 
the structure of construction of the diffraction grating to the laminated 
one, the MTF in the low frequency region is improved. The desired MTF 
characteristic is thus obtained. 
Next, a system which uses the zoom lens of the retrofocus type having the 
diffractive optical element as the projection lens for a projector is 
described below. 
FIG. 41 to FIG. 43 in lens block diagram show embodiments 10 to 12 of zoom 
lenses used in the liquid crystal video projector with the main parts of 
the projector in schematic form. 
FIGS. 44A to 44D through FIGS. 46A to 46D show the aberrations of the 
embodiment 10 in the wide-angle end, a middle focal length position and 
the telephoto end, respectively. FIGS. 47A to 47D through FIGS. 49A to 49D 
show the aberrations of the embodiment 11 in the wide-angle end, a middle 
focal length position and the telephoto end, respectively. FIGS. 50A to 
50D through FIGS. 52A to 52D show the aberrations of the embodiment 12 in 
the wide-angle end, a middle focal length position and the telephoto end, 
respectively. In these aberration curves, B and G are the wavelengths of 
light of 470 nm and 530 nm, respectively, and .DELTA.M and .DELTA.S 
represent the meridional and sagittal image focuses, respectively. 
In FIGS. 41 to 43, the zoom lens PL comprises, from front to rear, a first 
lens unit of negative refractive power, a second lens unit L2 of positive 
refractive power and a third lens unit L3 whose positive refractive power 
is weak. At least one of these lens units is provided with at least one 
diffractive optical element of revolution symmetry with respect to an 
optical axis. In the embodiments 10 to 12, the first lens unit L1 
corresponds to the front lens unit and the second and third lens units L2 
and L3 correspond to the rear lens unit. 
A screen S (the plane of projection) and a liquid crystal display panel LCD 
or like original picture (the plane to be projected) lie in conjugate 
relation. In the general case, the screen S is put at a conjugate point of 
long distance (first conjugate point) and the original picture LCD takes 
its place at a short conjugate point (second conjugate point). A color 
combining prism, a polarizing filter, color filters and others are shown 
by a glass block GB. A stop, although not shown, is positioned on the 
first conjugate point side of the second lens unit L2. 
The zoom lens PL is housed in an outer barrel which is releasably attached 
to a body PB of the liquid crystal video projector by a coupling members 
C. The glass block GB and those parts that follow including the liquid 
crystal display panel LCD are held in the projector body PB. 
In the embodiments 10 to 12, during zooming from the wide-angle end to the 
telephoto end, the first lens unit L1 and the second lens unit L2 axially 
move toward the first conjugate point (the screen side), as indicated by 
the arrows in FIGS. 41 to 43. Focusing is performed by axially moving the 
first lens unit L1. 
In the embodiments 10 to 12, the back focal distance has to be made even 
longer. For this purpose, the first lens unit L1 is strengthened in 
negative refractive power so that the entire lens system takes the 
retrofocus form. If the first lens unit L1 has too much strong a negative 
refractive power, the Petzval sum will increases to the negative 
direction, causing the image surface to begin declining. Also, the zooming 
movement of the first lens unit L1 causes large variation of astigmatism 
and distortion, which becomes difficult to correct. For this reason, in 
the embodiments 10 to 12, the rear lens unit is constructed with the 
second and third lens units of positive refractive powers. Each of these 
lens units is made to contribute to a weaker refractive power, thus 
assuring reduction of the Petzval sum. 
In the embodiments 10 to 12, at least one of the three lens units is 
provided with the diffractive optical element to correct chromatic 
aberrations well. 
Suppose, for example, the first lens unit L1 is selected to use the 
diffractive optical element therein, and assuming that the phase of the 
diffractive optical element is determined to be appropriate, then the 
lateral chromatic aberrations for two wavelengths of light, for example, 
d-line and g-line, produced in the first lens unit L1 are suppressed to a 
minimum for good stability of lateral chromatic aberration over the entire 
zooming range. Moreover, residual of longitudinal chromatic aberration 
(secondary spectrum) is prevented from worsening in the telephoto end. 
According to the prior art, to, achromatize the zoom lens, it is the common 
practice that a front or first lens unit is constructed with one or two 
negative lens or lenses of high dispersion and one or two positive lens or 
lenses of low dispersion. In more elaborate cases, the negative and 
positive lenses are cemented together, or the achromatism is shared by a 
plurality of lenses. Unlike this, in the zoom lens of the embodiment 10, 
as described above, use is made of the diffractive optical element, 
producing an advantage of reducing the number of lens elements necessary 
to use in correcting chromatic aberrations. In such a manner, the total 
number of constituent lenses is reduced. 
Alternatively, suppose, for example, the second lens unit is selected to 
use the diffractive optical element therein, and assuming that the phase 
of the diffractive optical element is determined to be appropriate, then 
the lateral chromatic aberrations for two wavelengths of light, for 
example, d-line and g-line, produced in the second lens unit L2 are 
suppressed to a minimum for good stability of lateral chromatic aberration 
over the entire zooming range. Moreover, residual of longitudinal 
chromatic aberration (secondary spectrum) residual is prevented from 
worsening in the telephoto end. 
According to the prior art, a second lens unit, too, is constructed with a 
negative lens of low dispersion and a positive lens of high dispersion 
each being one or two in number. The negative and positive lenses have to 
be cemented together, or a plurality of lenses have to be used for sharing 
the achromatism. In the zoom lens of the embodiment 11, on the other hand, 
as described above, by using the diffractive optical element, the number 
of lens elements necessary to correct chromatic aberrations is lessened. 
The total number of constituent lenses is thus reduced. 
In the embodiments 10 and 11, this leads to achieve a zoom lens which is 
corrected for chromatic aberrations at a higher level. Even for such a 
zoom lens, further improvements of the compact form are attained while 
still maintaining the good optical performance. 
In the embodiment 12, the diffractive optical element is arranged in the 
third lens unit L3 to correct chromatic aberrations well throughout the 
entire zooming range. 
In the embodiments 10 to 12, as the surface on which to deposit the 
diffractive optical layer, the most outside surface is not used except in 
the particular situations such as that when the designer cannot but select 
this surface on aberration correction, because the diffractive optical 
surface is made of an array of annular grooves of very narrow widths of, 
for example, several microns, or on the submicron order. To protect the 
diffractive optical surface from dust or the like, it is, therefore, 
preferable not to arrange it on the outermost side. 
In the embodiments 10 to 12, as described above, the diffractive optical 
element is arranged in the interior of the first lens unit, or in the 
interior of the second lens unit or in the interior of the third lens unit 
to thereby suppress the lateral chromatic aberration the respective 
individual lens unit produces to a minimum. As the second lens unit moves 
to effect zooming, the range of variation of lateral chromatic aberration 
is also suppressed to a minimum. 
In the embodiments 10 to 12, when each lens unit is constructed as 
described above, good stability of the quality of the projected image on 
the screen S is maintained throughout the entire zooming range. 
The above-described characteristic features of the zoom lens PL suffice for 
projecting good images on the screen S. To attain further improved 
results, it is preferable to satisfy at least one of the following 
features or conditions. 
(a) From the equation (1) described before, it is understandable that the 
phase can be adjusted by the distance h from the optical axis. That is, 
the larger the lens diameter, the greater the influence of the 
coefficients in higher degrees. In the zoom lenses in the embodiments 10 
to 12 which are assumed to be of the telecentric type, the phase 
coefficients have to be effectively utilized in achieving advantageous 
correction of aberrations. For this purpose, it is preferred to satisfy 
the conditions (3) and (4) mentioned before. 
When the conditions (3) and (4) are violated, it becomes difficult not only 
to correct aberrations but also to manufacture the diffractive optical 
surfaces. So, the violations are objectionable. 
(b) If the refracting power of the diffractive optical element is 
strengthened, the difference in saw tooth-shaped pitch between the 
paraxial and marginal zones increases largely, causing the production 
technique to become difficult. The diffraction efficiency of finished 
products is also not good. 
For a case where, like the zoom lenses in the embodiments 10 to 12, instead 
of the cemented lens, the diffractive optical element is used in the first 
lens unit L1, or the second lens unit L2, or the third lens unit L3 to 
correct the chromatic aberrations, the refractive power of the diffractive 
optical element needs not to be necessarily much. 
Nonetheless, in order to correct some of the off-axial aberrations, 
especially field curvature and distortion, a refractive power may be given 
to diffractive optical surface. If so, letting the focal length of the 
diffractive optical surfaces in the i-th lens unit be denoted by Fboi, and 
the focal length of the i-th lens unit by Fi, the following condition is 
set forth. So long as this condition is satisfied, no difficult problems 
arise in manufacturing, and a good effect is produced to correct the 
aberrations including chromatic ones. 
EQU 0.05&lt;Fi/Fboi&lt;3.0 (7) 
(c) Distortion is sufficiently suppressed in the first lens unit, and a 
sufficient back focal distance must be secured. For this purpose, it is 
desired to satisfy the following condition: 
EQU 0.6&lt;.vertline.F1/.sqroot.Fw.multidot.Ft.vertline.&lt;0.95 (8) 
where Fw and Ft are the shortest and longest focal lengths of the entire 
lens system, respectively. 
This condition has an aim to make a good compromise between the correction 
of distortion and the elongation of the back focal distance. When the 
upper limit of the condition (8) is exceeded, the zooming movement 
increases, the total length of the entire lens system increases, and the 
back focal distance becomes short. So, the violation is objectionable. 
Conversely when the lower limit is exceeded, the zooming movement 
decreases, but it becomes difficult to correct distortion. At the same 
time, the Petzval sum increases to the negative direction, causing the 
image surface to decline. So, this violation is objectionable. 
(d) In general, the diffractive optical element produces chromatic 
aberrations in the reverse sense to that for the ordinary refraction. Now 
assuming that, for example, the cemented surface used in the conventional 
way to achromatize is removed as the cemented lens is replaced by a single 
lens to reduce the total number of lens elements, then it is preferable to 
select that surface which would be used to contribute the reverse 
chromatic aberrations to those the cemented surface contributed, in 
applying the diffractive optical surface. With this arrangement, it 
results that the reverse chromatic aberrations to those the ordinary 
refraction produces are produced by the diffractive optical surface and 
that their directions coincide with those when the cemented surface would 
otherwise be used. Thus, it is made possible for the single lens to do the 
same achromatism as the cemented lens does. 
From the point of view of the chromatic aberration coefficients, it is 
preferred that, as the diffractive optical surface takes its place on the 
object side of the stop, the surface of the same sign in the longitudinal 
and lateral chromatic aberration coefficients is selected to use. On the 
image side of the stop, the surface of opposite sign in both coefficients 
is selected to use for the diffractive optical surface. 
(e) Of the aims of the embodiments 10 to 12, there is one for increasing 
the range of the zoom lens. So, it is desired that the aberration that is 
produced when zooming is canceled in the first and second lens units. On 
this account, letting the focal length of the first lens unit be denoted 
by F1 and the focal length of the second lens unit by F2, the following 
condition is set forth: 
EQU 1.01&lt;.vertline.F2/F1.vertline.&lt;1.59 (9) 
When the upper limit of the condition (9) is exceeded, the Petzval sum 
increases to the negative direction objectionably. So, the image surface 
tends to largely decline toward the plus side. Conversely, when the lower 
limit is exceeded, the total zooming movement of the first lens unit must 
be taken large to assure increase of the zooming range. So, the diameter 
of the front lens members is caused to increase, and the physical length 
of the complete lens tends to increase. 
(f) The first lens unit has at least one negative lens and at least one 
pair of lenses cemented together. For the first negative lens in the first 
Lens unit, it is desired to satisfy the following condition: 
EQU 1.71&lt;f11N/F1&lt;2.76 (10) 
where f11N is the focal length of the first negative lens in the first lens 
unit. 
The distortion produced in the first lens unit is corrected well by this 
arrangement. Then the upper limit of the condition (10) is exceeded, 
spherical aberration in the telephoto end becomes under-corrected and 
inward coma is produced. Conversely, when the lower limit is exceeded, 
over-correction of longitudinal chromatic aberration results. So, these 
violations are objectionable. 
This negative lens may otherwise be made aspherical. If so, the performance 
is further improved. Also, the zoom lens has become a standard provision 
and, moreover, the demand for increasing the range is growing. Along with 
this, the variation of longitudinal chromatic aberration with zooming 
comes to affect the image quality. If large longitudinal chromatic 
aberration is produced, a picture of certain colors in the liquid crystal 
display panel, when projected onto the screen, become out of focus. The 
image quality is thus deteriorated. To correct this well, the rear lens in 
the first lens unit is made to be a cemented lens, thus making it possible 
to obtain a projected image of good quality over the whole gamut of 
colors. 
(g) To further improve the correction of aberrations, especially off-axial 
flare and chromatic aberrations, the second lens unit is constructed with 
inclusion of at least one aspherical lens and at least one diffractive 
optical element of revolution symmetry. 
The fineness of pixels in the liquid crystal display panel has been 
enhanced. Along with this, there arises a problem of the resolving power 
which was so far not very serious. Then, good correction of those 
aberrations which attribute to this has become inevitable. So, use is made 
of the aspheric surface in the second lens unit, thereby correcting the 
off-axial flare well. The rear lens in the second lens unit takes the 
position at which the off-axial rays pass relatively far away from the 
optical axis. For this reason, the diffractive optical element is put in 
this position to thereby correct lateral chromatic aberration well. 
Further improvements of the optical performance are thus achieved. 
(h) To improve the correction of aberrations, especially chromatic 
aberrations, the third lens unit includes at least one diffractive optical 
element of revolution symmetry with respect to the optical axis. As 
mentioned before, the use of a high definition liquid crystal display 
element leads to require good correction of chromatic aberrations, 
especially lateral one, which so far did not give rise to a very serious 
problem. This feature makes it possible to solve that problem. 
(i) To achieve a good telecentric optical system, it is preferred to 
satisfy the following condition: 
EQU 2.2&lt;F3/.sqroot.Fw.multidot.Ft&lt;3.7 (11) 
where F3 is the focal length of the third lens unit. 
The inequalities of condition (11) are for optimizing the back focal 
distance and the telecentric condition in good balance. When the upper 
limit is exceeded, the back focal distance becomes longer than necessary, 
causing the total length of the entire lens system to increase largely. 
Moreover, the telecentric condition collapses. When the lower limit is 
exceeded, it becomes difficult to secure the sufficiently long back focal 
distance which the invention aims at. 
(j) The aspheric surface to be used in the embodiments 10 to 12 is desired 
to have such a shape that the positive refractive power becomes 
progressively weaker toward the margin of the lens. 
It is to be noted that the liquid crystal video projector according to the 
embodiments 10 to 12 includes at least the above-described telecentric 
zoom lens, an element for color combination, three liquid crystal display 
elements of corresponding images to the separated colors in view of the 
color combining element, a drive circuit for the liquid crystal display 
elements, a signal processing circuit, a color separation mirror, a light 
source and fly-eye lenses. 
FIG. 53 schematically shows the zoom lens of the telecentric system of the 
embodiments 10 to 12 and a liquid crystal projector using the same with 
the parts of the projector functionally expressed, as viewed from the top 
thereof. In FIG. 53, the zoom lens 51 of any one of the embodiments 10 to 
12 (as the projection lens) is mounted on a lens holder 52 in a casing 53 
of the projector body PB. All the above-described optical parts are 
installed within an optical engine box 54 with a reflector 55. A color 
combining prism and color filters are shown as a glass block 56. Liquid 
crystal display elements 57 to 59 present images which correspond to the 
original colors R, G and B and are positioned in front of respective 
condenser lenses 60 to 62 for producing collimated light beams. The box 54 
further includes dichroic mirrors (color separation mirrors) or mere 
reflection mirrors 63, 65 and 68, condenser lenses 64 and 66 and dichroic 
mirrors 67 and 69. A fly-eye lens 72 lies in front of a light source 73, 
making uniform the illumination over the entire area of the image frame. 
Reference numeral 71 denotes a mere reflection mirror. A converter 70 uses 
the light from the light source 73 efficiently and produces a polarized 
light beam in order to increase the amounts of light impinging on the 
display panels. 
In FIG. 53, the white light issuing from the lamp 73 is reflected forward 
by the reflector 55, then passes through the fly-eye lens 72 to the total 
reflection mirror 71 and then passes through the polarized light converter 
70, thus becoming a light beam of uniform intensity in cross-section, 
before it enters the first dichroic mirror 69. In passing through the 
first dichroic mirror 69, two colors, for example, red (R) and greenish 
blue (G, B), are separated out. Of these, the red light (R) passes through 
the first dichroic mirror 69 to the third dichroic mirror or total 
reflection mirror 68 and therefrom is reflected to the condenser lens 60. 
The other light (G,B) is reflected from the first dichroic mirror 69 to the 
second dichroic mirror 67 where two more colors G and B are separated out, 
one of which the green light G is reflected to the condenser lens 61. 
The other light B passes through the second dichroic mirror 67 to the first 
condenser lens 66, then is reflected by the fourth dichroic mirror or 
total reflection mirror 65, then passes through the second condenser lens 
64, then is reflected by the fifth dichroic mirror or total reflection 
mirror 63 and then enters the condenser lens 62. 
The entering light beams through the condenser lenses 60 to 62 illuminate 
the respective liquid crystal display elements 57 to 59 of corresponding 
images to the original colors. Three light beams that bear image 
information emerge from the respective liquid crystal display elements 57 
to 59 and then are combined to one light beam by the color combining prism 
56. This light beam is projected by the zoom lens 51 onto the screen S. 
In some cases, a polarizing filter is used as arranged in between the 
liquid crystal display element and the condenser or collimator lens. 
FIG. 54 is a side elevation view of the liquid crystal projector. In FIG. 
54, the optical axis of the zoom lens 51 is denoted by reference numeral 
81. The liquid crystal display element has an incidence-normal 82 at the 
center of the area thereof. As can be seen from FIG. 54, the axis 81 is 
not made to coincide with the central normal 82, but is made to displace 
from the central normal 82. This is because, as the image on the liquid 
crystal display element is projected onto the screen (not shown), the 
projected image takes its place on the upper side of the projector. When 
the user views the image on the screen from behind the projector, the 
shadow of the projector body overlaps the projected image on the screen in 
a lesser part, thus making it possible to provide a comfortable image to 
view. 
To assure sufficient comfortability of viewing the projected image, it is 
preferable that the amount of displacement .DELTA.Y of the optical axis 81 
of the zoom lens from the central normal 82 of the liquid crystal element 
lies in the following range: 
EQU 0.14&lt;.DELTA.Y/Fw&lt;0.24 (12) 
When the amount of displacement .DELTA.Y increases beyond the upper limit 
of the condition (12), the image is projected to too much higher a 
position than the liquid crystal projector. Although this makes it easier 
to entirely look at the projected image, the illumination on the upper 
marginal zone is extremely lowered. The display of the image is presented 
objectionably dark. Conversely, when the amount of displacement .DELTA.Y 
decreases beyond the lower limit, the projected image is hardly viewed as 
obstructed by the projector body. 
The diffractive optical element to be used in the embodiments 10 to 12 is 
constructed either with a single layer in the kinoform shown in FIG. 16, 
or with two layers of different thicknesses like that shown in FIG. 19 or 
of equal thickness like that shown in FIG. 22 in the stacked form. 
Concerning also the process for producing the diffractive optical element, 
the same as in the embodiments 1 to 5 may apply. 
FIG. 55 shows the characteristics of Modulation Transfer Function (MTF) 
versus spatial frequency of the zoom lens of the embodiment 10 using the 
grating form of FIG. 16. It is appreciated from FIG. 55 that the MTF in 
the low frequency region is somewhat lowered. 
FIG. 56 shows the spatial frequency response MTF characteristics of the 
zoom lens of the embodiment 10 using the grating form of FIG. 19. By 
altering the structure of construction of the diffractive optical element 
to the laminated one, the MTF in the low frequency region is improved to 
obtain the desired MTF characteristic. With the use of the laminated 
structure, the optical performance of the zoom lens is further improved by 
the diffractive optical element. 
Next, three numerical examples 10 to 12 of zoom lenses corresponding to the 
embodiments 10 to 12 are shown. In the numerical data for these examples 
10 to 12, ri is the radius of curvature of the i-th lens surface, when 
counted from the object side, di is the i-th axial lens thickness or air 
separation, and ni and .nu.i are respectively the refractive index and 
Abbe number of the material of the i-th lens element. The last lens 
surfaces in the numerical examples 10 to 12 define a glass block including 
the color separation prism, polarizing filter and color filters. 
The shape of the aspheric surface is expressed by the equation (2) 
described before. In the values of the aspheric and phase coefficients, 
the notation "e-Z" means "10.sup.-Z ". 
The values of the factors of the above-described conditions for the 
numerical examples 10 to 12 are also listed in Table-1. 
TABLE 1 
______________________________________ 
Condition 
Numerical Example 
No. 10 11 12 
______________________________________ 
(3) 0.30 0.0047 0.0016 
(4) 4.99e-4 1.79e-5 2.75e-6 
(7) 0.31 0.14 0.51 
(8) 0.749 0.781 0.788 
(9) 1.324 1.287 1.273 
(10) 2.136 2.269 2.301 
(11) 3.09 2.80 2.75 
(12) 0.168 0.147 0.147 
______________________________________ 
______________________________________ 
Numerical Example 10: 
f = 47.63.about.76.42 Fno = 2.57.about.3.60 2.omega. = 48.6.degree..abou 
t.31.5.degree. 
______________________________________ 
r1 = .infin. 
d1 = 2.50 n1 = 1.51633 
.nu.1 = 64.1 
r2 = .infin. 
d2 = 0.10 
r3 = 72.395 
d3 = 3.70 n2 = 1.49171 
.nu.2 = 57.4 
r4 = 28.232 
d4 = 23.64 
r5 = -23.044 
d5 = 1.60 n3 = 1.58144 
.nu.3 = 40.8 
r6 = 95.349 
d6 = 4.20 n4 = 1.80518 
.nu.4 = 25.4 
r7 = -67.524 
d7 = Variable 
r8 = .infin. (Stop) 
d8 = 3.70 n5 = 1.65844 
.nu.5 = 50.9 
r9 = -78.004 
d9 = 0.20 
r10 = 52.215 
d10 = 5.00 n6 = 1.51633 
.nu.6 = 64.1 
r11 = -180.896 
d11 = 9.46 
r12 = -68.004 
d12 = 2.00 n7 = 1.74077 
.nu.7 = 27.8 
r13 = -191.961 
d13 = 18.04 
r14 = 343.204 
d14 = 2.00 n8 = 1.62588 
.nu.8 = 35.7 
r15 = 54.449 
d15 = 2.53 
r16 = 235.377 
d16 = 2.00 n9 = 1.84666 
.nu.9 = 23.8 
r17 = 70.224 
d17 = 7.40 n10 = 1.51633 
.nu.10 = 64.1 
r18 = -70.224 
d18 = 0.30 
r19 = 74.728 
d19 = 5.10 n11 = 1.65844 
.nu.11 = 50.9 
r20 = -588.246 
d20 = Variable 
r21 = 238.154 
d21 = 4.00 n12 = 1.63854 
.nu.12 = 55.4 
r22 = -238.154 
d22 = 9.98 
r23 = .infin. 
d23 = 40.00 n13 = 1.51633 
.nu.13 = 64.1 
r24 = .infin. 
______________________________________ 
Variable Focal Length 
separation 47.63 63.13 76.42 
______________________________________ 
d7 16.84 6.56 1.07 
d20 34.00 61.78 85.60 
______________________________________ 
Aspheric Coefficients: 
r3: k = 3.98722e+00 
B = 3.57909e-06 
C = 4.66608e-09 
D = -1.54183e-11 
E = 3.68607e-14 
F = -1.98234e-17 
Phase Coefficients: 
r3: C1 = -3.63257e-07 
C2 = 1.08111e-07 
C3 = -1.8134e-10 
C4 = -3.614044e-13 
C5 = -9.41578e-18 
C6 = 3.42317e-20 
______________________________________ 
______________________________________ 
Numerical Example 11: 
f = 47.70.about.76.21 Fno = 2.50.about.3.65 2.omega. = 48.5.degree..abou 
t.31.5.degree. 
______________________________________ 
r1 = .infin. 
d1 = 2.50 n1 = 1.51633 
.nu.1 = 64.1 
r2 = .infin. 
d2 = 0.50 
r3 = 66.171 
d3 = 3.70 n2 = 1.49171 
.nu.2 = 57.4 
r4 = 28.805 
d4 = 23.98 
r5 = -24.089 
d5 = 1.60 n3 = 1.58144 
.nu.3 = 40.8 
r6 = 62.973 
d6 = 0.09 
r7 = 66.586 
d7 = 4.40 n4 = 1.80518 
.nu.4 = 25.4 
r8 = -79.065 
d8 = Variable 
r9 = .infin. (Stop) 
d9 = 4.20 n5 = 1.60311 
.nu.5 = 60.6 
r10 = -101.120 
d10 = 0.20 
r11 = 41.289 
d11 = 6.20 n6 = 1.63854 
.nu.6 = 55.4 
r12 = -309.303 
d12 = 18.24 
r13 = -46.518 
d13 = 1.90 n7 = 1.74077 
.nu.7 = 27.8 
r14 = 46.518 
d14 = 1.26 
r15 = 74.518 
d15 = 5.40 n8 = 1.49171 
.nu.8 = 57.4 
r16 = -227.254 
d16 = 4.76 
r17 = 105.081 
d17 = 11.50 n9 = 1.51633 
.nu.9 = 64.1 
r18 = -39.577 
d18 = Variable 
r19 = 174.232 
d19 = 5.10 n10 = 1.51633 
.nu.10 = 64.1 
r20 = -174.232 
d20 = 9.98 
r21 = .infin. 
d21 = 40.00 n11 = 1.51633 
.nu.11 = 64.1 
r22 = .infin. 
______________________________________ 
Variable Focal Length 
separation 47.70 63.05 76.21 
______________________________________ 
d8 16.97 6.62 1.06 
d18 35.01 62.79 86.61 
______________________________________ 
Aspheric Coefficients: 
r3: k = 4.71665e+00 
B = 2.51398e-06 
C = 1.38111e-09 
D = -1.89750e-12 
E = 2.77356e-15 
F = 6.42233e-18 
r16: k = -5.96357e+01 
B = 4.80456e-06 
C = 4.13110e-09 
D = -3.75093e-12 
E = -1.66195e-15 
F = 2.53167e-17 
Phase Coefficients: 
r16: C1 = -4.00568e-05 
C2 = 1.88104e-07 
C3 = -7.15433e-10 
C4 = -4.44106e-13 
C5 = -3.17967e-15 
C6 = -4.11617e-18 
______________________________________ 
______________________________________ 
Numerical Example 12: 
f = 47.64.about.76.24 Fno = 2.50.about.3.65 2.omega. = 48.6.degree..abou 
t.31.5.degree. 
______________________________________ 
r1 = .infin. 
d1 = 2.50 n1 = 1.51633 
.nu.1 = 64.1 
r2 = .infin. 
d2 = 0.50 
r3 = 62.810 
d3 = 3.70 n2 = 1.49171 
.nu.2 = 57.4 
r4 = 28.441 
d4 = 23.28 
r5 = -24.182 
d5 = 1.60 n3 = 1.58144 
.nu.3 = 40.8 
r6 = 63.150 
d6 = 0.09 
r7 = 67.012 
d7 = 4.40 n4 = 1.80518 
.nu.4 = 25.4 
r8 = -80.203 
d8 = Variable 
r9 = .infin. (Stop) 
d9 = 4.20 n5 = 1.60311 
.nu.5 = 60.6 
r10 = -104.921 
d10 = 0.20 
r11 = 41.696 
d11 = 6.20 n6 = 1.63854 
.nu.6 = 55.4 
r12 = -278.818 
d12 = 16.85 
r13 = -47.304 
d13 = 1.90 n7 = 1.74077 
.nu.7 = 27.8 
r14 = 47.304 
d14 = 1.36 
r15 = 74.540 
d15 = 5.40 n8 = 1.49171 
.nu.8 = 57.4 
r16 = -217.058 
d16 = 4.48 
r17 = 115.978 
d17 = 11.30 n9 = 1.51633 
.nu.9 = 64.1 
r18 = -38.801 
d18 = Variable 
r19 = 175.112 
d19 = 5.10 n10 = 1.51633 
.nu.10 = 64.1 
r20 = -175.112 
d20 = 9.98 
r21 = .infin. 
d21 = 40.00 n11 = 1.51633 
.nu.11 = 64.1 
r22 = .infin. 
______________________________________ 
Variable Focal Length 
separation 47.64 63.04 76.24 
______________________________________ 
d8 17.01 6.63 1.08 
d18 34.43 65.21 89.03 
______________________________________ 
Aspheric Coefficients: 
r3: k = 4.99966e+00 
B = 2.11176e-06 
C = 6.50188e-10 
D = -1.66201e-12 
E = 2.61361e-15 
F = 1.52356e-18 
r16: k = -6.86029e+01 
B = 4.54754e-06 
C = 4.29889e-09 
D = -9.24800e-12 
E = -8.31032e-15 
F = 3.46238e-17 
Phase Coefficients: 
r20: C1 = -7.63527e-05 
C2 = 1.22713e-07 
C3 = -2.09924e-10 
C4 = 1.62491e-13 
C5 = -2.46679e-17 
C6 = -3.19960e-21 
______________________________________ 
As in the embodiments 10 to 12, the negative lead type is used as the lens 
type and appropriate rules of design are set forth for each of the lens 
units. In particular, the diffractive optical element is used in an 
appropriate one of the lens units. Accordingly, the entire lens system is 
reduced to a compact size, while still maintaining the good telecentric 
condition over the entire zooming range. It is, therefore, made possible 
to achieve a zoom lens having good optical performance over the entire 
area of the image frame suited to be used with the liquid crystal display 
panels, and a projecting apparatus using the same. 
Further, by specifying all such design parameters described before, the 
zoom ratio is increased to 1.57 or higher and the large aperture ratio is 
secured at about 2.6 in F-number. Despite these, astigmatism and 
distortion are lessened and, while securing the back focal distance long 
enough to accommodate the color combining prism or like optical elements 
and various optical filters or like optical elements, chromatic 
aberrations are corrected well. It is, therefore, made possible to realize 
a telecentric zoom lens having good optical performance maintained stable 
over the entire zooming range and over the entire focusing range. In 
addition, a liquid crystal video projector can be realized which is 
adapted to be used with that zoom lens. 
Next, other embodiments of projection lenses for the projectors are 
described. 
FIG. 57, FIG. 60, FIG. 63, FIG. 66 and FIG. 69 are longitudinal section 
views of embodiments 13 to 17 of zoom lenses, respectively. In these 
figures, a plane of projection or screen S lies at a first conjugate point 
of long distance. A plane to be projected, or liquid crystal display 
element LCD lies at a second conjugate point of short distance. 
In these figures, the zoom lens comprises, from front to rear, a first lens 
unit L1 of negative refractive power, a second lens unit L2 of positive 
refractive power, a third lens unit L3 of negative refractive power, a 
fourth lens unit L4 of positive refractive power and a fifth lens unit L5 
of positive refractive power. A glass block GB represents an infrared cut 
filter and others. In the embodiments 13 to 17, the first lens unit L1 
corresponds to the front lens unit and the second to fifth lens units L2 
to L5 correspond to the rear lens unit. 
In these figures, the arrows show the loci of motion of the lens units 
during zooming from the wide-angle end to the telephoto end. 
In the embodiments 13 to 17, during zooming from the wide-angle end to the 
telephoto end, the second lens unit L2 and the fourth lens unit L4 axially 
move toward the first conjugate point. 
During this time, the separation between the second lens unit L2 and the 
third lens unit L3 increases and the separation between the third lens 
unit L3 and the fourth lens unit L4 decreases. The third lens unit L3, 
during zooming, either remains stationary, or axially moves toward the 
second conjugate point monotonously or moves in a locus convex toward the 
first conjugate point. The first and fifth lens units L1 and L5 remain 
stationary during zooming. 
Focusing is performed by moving the first lens unit L1. At least one of the 
first to fifth lens units L1 to L5 is provided with at least one 
diffractive optical element. 
Each of the embodiments 13 to 17, is next described. The embodiment 13 of 
FIG. 57 is an example of introduction of the diffractive optical element 
into the first lens unit that remains stationary daring zooming. During 
zooming from the wide-angle end to the telephoto end, the second and 
fourth lens units L2 and L4 axially move toward the first conjugate point, 
while simultaneously moving the third lens unit L3 toward the second 
conjugate point monotonously. The fifth lens unit L5 remains stationary 
during zooming. 
The embodiment 14 of FIG. 60 is an example of introduction of the 
diffractive optical element into the first lens unit that remains 
stationary during zooming. During zooming from the wide-angle end to the 
telephoto end, the second and fourth lens units axially move toward the 
first conjugate point. At the same time, the third lens unit axially moves 
first toward the first conjugate point and then turns toward the second 
conjugate point (while depicting a locus convex toward the first conjugate 
point). The fifth lens unit remains stationary during zooming. 
The embodiment 15 of FIG. 63 is an example of introduction of the 
diffractive optical elements into the first lens unit that remains 
stationary during zooming and also to the fifth lens unit. During zooming 
from the wide-angle end to the telephoto end, the second and fourth lens 
units axially move toward the first conjugate point. At the same time, the 
third lens unit axially moves first toward the first conjugate point and 
then turns toward the second conjugate point (while depicting a locus 
convex toward the first conjugate point). The fifth lens unit remains 
stationary during zooming. 
The embodiment 16 of FIG. 66 is an example of introduction of the 
diffractive optical elements into the first lens unit and the second lens 
unit. During zooming from the wide-angle end to the telephoto end, the 
second and fourth lens units axially move toward the first conjugate 
point. At the same time, the third lens unit axially moves first toward 
the first conjugate point and then turns toward the second conjugate point 
(while depicting a locus convex toward the first conjugate point). The 
fifth lens unit remains stationary during zooming. The diffractive optical 
element on the ninth surface is made by applying a diffractive optical 
surface on a flat plane glass. 
The embodiment 17 of FIG. 69 is an example of introduction of the 
diffractive optical elements into the first lens unit and the fourth lens 
unit. During zooming from the wide-angle end to the telephoto end, the 
second and fourth lens units axially move toward the first conjugate 
point. The first, third and fifth lens units remain stationary during 
zooming. 
In the figures, Li denotes the i-th lens unit (i=1.about.5). The lens units 
L1 to L5 constitute a zoom lens system which is attached to the liquid 
crystal video projector body through coupling members. The glass block GB 
and those parts that follow including the liquid crystal display panel LCD 
are held in the projector body. 
In the embodiments 13 to 17, during zooming from the wide-angle end to the 
telephoto end, zooming movements occur as indicated by the arrow. Also, 
the first lens unit is axially moved to effect focusing. 
Also, the first lens unit is preferably provided with an aspheric surface. 
According to this arrangement, the performance is further improved. 
To facilitate improvements of the correction of aberrations, especially 
off-axial flare and chromatic aberrations, the first lens unit is made to 
include at least one aspherical lens and at least one diffractive optical 
element of revolution symmetry with respect to the optical axis. As 
mentioned before, the fineness of pixels in the liquid crystal display 
panel has been enhanced. Along with this, there arises a problem of the 
resolving power which was so far not very serious. Then, good correction 
of those aberrations which attribute to this has become inevitable. So, 
use is made of the aspheric surface in the fifth lens unit, thereby 
correcting the off-axial flare well. The fourth lens unit takes the 
position at which the off-axial rays passes relatively far away from the 
optical axis. For this reason, the diffractive optical element is put in 
this position to thereby correct lateral chromatic aberration well. 
Further improvements of the optical performance are thus achieved. 
To improve the correction of aberrations, especially chromatic aberrations, 
the fifth lens unit includes at least one diffractive optical element of 
revolution symmetry with respect to the optical axis. As mentioned before, 
the use of a high definition liquid crystal display element leads to 
require good correction of chromatic aberrations, especially lateral one, 
which so far did not give rise to a very serious problem. This feature 
makes it possible to solve that problem. 
The construction features of the zoom lens described above provide a 
possibility of accomplishing the objects of the embodiments 13 to 17. It 
is more preferred to satisfy at least one of the following conditions. 
(A) Letting the longest and shortest focal lengths of the entire lens 
system be denoted by Fw and Ft, respectively, and the focal length of the 
i-th lens unit be denoted by Fi, the following conditions are satisfied: 
EQU 0.8&lt;.vertline.F1/F2.vertline.&lt;2.3 (13) 
EQU 0.6&lt;F2/.sqroot.Fw.multidot.Ft (14) 
The inequalities of conditions (13) and (14) are for determining an 
appropriate relationship between the main variator or the second lens unit 
and the first lens unit. 
When the lower limit of the condition (13) is exceeded, the diameter of the 
front lens member determined by the first lens unit increases greatly. 
Also, large distortion is produced in the wide-angle end. So, the 
violation is objectionable. When the upper limit is exceeded, the total 
zooming movement of the second lens unit must be made large to obtain the 
desired zoom ratio. So, the physical length of the complete lens is caused 
to increase objectionably. 
The inequality of condition (14) is for appropriately determining the power 
of the main variator unit or the second lens unit. When the lower limit is 
exceeded, the image plane is objectionably over-corrected. When the upper 
limit is exceeded, the total zooming movement of the second lens unit must 
be taken large to obtain the desired zoom ratio go, the physical length of 
the complete lens is caused to increase objectionably. 
(B) The whole lens system has to hold a nearly telecentric property. For 
this purpose, it is desired to satisfy the following condition: 
EQU 4&lt;.vertline.Tk.vertline./Fw (15) 
where Tk is the distance from the second conjugate point of short distance 
to the exit pupil of the zoom lens (or the distance from the panel (image 
plane) to the exit pupil which takes a minimum absolute value during 
zooming). 
The term "nearly telecentric" property used herein means that the exit 
pupil is far enough to remove the light distribution characteristics of 
the liquid crystal element or the influence of the angle dependence of the 
color combining dichroic mirror when a plurality of color beams are 
combined. In actual practice, this condition is prerequisite to remove its 
angle dependency. 
More preferably, the value of the factor of the condition (15) falls within 
the following range: 
EQU 9.0&lt;.vertline.Tk.vertline./Fw (15a) 
(C) To correct distortion well, it is preferred to satisfy the following 
condition: 
EQU 1&lt;.vertline.F1.vertline./Fw&lt;2 (16) 
When the upper limit of this condition is violated, distortion cannot be 
made appropriate in the wide-angle end. When the lower limit is exceeded, 
distortion cannot be made appropriate in the telephoto end. 
(D) With the diffractive optical element arranged in the first lens unit, 
when an appropriate phase for the diffractive optical element is selected, 
the lateral chromatic aberrations for two wavelengths of light, for 
example, d-line and g-line, produced in the first lens unit are suppressed 
to a minimum. So, a good stability of lateral chromatic aberration is 
maintained over the entire zooming range. Moreover, the longitudinal 
chromatic aberration (secondary spectrum) residual that exists in the 
telephoto end does not worsen. 
(E) With the diffractive optical element arranged in the second lens unit, 
when an appropriate phase for the diffractive optical element is selected, 
the lateral chromatic aberrations for two wavelengths of light, for 
example, d-line and g-line, produced in the second lens unit are 
suppressed to a minimum. So, a good stability of lateral chromatic 
aberration is maintained over the entire zooming range. Moreover, the 
longitudinal chromatic aberration (secondary spectrum) residual that 
exists in the telephoto end does not worsen. 
(F) The zoom lens is constructed so as to satisfy the features (D) and (E) 
at once. With this construction, a high standard of correction of 
chromatic aberrations is attained in order to insure that the requirements 
of maintaining good optical performance and of further improvement of the 
compact form are fulfilled at once. 
(G) The phase for the diffractive optical surface is expressed by the 
equation (1) described before. In the zoom lens of the telecentric type, 
the phase coefficients have to be effectively utilized in achieving 
advantageous correction of aberrations. For this purpose, it is preferred 
to satisfy the following condition: 
EQU fi.multidot.C1&lt;0 (17) 
where C1 is the phase coefficient of the term in the first degree in the 
equation for the diffractive optical element, and fi is the refractive 
power of the lens unit that has the diffractive optical element. C1 
represents the paraxial refractive power of the diffractive optical 
element. When C1 has a positive value, the refractive power of the 
diffractive optical element is negative. When C1 has a negative value, the 
refractive power of the diffractive optical element is positive. If this 
condition is satisfied, it results that, regardless of whether the 
diffractive optical element is put in the positive or negative lens unit, 
the curvature of that lens unit can be made looser, giving an advantage on 
the aberration correction. 
(H) The phase coefficients of the diffractive optical system are preferably 
determined so as to satisfy the conditions (3) and (4) mentioned before. 
When the conditions (3) and (4) are violated, it becomes difficult not only 
to correct aberrations but also to manufacture the diffractive optical 
surfaces. So, the violations are objectionable. 
(I) The diffractive optical element is arranged at least one lens in the 
interior of the first lens unit, or in the interior of the second lens 
unit or in the interior of the third lens unit to thereby suppress the 
lateral chromatic aberration the respective individual lens unit produces 
to a minimum. As the second lens unit moves to effect zooming, the range 
of variation of lateral chromatic aberration is also suppressed to a 
minimum. 
(J) As the diffractive optical element is applied on the optical surface, 
its base is spherical, or flat plane, or aspherical, or even quadric. 
Also, a layer of plastic is deposited as the aforesaid diffractive optical 
surface on any of these surface. That is, the so-called "replica" 
diffraction grating may be employed. According to this, it becomes easy to 
obtain the high optical performance. 
(K) If the refracting power of the diffractive optical element is 
strengthened, the difference in pitch between the paraxial and marginal 
zones increases largely, causing the production technique to become 
difficult. The diffraction efficiency of finished products is also not 
good. 
As in the embodiments 13 to 17, instead of the cemented lens, the 
diffractive optical element is used in the first lens unit, or the second 
lens unit, or the third lens unit to correct the chromatic aberrations. In 
this case, the refractive power of the diffractive optical element needs 
not to be necessarily much. 
Nonetheless, in order to correct some of the off-axial aberrations, 
especially field curvature and distortion, a refractive power may be given 
to the diffractive optical element. If so, the above-mentioned condition 
(7) must be satisfied. In this case, no difficult problems arise in 
manufacturing, and a good effect is produced to correct the aberrations 
including chromatic ones. 
(L) For the second lens unit as the main variator, the following conditions 
are set forth: 
EQU 0.8&lt;Z2/Z&lt;1.1 (18) 
EQU 0.9&lt;M2/M4&lt;15 (19) 
EQU 0.4&lt;M2/(Ft-Fw)&lt;1.5 (20) 
where Z2 is the magnification change of the second lens unit as defined by 
Z2=.beta.2t/.beta.2w wherein .beta.2w and .beta.2t are the magnifications 
of the second lens unit in the wide-angle end and the telephoto end, 
respectively, Z is the change of the focal length of the entire lens 
system as defined by Z=Ft/Fw, and M2 and M4 are the total zooming 
movements of the second and fourth lens units as the variators, 
respectively. 
The inequalities of condition (18) give a proper range for the ratio of the 
changes of magnification by the second and fourth lens units. Since the 
third lens unit decreases the magnification during zooming, it is 
preferred to satisfy this condition. 
The inequalities of conditions (19) and (20) have an aim to make 
appropriate the physical length of the entire lens system and the zooming 
movements of the variators. Particularly, the second and fourth lens units 
give a fact that the fourth lens unit tends to be rather weaker in 
refractive power. To make appropriate contributions to the variation of 
the focal length, this range is preferable. It is more preferred that, in 
particular, the zooming movement of the second lens unit exceeds the 
zooming movement of the fourth lens unit. 
EQU 1.ltoreq.M2/M4&lt;1.6 (19a) 
(M) As described above, compared with the second lens unit, the fourth lens 
unit tends to weaken in refractive power. It is preferred to satisfy, in 
particular, the following condition: 
EQU 0.4&lt;F2/F4&lt;1.5 (21) 
The inequalities of condition (21) is necessary to determine an appropriate 
Petzval sum in such a manner as to make good compromise between the power 
arrangement and the magnification change of the main variator. 
(N) To make appropriate the exit pupil of the entire lens system and 
distortion, it is preferred to satisfy the following conditions: 
EQU 0.1&lt;bf/F5&lt;0.5 (22) 
EQU 0.5&lt;.vertline.F1.vertline./bf&lt;2.2 (23) 
where bf is the distance from the fifth lens unit to the display (LCD) or 
the reduced length to air with the dichroic mirrors removed. 
The inequalities (22) are necessary to make the entire lens system in an 
appropriately telecentric form. When the upper limit is exceeded, the size 
increases greatly. When the lower limit is exceeded, distortion is 
produced. The inequalities (23), too, have an aim to take appropriate 
distortion, while elongating the exit pupil to get the telecentric form. 
(O) The power arrangement of all the lens units is made appropriate and the 
zooming movements of all the variators are made appropriate to improve the 
compact form. For this purpose, it is preferred to satisfy the following 
condition: 
EQU 0.7&lt;.vertline.F1.vertline./.sqroot.Fw.multidot.Ft&lt;2.1 (24) 
In this connection, it should be noted that distortion must be suppressed 
sufficiently in the first lens unit and also a sufficient back focal 
distance must be secured. 
When the upper limit is exceeded, the focusing movement increases to 
increase the physical length of the entire lens system, and the back focal 
distance shortens. So, the violation is objectionable. Conversely, when 
the lower limit is exceeded, the focusing movement decreases, but it 
becomes difficult to correct distortion. At the same time, the Petzval sum 
increased to the negative direction, causing the image surface to decline. 
So, this violation is objectionable. 
(P) Letting the focal length of the i-th lens unit be denoted by Fi, and 
the shortest and longest focal lengths of the entire lens system by Fw and 
Ft, respectively, the following conditions are set forth: 
EQU 0.6&lt;.vertline.F3.vertline./.sqroot.Fw.multidot.Ft&lt;1.4 (25) 
EQU 0.8&lt;F4/.sqroot.Fw.multidot.Ft&lt;1.8 (26) 
EQU 1.5&lt;F5/.sqroot.Fw.multidot.Ft&lt;6.0 (27) 
The inequalities (25) and (26) express an appropriate power distribution 
over those lens units which contribute to variations of the focal length. 
When the upper limit of either condition is exceeded, the zooming movement 
increases to obtain the desired zoom ratio, causing the physical length of 
the entire lens system to increase objectionably. When the lower limit is 
exceeded, the zooming movement of each of the lens units decreases, but 
the variation with zooming of aberrations, especially curvature of field, 
increases objectionably. 
The inequalities (27), together with the inequalities (22), are necessary 
to make farther the exit pupil to secure the telecentric form. When the 
lower limit is exceeded, the telecentric form is secured, but the fifth 
lens unit produces distortion objectionably. Also, when the upper limit is 
exceeded, the size of the entire lens system increases objectionably. 
(Q) The lateral chromatic aberration is reduced at any zooming station. 
Moreover, its range of variation with zooming, too, is suppressed to a 
minimum. For these purposes, it is preferred that the third lens unit 
includes a lens whose material has an Abbe number .nu.3 lying in the 
following range: 
EQU 55&lt;.nu.3 (28) 
More preferably, 
EQU 60&lt;.nu.3 (28a) 
(R) The mean Abbe number .nu.1n of the negative lenses in the first lens 
unit lies in the following range: 
EQU 60&lt;.nu.1n (29) 
With the selection of such a material, it becomes possible to reduce the 
chromatic aberrations and their range of variation with zooming. 
(S) The telecentric system is made optimum in such a manner as to optimize 
the distance from the zoom lens to the display panel. For this purpose, 
the following condition is set forth: 
EQU 2&lt;F5/Fw&lt;7 (30) 
When the lower limit is exceeded, the optimum telecentricity is no longer 
realized. When the upper limit is exceeded, the size increases 
objectionably. 
(T) In general, the diffractive optical element produces chromatic 
aberrations in the reverse sense to that for the ordinary refraction. 
Assuming that, for example, the cemented surface used in the conventional 
way to achromatize is removed as the cemented lens is replaced by a single 
lens to reduce the total number of lens elements, then it is preferable to 
select that surface which would be used to contribute the reverse 
chromatic aberrations to those the cemented surface contributes, when in 
applying the diffractive optical surface. With this arrangement, it 
results that the reverse chromatic aberrations to those the ordinary 
refraction produces are produced by the diffractive optical surface and 
that their directions coincide with those when the cemented surface would 
otherwise be used. Thus, it is made possible for the single lens to do the 
same achromatism as the cemented lens does. 
From the point of view of the chromatic aberration coefficients mentioned 
before, it is preferred that, as the diffractive optical surface takes its 
place on the object side of the stop, the surface of the same sign in the 
longitudinal and lateral chromatic aberration coefficients is selected to 
use. On the image side of the stop, the surface of the opposite sign in 
both coefficients is selected to use for the diffractive optical surface. 
In the embodiments 13 to 17, the chromatic aberrations are reduced by using 
the diffractive optical element of the structure shown in FIG. 16 or FIG. 
19 or FIG. 22. In turn, the number of constituent lenses is reduced. 
Further improvements of the compact form are thus achieved, while still 
maintaining good optical performance. 
Next, five numerical examples 13 to 17 corresponding to the embodiments 13 
to 17 are shown. In the numerical data for these examples 13 to 17, ri is 
the radius of curvature of the i-th lens surface, when counted from the 
first conjugate point side, di is the i-th axial lens thickness or air 
separation, and ni and .nu.i are respectively the refractive index and 
Abbe number of the material of the i-th lens element. 
Also, the flat plate glass in the numerical examples 13 to 17 is a glass 
block including the color combining prism, polarizing filter and color 
filters. The values of the factors of the above-described conditions for 
the numerical examples 13 to 17 are listed in Table-2. The values of the 
focal lengths of all the lens units and the focal length of the 
diffractive optical element for the numerical examples 13 to 17 to 
determine the values of the factors in the conditions (17) and (7) are 
also listed in Table-3. 
In the values of the phase coefficients, the notation "e-Z" means 
"10.sup.-Z." 
______________________________________ 
Numerical Example 13: 
f = 33.29.about.42.1 Fno = 1.18.about.2.1 2.omega. = 54.1.degree..about. 
44.0.degree. 
______________________________________ 
r1 = 81.480 
d1 = 7.30 n1 = 1.51633 
.nu.1 = 64.1 
r2 = -215.459 
d2 = 0.20 
r3 = 127.474 
d3 = 2.20 n2 = 1.51633 
.nu.2 = 64.1 
r4 = 27.091 
d4 = 10.34 
r5 = -45.890 
d5 = 2.00 n3 = 1.51633 
.nu.3 = 64.1 
r6 = 41.527 
d6 = Variable 
r7 = 97.271 
d7 = 5.00 n4 = 1.72000 
.nu.4 = 50.2 
r8 = -100.178 
d8 = 14.08 
r9 = 51.381 
d9 = 8.00 n5 = 1.69680 
.nu.5 = 55.5 
r10 = -38.917 
d10 = 1.40 n6 = 1.80518 
.nu.6 = 25.4 
r11 = -76.413s 
d11 = Variable 
r12 = -44.205 
d12 = 1.30 n7 = 1.51633 
.nu.7 = 64.1 
r13 = 34.093 
d13 = 2.50 n8 = 1.80518 
.nu.8 = 25.4 
r14 = 41.389 
d14 = Variable 
r15 = -521.769 
d15 = 12.00 n9 = 1.69680 
.nu.9 = 55.5 
r16 = -20.868 
d16 = 2.00 n10 = 1.80518 
.nu.10 = 25.4 
r17 = -45.034 
d17 = 0.20 
r18 = 337.807 
d18 = 5.00 n11 = 1.60311 
.nu.11 = 60.6 
r19 = -99.198 
d19 = Variable 
r20 = 57.149 
d20 = 6.00 n12 = 1.60311 
.nu.12 = 60.6 
r21 = 190.809 
d21 = 7.10 
r22 = .infin. 
d22 = 32.00 n13 = 1.51633 
.nu.13 = 64.2 
r23 = .infin. 
______________________________________ 
(r22, r23) = GB 
s) Stop 
Variable Focal Length 
separation 33.31 37.70 42.11 
______________________________________ 
d6 10.31 7.62 5.59 
d11 10.98 15.59 20.10 
d14 11.53 8.47 5.13 
d19 1.00 2.14 3.00 
______________________________________ 
r3: Diffractive Optical Surface 
C1 C2 C3 
9.78669e-05 -2.01981e-07 
2.71608e-10 
______________________________________ 
______________________________________ 
Numerical Example 14: 
f = 33.22.about.42.12 Fno = 1:1.8.about.2.07 2.omega. = 54.2.degree..abo 
ut.43.96.degree. 
______________________________________ 
r1 = 93.471 
d1 = 7.30 n1 = 1.51805 
.nu.1 = 64.1 
r2 = -150.853 
d2 = 0.20 
r3 = 123.856 
d3 = 2.20 n2 = 1.51805 
.nu.2 = 64.1 
r4 = 23.512 
d4 = 12.55 
r5 = -30.818 
d5 = 2.00 n3 = 1.51805 
.nu.3 = 64.1 
r6 = 40.912 
d6 = 3.18 
r7 = 59.942 
d7 = 5.00 n4 = 1.72305 
.nu.4 = 50.2 
r8 = -91.111 
d8 = Variable 
r9 = 63.992 
d9 = 7.00 n5 = 1.69948 
.nu.5 = 55.5 
r10 = -32.801 
d10 = 1.40 n6 = 1.81185 
.nu.6 = 25.4 
r11 = -60.063s 
d11 = Variable 
r12 = -31.727 
d12 = 1.30 n7 = 1.51805 
.nu.7 = 64.1 
r13 = 68.198 
d13 = Variable 
r14 = -378.228 
d14 = 13.00 n8 = 1.69948 
.nu.8 = 55.5 
r15 = -21.251 
d15 = 2.00 n9 = 1.81185 
.nu.9 = 25.4 
r16 = -40.023 
d16 = 0.20 
r17 = 132.292 
d17 = 7.00 n10 = 1.60524 
.nu.10 = 60.6 
r18 = -100.879 
d18 = Variable 
r19 = 68.011 
d19 = 7.00 n11 = 1.60524 
.nu.11 = 60.6 
r20 = 510.719 
d20 = 7.10 n12 = 1.51805 
.nu.12 = 64.2 
r21 = .infin. 
d21 = 32.00 
r22 = .infin. 
______________________________________ 
(r21, r22) = GB 
s) Stop 
Variable Focal Length 
separation 33.22 36.72 42.12 
______________________________________ 
d8 11.10 5.67 1.58 
d11 20.02 24.44 30.51 
d13 5.23 5.57 3.09 
d18 1.00 1.66 2.17 
______________________________________ 
r3: Diffractive Optical Surface 
C1 C2 C3 
2.54526e-04 -3.86445e-07 
5.88535e-10 
______________________________________ 
______________________________________ 
Numerical Example 15: 
f = 33.37.about.44.28 Fno = 1:1.8.about.2.09 2.omega. = 54.0.degree..abo 
ut.42.0.degree. 
______________________________________ 
r1 = 83.975 
d1 = 7.30 n1 = 1.51805 
.nu.1 = 64.1 
r2 = -163.245 
d2 = 0.20 
r3 = 146.222 
d3 = 2.20 n2 = 1.51805 
.nu.2 = 64.1 
r4 = 22.688 
d4 = 11.73 
r5 = -32.876 
d5 = 2.00 n3 = 1.51805 
.nu.3 = 64.1 
r6 = 44.145 
d6 = 3.12 
r7 = 60.547 
d7 = 5.00 n4 = 1.72305 
.nu.4 = 50.2 
r8 = -94.905 
d8 = Variable 
r9 = 64.610 
d9 = 7.00 n5 = 1.69948 
.nu.5 = 55.5 
r10 = -33.125 
d10 = 1.40 n6 = 1.81185 
.nu.6 = 25.4 
r11 = -63.703s 
d11 = Variable 
r12 = -33.174 
d12 = 1.30 n7 = 1.48898 
.nu.7 = 70.2 
r13 = 70.120 
d13 = Variable 
r14 = -697.326 
d14 = 13.00 n8 = 1.69948 
.nu.8 = 55.5 
r15 = -21.251 
d15 = 2.00 n9 = 1.81185 
.nu.9 = 25.4 
r16 = -39.476 
d16 = 0.20 
r17 = 128.348 
d17 = 6.00 n10 = 1.60524 
.nu.10 = 60.6 
r18 = -109.879 
d18 = Variable 
r19 = 50.848 
d19 = 6.00 n11 = 1.60524 
.nu.11 = 60.6 
r20 = 91.643 
d20 = 7.10 
r21 = .infin. 
d21 = 32.00 n12 = 1.51805 
.nu.12 = 64.2 
r22 = .infin. 
______________________________________ 
(r21, r22) = GB 
s) Stop 
Variable Focal Length 
separation 33.37 37.19 42.28 
______________________________________ 
d8 10.13 5.26 5.58 
d11 19.69 24.85 31.02 
d13 7.07 6.35 3.52 
d18 1.00 1.44 1.76 
______________________________________ 
r3: Diffractive Optical Surface 
C1 C2 C3 
2.88580e-04 -5.05548e-07 
1.02969e-09 
r19: Diffractive Optical Surface 
C1 C2 C3 
-6.31175e-05 1.97625e-07 
-1.01560e-10 
______________________________________ 
______________________________________ 
Numerical Example 16: 
f = 33.24.about.42.30 Fno = 1:1.8.about.2.07 2.omega. = 54.2.degree..abo 
ut.43.78.degree. 
______________________________________ 
r1 = 76.274 
d1 = 7.30 n1 = 1.51805 
.nu.1 = 64.1 
r2 = -173.754 
d2 = 0.20 
r3 = 134.762 
d3 = 2.20 n2 = 1.51805 
.nu.2 = 64.1 
r4 = 22.231 
d4 = 13.01 
r5 = -29.890 
d5 = 2.00 n3 = 1.51805 
.nu.3 = 64.1 
r6 = 35.723 
d6 = 0.96 
r7 = 40.813 
d7 = 6.00 n4 = 1.72305 
.nu.4 = 50.2 
r8 = -103.044 
d8 = Variable 
r9 = .infin. 
d9 = 1.50 n5 = 1.51805 
.nu.5 = 64.1 
r10 = .infin. 
d10 = 0.50 
r11 = 68.588 
d11 = 7.00 n6 = 1.69948 
.nu.6 = 55.5 
r12 = -59.096 
d12 = 1.40 n7 = 1.81185 
.nu.7 = 25.4 
r13 = -68.564s 
d13 = Variable 
r14 = -32.062 
d14 = 1.30 n8 = 1.48898 
.nu.8 = 70.2 
r15 = 73.326 
d15 = Variable 
r16 = -174.341 
d16 = 12.50 n9 = 1.69948 
.nu.9 = 55.5 
r17 = -21.251 
d17 = 2.00 n10 = 1.81185 
.nu.10 = 25.4 
r18 = -38.132 
d18 = 0.20 
r19 = 102.962 
d19 = 6.00 n11 = 1.60524 
.nu.11 = 60.6 
r20 = -127.656 
d20 = Variable 
r21 = 68.423 
d21 = 6.00 n12 = 1.60524 
.nu.12 = 60.6 
r22 = 406.902 
d22 = 7.10 
r23 = .infin. 
d23 = 32.00 n13 = 1.51805 
.nu.13 = 64.2 
r24 = .infin. 
______________________________________ 
(r23, r24) = GB 
s) Stop 
Variable Focal Length 
separation 33.25 37.10 42.31 
______________________________________ 
d8 11.19 5.82 1.64 
d13 18.69 23.40 29.36 
d15 5.95 5.83 3.46 
d20 1.00 1.77 2.36 
______________________________________ 
r3: Diffractive Optical Surface 
C1 C2 C3 
5.27641e-04 -7.27557e-07 
8.51180e-10 
r9: Diffractive Optical Surface 
C1 C2 C3 
-6.51658e-04 4.44622e-07 
3.02396e-10 
______________________________________ 
______________________________________ 
Numerical Example 17: 
f = 33.30.about.42.33 Fno = 1:1.8.about.2.06 2.omega. = 54.1.degree..abo 
ut.42.76.degree. 
______________________________________ 
r1 = 62.031 
d1 = 9.00 n1 = 1.51805 
.nu.1 = 64.1 
r2 = -237.395 
d2 = 0.40 
r3 = 132.374 
d3 = 2.20 n2 = 1.51805 
.nu.2 = 64.1 
r4 = 23.785 
d4 = 12.91 
r5 = -34.574 
d5 = 2.00 n3 = 1.51805 
.nu.3 = 64.1 
r6 = 41.772 
d6 = 5.18 
r7 = 66.677 
d7 = 5.00 n4 = 1.72305 
.nu.4 = 50.2 
r8 = -144.908 
d8 = Variable 
r9 = 68.753 
d9 = 7.00 n5 = 1.69948 
.nu.5 = 55.5 
r10 = -29.259 
d10 = 1.40 n6 = 1.81185 
.nu.6 = 25.4 
r11 = -58.639s 
d11 = Variable 
r12 = -30.217 
d12 = 1.30 n7 = 1.48898 
.nu.7 = 70.2 
r13 = 79.640 
d13 = Variable 
r14 = -935.943 
d14 = 13.00 n8 = 1.69948 
.nu.8 = 55.5 
r15 = -21.251 
d15 = 2.00 n9 = 1.81185 
.nu.9 = 25.4 
r16 = -37.510 
d16 = 0.20 
r17 = 93.028 
d17 = 6.00 n10 = 1.60524 
.nu.10 = 60.6 
r18 = -176.394 
d18 = Variable 
r19 = 60.531 
d19 = 6.00 n11 = 1.60524 
.nu.11 = 60.6 
r20 = 124.077 
d20 = 7.10 
r21 = .infin. 
d21 = 32.00 n12 = 1.51805 
.nu.12 = 64.2 
r22 = .infin. 
______________________________________ 
(r21, r22) = GB 
s) Stop 
Variable Focal Length 
separation 33.30 37.85 42.33 
______________________________________ 
d8 11.27 5.56 1.25 
d11 21.33 27.04 31.35 
d13 6.17 5.21 3.58 
d18 1.00 1.96 3.59 
______________________________________ 
r3: Diffractive Optical Surface 
C1 C2 C3 
4.66063e-04 -4.55072e-07 
5.17981e-10 
r7: Diffractive Optical Surface 
C1 C2 C3 
1.79630e-05 2.26701e-07 
-1.32203e-10 
______________________________________ 
TABLE 2 
__________________________________________________________________________ 
Condition 
Numerical Example 
No. 13 14 15 16 17 
__________________________________________________________________________ 
(13) 0.99856 
1.34858 
1.33194 
1.36191 
1.2841 
(14) 0.892517 
1.304911 
1.352071 
1.283969 
1.352646 
(15) 6.54831 
23.389 23.5523 
17.9448 
24.6082 
(16) 1.00225 
1.9814 2.02703 
1.97257 
1.95829 
(18) 0.974203 
0.973322 
0.955566 
0.981493 
0.998436 
(19) 2.35945 
8.172115 
11.18705 
7.026132 
4.026117 
(20) 0.53557 
1.07083 
0.96009 
1.05353 
1.10973 
(21) 0.645296 
1.162918 
1.243427 
1.125315 
1.297897 
(22) 0.284965 
0.293431 
0.215861 
0.279953 
0.200228 
(23) 0.88338 
1.74078 
1.79058 
1.73525 
1.72737 
(24) 0.89123 
1.75977 
1.80088 
1.74865 
1.73693 
(25) 1.16589 
1.1125 1.22099 
1.21153 
1.18851 
(26) 1.383112 
1.122101 
1.087375 
1.140986 
1.042183 
(27) 3.540393 
3.445142 
4.659265 
3.599603 
5.021953 
(30) 3.981408 
3.879022 
5.244359 
4.060547 
5.661969 
(3) 2.06e-03 
1.52e-03 
1.75e-03 
1.38e-03 
9.76e-04 
(4) 2.78e-06 
2.31e-06 
3.57e-06 
1.61e-06 
1.11e-06 
__________________________________________________________________________ 
TABLE 3 
______________________________________ 
Numerical Example 
13 14 15 16 17 
______________________________________ 
F1 -33.368 -65.824 -67.648 -65.582 
-65.2169 
F2 33.416 48.81 50.789 48.155 50.788 
F3 -43.651 -41.613 -45.865 -45.4376 
-44.625 
F4 51.784 41.972 40.846 42.792 39.131 
F5 132.553 128.865 175.02 135.001 
188.56 
Fbo1 257.682 268.819 333.037 350.089 
328.83 
Fbo2 819.72 
Fbo3 
Fbo4 158.5035 
Fbo5 83.186 
______________________________________ 
Incidentally, FIGS. 58A to 58D ard FIGS. 59A to 59D show the aberrations of 
the embodiment 13 in the wide-angle and telephoto ends, respectively. 
FIGS. 61A to 61D and FIGS. 62A to 62D show the aberrations of the 
embodiment 14 in the wide-angle and telephoto ends, respectively. FIGS. 
64A to 64D and FIGS. 65A to 65D show the aberrations of the embodiment 15 
in the wide-angle and telephoto ends, respectively. FIGS. 67A to 67D and 
FIGS. 68A to 68D show the aberrations of the embodiment 16 in the 
wide-angle and telephoto ends, respectively. FIGS. 70A to 70D and FIGS. 
71A to 71D show the aberrations of the embodiment 17 in the wide-angle and 
telephoto ends, respectively. 
As described above, the five lens units are used in total. Of these, a 
certain one is provided with a diffractive optical element whose phase is 
made appropriate to lessen astigmatism and distortion. In addition, the 
lateral chromatic aberration is corrected so well as to be suited to the 
high definition liquid crystal display. It is, therefore, made possible to 
achieve a zoom lens of telecentric system with the back focal distance 
elongated, while still maintaining good optical performance. 
In particular, according to the zoom lenses of the embodiments 13 to 17, 
based on the rules of design described before, the zoom ratio is increased 
to 1.3 or higher and the large aperture ratio is secured at about 1.8 in 
F-number. Despite these advantages, astigmatism and distortion are 
lessened and, while securing the back focal distance long enough to 
accommodate the color combining prism or like optical elements and various 
optical filters or like optical elements, longitudinal chromatic 
aberration is corrected well. It is, therefore, made possible to realize a 
zoom lens of telecentric optical system having good optical performance 
maintained stable over the entire zooming range and over the entire 
focusing range. In addition, a liquid crystal video projector can be 
realized which is adapted to be used with that zoom lens.