Diffractive optical element both surfaces of which comprise diffractive surfaces

The invention has for its object to reduce the overall length of a single lens using a diffractive optical element, and provides a diffractive optical element applicable to an optical system for cameras such as silver salt cameras, and electronic cameras, in which both surfaces of the single lens are constructed of diffractive surfaces, are plane surfaces or have curvature, and comprise diffractive surfaces having, in order from a subject side thereof, positive power and positive power, positive power and negative power, and negative power and positive power.

BACKGROUND OF THE INVENTION 
The present invention relates generally to a diffractive optical element 
(hereinafter DOE for short) comprising a diffractive surface having lens 
action based on diffraction phenomena, and more particularly to a lens 
system comprising a single lens both surfaces of which are constructed of 
diffractive surfaces. 
In optical systems used on silver salt cameras, electronic cameras or the 
like, much more lenses and much more sophisticated arrangements are 
required to satisfy much higher performance, as represented by phototaking 
lenses. However, all available optical systems are not always structurally 
complicated; some optical systems are made up of one single lens. One 
example is an active range finder as shown in FIG. 1. This is based on the 
principle of trigonometric measurement as explained briefly below with 
reference to FIG. 1. Reference numeral 11 is an infrared-emitting diode or 
IRED; 12 a light projecting lens element for projecting infrared light 
emitted from IRED 11; 13 a subject; 14 a light receiving element for 
receiving light reflected from the subject 13; and 15 a position sensing 
device or PSD for sensing the position of the received light. IRED 11 
emits infrared light, which is in turn projected through the projecting 
lens element 12 on the subject 13. Light reflected by the subject 13 is 
focused on PSD 15 through the receiving lens element 14 positioned away 
from the projecting lens element 12 by a base length. The subject distance 
is calculated from position information on PSD 15. 
Light-projecting, and -receiving lens elements used on such an active range 
finder are often made up of one single lens. Though some lens elements are 
produced in the form of prisms having a reflecting surface, yet they are 
fundamentally composed of one single lens. These light-projecting, and 
-receiving lens elements are unavoidably increased in both diameter and 
thickness because brightness is of importance. 
A lens element used on photometric devices for external photometry is again 
made up of a single lens. This is mounted within a camera body separately 
from other parts such as a phototaking lens and a finder lens to make a 
photometric measurement of the subject, as explained below with reference 
to FIG. 2. Reference numeral 21 is a condenser lens; 22 a filter; and 23 a 
light-receiving element. The filter 22 is to bring the spectral 
sensitivity of the light-receiving element 23 in conformity to film 
properties, and has fundamental action on cutting infrared light. The 
condenser lens 21 is often made up of one single lens for the purpose of 
achieving compactness and cost reductions. However, this lens is again 
unavoidably increased in size because sufficient brightness and the angle 
of photometry in conformity to the field angle of a photo-taking lens are 
needed. 
The phototaking lens, too, is made up of a plastic single lens when it is 
used on inexpensive cameras as represented by a combined lens and film 
camera which, as schematically shown in FIG. 3, comprises a phototaking 
lens 31 made up of a single lens, an aperture stop 32, and a film surface 
33. The film surface 33 is bent along its longitudinal direction and 
concave on the subject side. A single lens has some degrees of freedom in 
reducing spherical aberration or low order coma, but has no room for a 
choice of bending shape. In other words, the single lens is often designed 
in the form of a meniscus lens having a concave surface directed toward a 
stop, and so there is no room for making its overall length short because 
lens shape is predetermined in view of correction of aberrations. 
For recently developed cameras, on the other hand, considerable size 
reductions have been desired. Many parts are mounted in a camera body. To 
achieve compactness, it is required to reduce the number and size of these 
parts. For such various lens elements as mentioned above, too, it is 
required to reduce their size. In view of such situations, an object of 
the present invention is to make a single lens smaller, especially thinner 
than ever before, by making use of a diffractive optical element. 
Here, the diffractive optical element or DOE is explained. For details of 
DOE, however, see "Optics", Vol. 22, pp. 635-642, and 730-737. 
While a conventional lens is based on the refraction of light at a medium 
interface, DOE is based on the diffraction of light. Now consider the 
incidence of light on such a diffraction grating as shown generally in 
FIG. 4. Emergent light upon diffracted satisfies the following equation 
(a): 
EQU sin .theta.-sin .theta.'=m.lambda./d (a) 
where .theta. is the angle of incidence, .theta.' is the exit angle, 
.lambda. is the wavelength of light, d is the pitch of the diffraction 
grating, and m is the order of diffraction. 
Therefore, if the pitch of a ring form of diffraction grating is properly 
determined according to equation (a), it is then possible to converge 
light on one point, i.e., impart lens action to the diffraction grating. 
Here let r.sub.j and f the radius of a j-th ring on the grating and the 
focal length of the diffractive surface, respectively. Then, the following 
equation (b) is satisfied in a region of a first approximation: 
EQU r.sub.j.sup.2 =2j.lambda.f (b) 
For a diffraction grating, on the other hand, a bright-and-dark ring form 
of amplitude-modulated type grating, and a phase-modulated type grating 
with a variable refractive index or optical path length has been proposed. 
In an amplitude-modulated type DOE, for instance, the ratio between the 
quantity of incident light and the quantity of the first order of 
diffracted light is about 6% at most because plural orders of diffracted 
light are produced. Hereinafter, this ratio will be called the 
"diffraction efficiency". Even though this amplitude-modulated type DOE is 
modified as by bleaching into the phase-modulated type, the diffraction 
efficiency is about 34% at most. If the same phase-modulated type DOE as 
mentioned above is modified such that its section is of such saw-toothed 
shape as depicted in FIG. 5(a), however, the diffraction efficiency can 
then be increased to 100%. Such a DOE is called a kinoform. In this case, 
the height of each tooth is given by 
EQU h=m.lambda./(n-1) (c) 
where h is the height of the tooth, and n is the index of refraction of 
material. 
As can be predicted from equation (c), a diffraction efficiency of 100% is 
achievable at only one wavelength. The kinoform shape may be stepwise 
approximated as shown in FIG. 5(c) to obtain a so-called binary optical 
element. This element can be relatively easily fabricated by lithography 
techniques. As well known in the art, the binary optical element has a 
diffraction efficiency of 81% to a four-step approximation, 95% to an 
eight-step approximation, and 99% to a sixteen-step approximation. 
DOEs may be designed by some known methods. However, the present invention 
makes use of an ultra-high index method as set forth in an article 
"Mathematical equivalence between a holographic optical element and 
ultra-high index lens", J. Opt. Sos. Am. 69, pp. 485-487 or an article 
"Using a conventional optical design program to design holographic optical 
elements", Opt. Eng. 19, pp. 649-653. That is, the DOE is known to be 
equivalent to a refractive surface having null thickness and an ultra-high 
refractive index. 
A DOE has two important features when used in the form of a lens. The first 
feature is aspheric action. If the pitch of a diffraction grating is 
properly determined, it is then possible to converge light perfectly on 
one point. This is tantamount to reducing spherical aberration to zero by 
use of an aspheric surface. The second feature is that chromatic 
dispersion is very large or, in another parlance, an Abbe number of -3.45 
is obtainable. Chromatic aberration several tens times as large as that of 
a conventional refractive material is produced with a minus sign or in the 
opposite direction. Large dispersion offers the gravest problem when the 
ODE is applied to a lens element used under natural light. The refractive 
index of DOE at any wavelength is given by 
EQU n(.lambda.)=1+[n(.lambda..sub.0)-1].multidot..lambda./.lambda..sub.0(d) 
where k is any wavelength, n(.lambda.) is the refractive index of DOE at 
wavelength .lambda., .lambda..sub.0 is a reference wavelength, and 
n(.lambda..sub.0) is the refractive index of DOE at wavelength 
.lambda..sub.0. 
An example of applying such a DOE to an active range finder is disclosed in 
JP-A 7-63982. This publication shows that zooming is carried out with a 
converter lens inserted on the IRED side of a master lens, and that the 
master lens is in a plano-convex form while the converter lens is in a 
plano-concave form, with each plane made up of a diffractive surface. 
Thus, zooming is achievable while the master lens remains fixed. However, 
this publication says nothing about how compactness is achieved. 
An example of applying a DOE to a phototaking lens is set forth in an 
article "Hybrid diffractive-lenses and achromats", Appl. Opt. 27, pp. 
2960-2971. This prior publication shows an example of calculation in the 
case where, based on the principle of correction of paraxial chromatic 
aberration, a diffractive lens having an Abbe number of -3.45 is used in 
combination with a conventional refractive lens to make correction for 
chromatic aberration. Specifically, the publication shows a lens with the 
object-side surface constructed of a convex surface and the image-side 
surface constructed of a plane surface, wherein a diffractive surface is 
formed on the image-side plane, and refers to the achromatization of axial 
chromatic aberration and the remaining secondary spectrum. However, this 
publication does neither refer to chromatic aberration of magnification 
and other aberrations nor give any specific design data. 
WO95/18393 shows an arrangement wherein a positive meniscus lens convex on 
a subject side and a stop are positioned, and an image-side surface of the 
positive lens is constructed of a diffractive surface. This publication 
teaches that chromatic aberration is corrected by a combined refractive 
and diffractive system, and alleges that high performance is achieved 
without any increase in the number of lens parts. 
Both publications directed to the application of DOEs to phototaking lenses 
are primarily to make correction for chromatic aberration and state that 
compactness is achievable by reason of any increase in the number of lens 
parts. However, they fail to provide a disclosure of how the overall 
length of a single lens is reduced. 
SUMMARY OF THE INVENTION 
In view of such problems with the prior art, an object of the present 
invention is to reduce the overall length of a single lens by making use 
of a diffractive optical element, and to provide a diffractive optical 
element applicable to optical systems for cameras such as silver salt 
cameras, and electronic cameras. 
The aforesaid object is achievable by the provision of a diffractive 
optical element, characterized in that both surfaces of said element are 
constructed of diffractive surfaces. 
Preferably in this case, said both surfaces are constructed of plane 
surfaces. It is also preferable that the diffractive optical element 
comprises a diffractive surface of positive power and a diffractive 
surface of negative power in order from a subject side thereof 
A detailed account will now be given of why such an arrangement is used, 
and how it acts. 
The diffractive optical element of the present invention is characterized 
in that both surfaces thereof are constructed of diffractive surfaces. The 
present invention also provides a lens system comprising a diffractive 
optical element characterized in that both surfaces of said diffractive 
optical element are constructed of diffractive surfaces. 
To shorten the overall length of a lens by constructing both its surfaces 
of plane surfaces, it is required to provide diffractive surfaces on both 
its surfaces thereby making correction for coma, as will be described 
later. The overall length of a lens comprising a surface having curvature 
may be made short by bring the image-side principal point close to the 
subject side. To this end, however, it is required to use a strong 
meniscus form of lens, resulting in an increase in the quantity of 
aberrations produced due to strong surface power. If both surfaces of such 
a lens are constructed of diffractive surfaces, it is then possible to 
make correction for these aberrations and so shorten the overall length of 
the lens. 
According to one specific embodiment of the present invention designed to 
shorten the overall length of a lens element, there is provided a 
diffractive optical element whose two surfaces are constructed of 
diffractive surfaces, wherein said diffractive surfaces are constructed of 
plane surfaces. 
In a conventional lens element used with an active range finder or a 
photometric device, the power of the lens surface becomes too strong with 
a very reduced F-number, leading to considerable increases in the amount 
of sag of the lens surface (a change in the distance from the midpoint of 
an arc to the midpoint of its chord). For this reason, there are increases 
in both lens diameter and lens thickness, which make it difficult to 
diminish lens size. Size reductions may be achieved by allocating power to 
both surfaces of a lens, but this is unfeasible because it is unavoidably 
required to concentrate the power on the subject-side surface of the lens 
for the purpose of correction of aberrations. When constructing a thin 
lens, a diffractive surface is more favorable than a refractive surface 
because the amount of sag can be reduced to zero. 
Referring again to a kinoform type of diffractive surface, it can 
substantially be regarded as being a plane surface although there are 
asperities of the order of a few wavelengths to several tens of 
wavelengths, as can be seen from equation (c). When the kinoform type of 
diffractive surface is applied to a lens, it is possible to make the lens 
thin to such degrees as determined depending on lens-processing and 
fabricating conditions. By designing a diffractive optical element in a 
plane plate lens form whose both surfaces are constructed of plane 
surfaces, it is therefore possible to achieve considerable lens thickness 
reductions. Reference is here made to the reason the two surfaces are 
constructed of diffractive surfaces for the purpose of correction of 
aberrations. 
When a lens element is used at a sufficiently small field angle, only the 
correction of spherical aberration is needed; that is, the spherical 
aberration can be well corrected by one diffractive surface having 
aspheric action. However, when the field angle used is wide or, more 
specifically, when the field angle is about 5.degree. for a lens element 
used on a range finder and about 20.degree. for a lens element used on a 
photometric device, it is required to make correction for not only 
spherical aberration but coma as well. With a plane plate form of lens, 
however, coma cannot be prevented. To make correction for both spherical 
aberration and coma at the same time, it is thus required that both 
surfaces of the plane plate form of lens be constructed of plane surfaces. 
Referring here to FIG. 6, reference numeral 61 is a diffractive surface on 
a subject side, and 62 a diffractive surface on the opposite side, with a 
stop in coincidence with the surface 61. When parallel light is incident 
from an object point at infinity on the diffractive surface 61, let y and 
y' denote the heights of a marginal ray 64 and a principal ray 65 at each 
surface, respectively. According to the ultra-high index method, the 
spherical aberration and coma produced at the subject-side diffractive 
surface 61 are substantially reduced to zero because its refractive index 
is very large whereas its curvature is very small. At the opposite 
diffractive surface 62, on the other hand, negative spherical aberration 
and positive coma are produced, resulting a performance drop. In this 
case, it is difficult to make correction for the positive coma produced at 
the diffractive surface 62. From an article "Design of a wide field 
diffractive landscape lens", Appl. Opt. 28, pp. 3950-3959, it is found tha 
t 
EQU SI*=SI (e) 
EQU SII*=SII+(y'/y)SI (f) 
where SI and SII are third-order spherical aberration and coma 
coefficients, respectively, when the stop is in close contact with the 
surface 61, and SI* and SII** are similar aberration coefficients when the 
stop is in no coincidence with the surface 61. In the case of FIG. 6, SII 
is designed to be canceled by SI at the diffractive surface 62 according 
to equation (f). In this case, SI has a negative large value due to a 
small value of y'/y. It is thus required to produce positive large 
spherical aberration at the diffractive surface 61, thereby canceling the 
negative spherical aberration produced at the diffractive surface 62. 
In order to enable the plane form of lens to be used at a wide field angle, 
it is thus important to make correction for spherical aberration and coma, 
and so it is required to construct both its surfaces of diffractive 
surfaces. The diffractive surfaces are characterized in that the 
subject-side diffractive surface has diverging action at its peripheral 
portion while the opposite diffractive surface has converging action at 
its peripheral portion. 
As explained above, large spherical aberrations with opposite signs 
produced at both sides of the lens are designed to be mutually canceled, 
and this imposes some severe limitation on the decentering accuracy of 
both the surfaces. Such a problem can be solved by making lens thickness 
larger relative to lens diameter, because the quantity of spherical 
aberration necessary for correction of coma can be so reduced that both 
surfaces can be designed with acceptably low decentering accuracy. That 
is, it is desired to satisfy the following condition (1): 
EQU 0.3&lt;d/.phi.&lt;1.5 (1) 
where d is the center thickness of a diffractive optical element and .phi. 
is the diameter of the diffractive optical element. 
When the thickness of the lens element is less than the lower limit of 0.3 
in condition (1), the decentering accuracy placed on both its surfaces 
becomes severe because the positive and negative spherical aberrations 
produced thereat become large. It is contrary to the object of reducing 
the overall length of the lens element that the thickness of the lens 
element exceeds the upper limit of 1.5 in condition (1). 
In another more specific embodiment of the present invention, both surfaces 
of a diffractive optical element are constructed of diffractive surfaces, 
and positive and negative powers are given to the diffractive surfaces in 
order from a subject side of the diffractive optical element, thereby 
shortening the overall length thereof. 
Such a positive-negative power profile or a so-called telephoto type power 
profile enables the overall length of the lens element to be shortened 
because the principal point position can be moved toward the subject side 
irrespective of whether the lens surface is a plane surface or a surface 
having curvature. When the aforesaid power profile is applied to a 
conventional refractive system, it is impossible to make sufficient 
correction for aberrations because when power just enough to shorten the 
overall length of the lens element is imparted to a surface, that surface 
has too large a curvature. However, the use of the diffractive system can 
make a reasonable compromise between correction of aberrations and a 
decrease in the overall length of the lens element. 
Herein it is desired to satisfy the following condition (2) or (3): 
EQU -20&lt;f.sub.2 /f&lt;-2 (2) 
EQU -5&lt;f.sub.2 /f&lt;-0.5 (3) 
where f is the focal length of the diffractive optical element, and f.sub.2 
is the focal length of the diffractive surface that is not opposite to the 
subject side. 
Condition (2) is generally applied to a lens element where a high level of 
aberration correction is needed, for instance, a phototaking lens element. 
A plane plate form of diffractive lens is practically unacceptable for a 
phototaking lens even if it is constructed of an inexpensive single lens, 
because some considerable chromatic aberration is produced. Even with a 
plano-convex form of lens element such as one explained with reference to 
the prior art, it is impossible to obtain sufficient performance because 
coma remains under-corrected and large chromatic aberration of astigmatism 
is produced. This is true of even when a diffractive surface is used with 
the plano-convex form of lens element. To make good correction for 
monochromatic aberration and chromatic aberration, therefore, it is 
required that both surfaces be constructed of lens surfaces having 
curvature, and that one diffractive surface be used. Only by use of this, 
however, it is difficult to shorten the overall length of the lens 
element. In the practice of the present invention, therefore, both 
surfaces are constructed of diffractive surfaces, and are provided with 
positive power and negative power in order from the subject side. It is 
then desired to satisfy condition (2). When the negative power is less 
than the lower limit of -20 in condition (2), no action is obtained on 
shortening the overall length of the lens element. Negative power 
exceeding the upper limit of -2 in condition (2) is preferable to shorten 
the overall length of the lens element, but is unfavorable for the present 
invention because large chromatic aberration of magnification is 
introduced therein. Because of large dispersion, a diffractive surface 
yields noticeable chromatic aberration relative to power changes. 
On the other hand, condition (3) is generally applied to a lens element 
used on a range finder or a photometric device. The overall length of this 
lens element can be shortened by giving thereto power relatively stronger 
than defined by condition (2), because chromatic aberration offers little, 
if any, problem. It is then desired to satisfy condition (3). When the 
negative power is less than the lower limit of -5 in condition (3), no 
action is obtained on shortening the overall length of the lens element. 
Negative power exceeding the upper limit of condition (3) is preferable to 
shorten the overall length of the lens element, but make it unacceptably 
difficult to make correction for monochromatic aberration. 
As explained with reference to condition (2), it is preferred that both 
surfaces have curvature, because there is obtained a high-performance lens 
element having a high degree of freedom in correction of aberrations. It 
is herein preferable that the DOE is of such shape that a convex surface 
thereof is directed toward the subject side. It is consequently possible 
to allocate most of the positive power of the subject-side surface to the 
refractive surface, so that the power of the diffractive surface can be 
reduced. The smaller the power of the diffractive surface, the larger the 
inter-pattern space of the diffractive pattern, and hence the easier the 
pattern processing. If the surface that is not opposite to the subject 
side is constructed of a concave surface, as in the case of a phototaking 
lens element or a lens element used on a range finder, such as those 
explained in the examples to be given later, it is possible to allocate 
most of the negative power to the refractive surface, so that the power of 
the diffractive surface can be reduced. In other words, the lens element 
is preferably of meniscus shape with a convex surface directed toward the 
subject side. 
In such a positive-negative power profile, it is preferred that a large 
space is given between both powers because a telephoto arrangement is 
easily achievable. In other words, it is preferable for correction of 
aberrations to make lens thickness as large as possible, because the 
larger the lens thickness, the lower the power of each diffractive surface 
can be. It is then desired to satisfy the following condition (4): 
EQU 0.2&lt;d/f&lt;1.5 (4) 
where d is the center thickness of the diffractive optical element, and f 
is the focal length of the diffractive optical element. 
When the thickness of the diffractive optical element is less than the 
lower limit of 0.2 in condition (4), it is difficult to make correction 
for monochromatic aberration because the power of each surface becomes too 
strong to reduce the overall length of the single lens. When the thickness 
of the diffractive optical element exceeds the upper limit of 1.5 in 
condition (4), the size of the single lens element becomes too large due 
to the thickness of the DOE itself. In this connection, it is noted that 
condition (4) is not applied to the DOE when it is designed in the form of 
a prism having a reflecting surface. 
When both surfaces are plane surfaces, there arises a problem that the 
inter-pattern space of the diffraction pattern becomes too narrow because 
all powers are allocated to the diffractive surfaces. Consequently, it is 
very difficult to process and fabricate DOEs. Further, if the space 
becomes narrow a few times as fine as wavelength, the diffractive optical 
element is no longer regarded as being a plane form of DOE. By 
constructing both surfaces of a plane plate form of lens of diffractive 
surfaces having positive power, however, it is possible to improve 
processability because power can be allocated to both surfaces to make the 
inter-pattern space wide. 
As already explained with respect to a plane plate form of lens, the lens 
is designed such that, for the purpose of correction of aberrations, the 
subject-side surface has diverging action while the opposite surface has 
converging action. When, in this case, paraxial power-converging action is 
given to the subject-side surface, production difficulty is expected, 
because the converging action changes to the diverging action from the 
center to periphery of the lens, leading to a shape where positive power 
is mixed with negative power. If negative power is allocated to the 
subject-side surface of a plane plate form of lens and positive power is 
allocated to the opposite side thereof, however, it is then possible to 
fabricate the plane plate form of lens easily because a reasonable 
compromise can be made between processability and correction of 
aberrations. In this case, it is preferable to use the higher orders of 
diffracted light because the inter-pattern space of the diffraction 
pattern remains narrow. In this regard, it is noted that the higher the 
order of diffraction, the lower the diffraction efficiency is when the 
wavelength used differs from the designed wavelength. In DOEs used over a 
wide wavelength region, the designed order of diffraction is at most about 
second order, as is the case with a phototaking lens. For a lens system 
used with a range finder, on the other hand, it is possible to use at 
least the tenth order of diffraction because the wavelength region of IRED 
is narrow. In this case, too, the depth of the diffraction pattern becomes 
large as the inter-pattern space of the diffraction pattern become wide. 
Still other objects and advantages of the present invention will in part be 
obvious and will in part be apparent from the specification. 
The present invention accordingly comprises the features of construction, 
combinations of elements, and arrangement of parts which will be 
exemplified in the construction hereinafter set forth, and the scope of 
the present invention will be indicated in the claims.