Optical systems employing refractive and diffractive optical elements to correct for chromatic aberration

Optical structures are disclosed that comprise selected combinations of refractive and diffractive type optical elements wherein net chromatic aberrational effects are minimized in images formed by said structures. With the disclosed structures, chromatic aberrational contributions from each type of optical element, having characteristically opposite algebraic sense, are essentially cancelled out by means of proper distribution of optical power plus suitable arrangement and relative location of the said optical elements. Advantages over the prior art are demonstrated in four general types of optical structures.

BACKGROUND OF THE INVENTION 
All optical systems suffer from image aberrations. The ultimate quality and 
performance of an optical system is determined by the extent to which 
aberrations, particularly chromatic aberrations, are corrected. In the 
present invention, significant improvement is achieved over the prior art 
by minimizing chromatic aberrations. Additional advantages are obtained by 
reducing the number of optical elements needed to achieve equivalent or 
superior results. 
The present invention relates generally to improved structure for 
assemblies of optical systems in which refractive and diffractive optical 
elements are combined advantageously to achieve significant improvement in 
chromatic aberration. The diverse characteristic properties of these two 
types of optical elements are cancelled out by suitably opposing and 
balancing these properties against each other to achieve hitherto 
unobtainable image quality. 
In the prior art, achromatic lens assemblies have been employed with 
limited success since the time of Isaac Newton. In these achromats, two 
optical elements (one with positive power and one with negative power) 
made from conventional glass materials (e.g. crown and flint glass) with 
differing dispersive characteristics are combined to reduce net chromatic 
aberrational effects. Ever increasing sophistication with both methods and 
materials has been applied to the fundamental problem of correcting 
chromatic aberration, and powerful computational methods combined with 
development of special glass materials have achieved significant 
improvement. It is typical of such effort, however, that ever smaller 
incremental gains are achieved at continually increasing cost. 
In examples of the immediate prior art, the use of binary optics has been 
proposed (reference 1) to correct axial chromatic aberration in an 
infrared optical system and (reference 2) to correct primary lateral 
chromatic aberration without aggravating the secondary chromatic 
aberration of an Erfle eyepiece. 
Reference 1 is a paper by Gary. J. Swanson and Wilfred. B. Veldcamp, SPIE 
Poceedings, Vol. 885, Paper #22, 1988. They propose using binary optics to 
correct axial chromatic aberration. In binary optics, the functional 
effect of a grating is achieved with grooves that are etched with typical 
fabrication processes employed in microelectronics. Their system has 
serious deficiencies, because as numerical aperture increases, marked 
spherochromatism is exhibited. Consequently, the minimum useable f-number 
is severly limited. This limitation is particularly unfortunate in 
advanced infrared optical systems that require low f-numbers (typically 
f/1.0 to f/1.5) to help reduce size and weight. 
Reference 2 is by D. Shafer and T. McHugh of the Perkin-Elmer Corporation: 
"Binary Optics Design Surprises for the 1990's," SPIE, Orlando, Fla (March 
1989). Binary optics are used to correct lateral chromatic aberration of 
an Erfle eyepiece without aggravating secondary chromatic aberration. 
Unfortunately, their approach is applicable only to systems with low 
numerical aperture (high f-number) and modest fields of view, as is 
characteristic of the Erfle eyepiece. As the aperture stop is opened, 
spherochromatism, chromatic coma, axial primary color, and axial secondary 
color are aggravated severely. Similarly, as field of view increases, 
chromatic distortion and chromatic coma are aggravated severely. 
SUMMARY OF THE INVENTION 
The present invention has many important and novel features. Many 
deficiencies of the prior art are substantially reduced or eliminated, 
such as those associated with f-number and field of view. Several kinds of 
chromatic aberration are corrected including axial primary, axial 
secondary, lateral primary, and lateral secondary. Correction is provided 
for all orders of spherochromatism, chromatic coma, and chromatic 
distortion. In the spectral intervals between the three selected design 
wavelengths, residual chromatic aberrations are significantly reduced. 
In addition, a novel method is disclosed for correcting field curvature for 
all orders without introducing lateral chromatic aberrations. Because 
elements made of special optical glass need not be employed, cost is 
reduced and substantial resistance to radiation damage is obtained. 
Finally, because these improvements are achieved with fewer optical 
elements in the optical structure, cost, size, and weight are reduced. 
The use of this invention will improve significantly the image quality of 
optical systems including both refractive and catadioptric types and will 
apply over wavelengths ranging from the ultraviolet to the infrared. The 
structure disclosed for axial chromatic aberration, axial secondary color, 
and spherochromatism is well suited for telephoto lens systems. The 
structure that is disclosed to correct lateral chromatic aberration, 
secondary lateral color, chromatic distortion and chromatic coma is 
particularly effective for optical systems employing external pupils. The 
structure disclosed for correcting field curvature without aggravating 
lateral chromatic aberration is particularly useful for optical systems 
with wide fields of view and for systems employing Petzval type lenses. 
The considerable advantages of this invention are achieved through the use 
of carefully selected combinations and distributions of refractive and 
diffractive optics that are employed so that net resulting aberrational 
effects are substantially reduced relative to what can be achieved with 
the exclusive use of refractive optical components. 
Examples of typical wavelength response will demonstrate the value of 
forming optical structures employing this invention. Chromatic aberrations 
result from the varying characteristic response as a function of 
wavelength for the optical element. An important example is the variation 
of focal length along the central axis. For a typical glass achromat, 
consider that the effective focal length (EFL) as a function of wavelength 
exhibits a minimum value near the central wavelength region over which it 
operates. On the other hand, a corresponding EFL of a typical 
glass-diffractive achromat exhibits a maximum value near its central 
wavelength region of operation. As will be explained subsequently, these 
characteristic aberrations of opposite algebraic sense can be matched so 
that they essentially cancel each other to reduce overall chromatic 
aberration in the complete lens structure. Finally, the special optical 
glasses that are eliminated have at least two disadvantages: they are more 
expensive and have substantially less resistance to damage from radiation.

DETAILED DESCRIPTION OF THE DISCLOSURE 
In the following detailed description and in the several figures provided, 
like elements are identified with like reference numerals. 
To assure good image quality, typical high quality optical systems require 
proper corrections for chromatic aberrational effects. These aberrations 
include primary axial color, primary lateral color, secondary axial color, 
and secondary lateral color. With primary correction, proper correction is 
achieved at only two specific design wavelengths within the operating 
spectral interval. With secondary correction, proper correction is 
achieved at three specific design wavelengths. Aberrations for primary 
axial color and primary lateral color are usually corrected through the 
use of either cemented or air-spaced achromats. 
Secondary color correction, however, has proven to be difficult in the 
prior art. Such correction generally requires the use of expensive special 
glass materials. The utility of special glass materials results from their 
unusual characteristics of index of refraction as a function of wavelength 
as compared to conventional glass materials. Some examples of such special 
glasses are KZFS1, KZFSN2, KZFSN5, and LGSK2. These special glasses are 
needed because if normal glasses are used to assemble an achromat, 
secondary color contributions (having the same algebraic sense) from the 
two elements are additive. 
The significant advantages obtained with this invention result from 
assembling and combining the two types of optical elements with diverse 
(i.e. having opposite algebraic sense) spectral characteristics and 
chromatic aberrational contributions into structures exhibiting marked 
improvement in net chromatic aberrational effects over approaches employed 
in the prior art. This improvement results from suitably arranging and 
locating optical elements relative to each other plus appropriately 
distributing optical power of these elements throughout the structure so 
as to cancel out essentially the chromatic aberrational contributions from 
each of the two types of optical elements. 
A glass-diffractive element comprises at least two portions. One portion 
functions refractively and contains at least one refractive element. The 
second portion functions diffractively and contains at least one 
diffractive element. The diffractive portion is applied to, formed upon, 
or otherwise physically associated with the refractive portion. 
Diffractive elements can take several physical forms, but all forms 
function on the basis of the grating equation: 
EQU sin A=nL/d-sin I 
where the following notation applies: 
A: angle of diffraction 
I: angle of incidence 
L: wavelength 
n: order of diffraction 
d: spacing of adjacent lines on the grating 
Diffractive elements can be circular (Fresnel zone plate), rectangular, or 
of any other suitable shape. They can be formed with ruled grooves or 
etched lines. They also can be blazed for enhanced performance at 
particular wavelengths. One form of etched diffractive elements, called 
binary optics, is applicable for purposes of this invention. 
In the prior art, two approaches are employed for making achromatic optical 
assemblies with perfect correction at three selected design wavelengths. 
In the first approach, conventional glass achromats are replaced with 
apochromats, which are expensive. An apochromat consists of at least two 
refractive optical elements, at least one of which is made of special 
optical glass. In the second approach, more refractive optical elements 
are inserted into the system to reduce the optical power demanded of each 
individual element. Unfortunately with either of these approaches, optical 
systems become complicated and suffer from the higher orders of spacial 
and chromatic aberrations. 
With the present invention, these fundamental problems are solved by 
utilizing to advantage the opposite algebraic sense for secondary axial 
chromatic aberration of the two different types of achromats previously 
described, i.e. glass-refractive and glass-diffractive. Proper 
distribution of optical power among glass-refractive and glass-diffractive 
achromats can correct simultaneously for contributions to both primary and 
secondary axial chromatic aberration. With this construction, special 
glasses typically used in the prior art are not necessary. 
An additional advantage of the combined glass-diffractive lens structure is 
that optical power demanded from each individual optical element of the 
achromat is reduced but in a manner different from that employed in the 
prior art with glass-refractive structures, i.e. not by merely introducing 
more refractive elements. With the present invention, optical power 
required from individual elements can be reduced because in a 
glass-diffractive achromat only elements (both refractive and diffractive) 
with positive optical power are needed; whereas in an glass-refractive 
achromatic lens both positive and negative elements must be employed. As a 
result, structures employing glass-diffractive elements as prescribed by 
this invention achieve significant improvement in Petzval curvature, 
higher order spacial aberrations, and higher order chromatic aberrations. 
A further application of this invention is to employ glass-diffractive 
elements to correct for primary lateral color. When using a 
glass-diffractive element with a very small amount of primary axial 
chromatic aberration near the image plane, a significant amount of 
beneficial primary lateral chromatic aberration will be introduced as a 
result of the large ratio of chief ray height to marginal ray height. A 
chief ray lies at the edge of the image; the marginal ray lies at the 
center of the image. Although a conventional glass doublet performs a 
similar function, its use generally upsets the correction for the Petzval 
curvature and introduces higher order aberrations. 
An additional advantage of this invention is the use of combinations of 
glass-diffractive elements to correct for chromatic distortion. Such 
correction is related to the approach just described for introducing 
beneficial primary lateral chromatic aberration. If a corrective higher 
order (i.e. third order and higher order) aspherical wavefront is encoded 
in the diffractive portion of the glass-diffractive element described 
above, chromatic distortions of all orders can be corrected 
simultaneously. Such encoding is achieved, for example, by varying 
appropriately the spacing between lines of a Fresnel zone plate as a 
function of radius. 
FIG. 1 shows a conventional glass-refractive achromat with two elements. It 
consists of an assembly of a crown glass element 2 with positive optical 
power and a flint glass element 4 with negative optical power. FIG. 2 
shows a comparable glass-diffractive achromat assembled with a 
conventional refractive element 6 of positive optical power and a 
diffractive element 8 also with positive optical power applied to or 
formed upon the refractive element. It is important to note that typical 
diffractive elements are extremely thin and occupy virtually zero space in 
optical structures that employ them. 
FIG. 3 illustrates some significant differences in performance of these two 
achromats involving the effective focal length (EFL) that is exploited to 
great advantage in this invention. It is seen in this figure that EFLs as 
a function of wavelength for (a) a typical refractive glass achromat and 
(b) for a typical glass-diffractive achromat are of significantly 
different shape. Although the vertical scale is greatly expanded, FIG. 3 
shows that for a typical glass-refractive achromat, minimum EFL occurs in 
the central wavelength region, while at the outer wavelengths EFLs are 
longer. For the glass-diffractive achromat, maximum EFL occurs in the 
central wavelength region, while shorter EFLs pertain in the outer 
wavelength regions. 
This marked difference in performance results from the opposite algebraic 
signs for the associated Abbe numbers for glass refractive elements and 
for diffractive elements. Abbe number is defined as (N2-1)/(N1-N3). The N 
values refer to index of refraction associated with corresponding 
wavelengths having increasing values: L1, L2, and L3. Because the Abbe 
number for any kind of glass is always positive, EFLs for central 
wavelengths over the spectral range of a glass achromat must be shorter 
than those for outer wavelengths. It follows that secondary axial 
chromatic aberration cannot be corrected properly using a series of 
different glass achromats. 
The novel method employed in this invention for correcting chromatic 
aberration is to utilize the opposite algebraic sense previously 
established in this disclosure for the secondary axial chromatic 
aberrations of these two different types of achromats. By properly 
distributing optical power among a plurality of achromats, both primary 
axial and secondary axial chromatic aberrations can be corrected 
simultaneously. Thus, it has been shown (1) that there is no need for 
optical elements made of special glass materials as required in the prior 
art and (2) that the optical power required of each individual optical 
element of the achromats is reduced. Further, significant reductions are 
achieved in Petzval curvature, higher order aberrations, and higher order 
chromatic aberrations. 
Major advantages of this invention over the prior art will be illustrated 
schematically and described in detail with the aid of four general optical 
structures that span a significant range of practical and high quality 
applications. 
FIG. 4 illustrates two general schematic diagrams for eyepiece lenses. FIG. 
4a shows a typical eyepiece employing conventional construction. FIG. 4b 
shows a comparable eyepiece lens that employs the principles of this 
invention. In the conventional structure (FIG. 4a), lens group 10 contains 
a plurality of refractive elements with positive optical power overall. 
Eye 13 is located near aperture stop 14 at the left end of optical axis 
11; image 12 being viewed by the eye is shown at the far end of the 
optical axis at the right. 
In the structure of FIG. 4a, it is difficult to correct simultaneously for 
lateral color, distortion, chromatic distortion, and field curvature. 
Further, this structure contains more optical elements than that of FIG. 
4b. 
In the glass-diffractive structure of FIG. 4b, lens group 16 with positive 
optical power contains at least one refractive optical element and at 
least one diffractive optical element. In this example, diffractive 
element 17 is placed between the third and fourth refractive elements of 
lens group 16. It is understood that detailed arrangements and locations 
of optical elements within lens group 16 other than those described in 
this example are consistent with the spirit of this invention. Eye 19 and 
aperture stop 18 are located in a fashion similar to that shown in FIG. 
4a. Image 20 being viewed by the eye is shown at the far end of optical 
axis 15. In schematic diagram FIG. 4b, the significantly smaller size of 
the structure obtained employing the principles of this invention is 
evident when compared to the corresponding conventional structure. In this 
eyepiece structure, lateral color, distortion, chromatic distortion, and 
field curvature are easily corrected by employing a single diffractive 
optical element. The structure contains fewer refractive optical elements, 
and is more compact than that of FIG. 4a. Further, eye relief is long, and 
field of view is large. 
FIG. 5 illustrates two general schematic diagrams for Petzval lenses that 
in this example contain an internal aperture stop (also called a pupil). 
Each of these structures employs three lens groups. FIG. 5a shows a 
typical conventional structure for a Petzval lens; FIG. 5b shows a 
comparable structure employing the principles of this invention. 
In the conventional structure, input lens group 21, located at the left end 
of optical axis 23, contains refractive elements with positive overall 
optical power. At least one element (shown in this example as 22) of lens 
group 21 is made of special optical glass. Aperture stop 24 is located to 
the right of lens group 21. Lens group 26 to the right of the aperture 
stop consists of refractive optical elements with positive overall optical 
power. At least one refractive element (shown in this example as the third 
element from the left 28) in lens group 26 is made of special optical 
glass. The last optical element on the right end of the optical axis is 
field lens 30. Image 32 is formed at the far right end of the optical 
axis. 
For the structure of FIG. 5a, it is important to note that special optical 
glass is required in lens group 21, lens group 26, or both. Aperture size 
is limited because otherwise it is difficult to correct simultaneously for 
spherochromatism and secondary color aberrations. Field of view is limited 
because otherwise it is difficult to correct simultaneously for both field 
curvature and lateral color aberrations. Finally, this structure is larger 
than that of FIG. 5b because more optical elements are required. 
FIG. 5b shows an equivalent typical structure for a Petzval lens employing 
the principles of this invention. Input lens group 40 at the left end of 
optical axis 41 contains refractive elements with overall positive optical 
power. Internal aperture stop 42 is located to the right of lens group 40. 
Lens group 44 to the right of the aperture stop in this figure contains 
refractive optical elements and at least one diffractive optical element. 
It is within the spirit of this invention to include alternatively at 
least one diffractive element in either lens group 40 or lens group 44, or 
to employ diffractive elements in both lens groups. The overall optical 
power of lens group 44 is positive. In this example, one element of lens 
group D (shown as the right-most element 46) is diffractive. It is 
understood that detailed arrangements and locations of such refractive and 
diffractive optical elements of lens group 44 other than those described 
in this example are within the spirit of this invention. Field lens group 
48 lies next to the right along the optical axis and contains refractive 
elements and at least one diffractive optical element. In this example, 
one element of the field lens group (shown as element 50 on the right) is 
diffractive. Image 51 is formed to the right of field lens group 48. 
Comparison of the two Petzval lenses in FIG. 5 demonstrates substantial 
advantages obtained from the use of this invention. In the 
glass-diffractive structure of FIG. 5b, fewer optical elements are 
required and as a result, the overall structure is more compact. 
Spherochromatism and secondary color aberrations can be corrected 
simultaneously with suitable employment of diffractive optical elements in 
lens group 40, lens group 44, or both. Special optical glass is not 
needed. Aperture size is larger than that for the conventional structure 
of FIG. 5a. Employing at least one diffractive element in the field lens 
group permits simultaneous correction for both field curvature and lateral 
color. A larger field of view is obtained as a result of achieving better 
correction for lateral color aberrations and field curvature. 
FIG. 6 illustrates two general schematic diagrams for large aperture lenses 
with an external pupil. Each of these structures employs three lens 
groups. FIG. 6a shows a conventional structure, and FIG. 6b shows a 
comparable structure employing the principles of this invention. 
For the typical conventional structure in FIG. 6a, input aperture stop 52 
is at the left end of optical axis 53. Next to the right along the optical 
axis is lens group 54 that contains refractive optical elements with 
positive overall optical power. At least one element in lens group 54 is 
made of special optical glass. In this example, lens group 54 contains 
four refractive elements, and the third element from the left 56 in lens 
group 54 is made of special optical glass. In actual practice of the prior 
art, other arrangements and locations of such refractive optical elements 
employed throughout this typical structure need not affect the 
illustrative value of this example. Next along the optical axis to the 
left is lens group 58 that contains refractive optical elements having 
positive overall optical power. At least one element in lens group 58 will 
be made of special optical glass. In this example, the third element from 
the left 60 in lens group 58 is made of special optical glass. The field 
lens group 62 is the last on the right and contains refractive elements. 
In this example, the field lens group contains one element. Image 64 is 
formed at the right end of the optical axis. 
Significant features for the example of the prior art shown in FIG. 6a are 
as follows. Special optical glass is likely to be used in lens group 54, 
lens group 58, or both. Aperture size is limited because otherwise it is 
difficult to correct simultaneously for spherochromatism, secondary color, 
secondary lateral color, and chromatic coma. Field of view is limited 
because it is difficult to correct simultaneously for field curvature and 
lateral color. Because more optical elements are required, this structure 
is more bulky than the structure of FIG. 6b. 
FIG. 6b shows a comparable optical structure for a typical large aperture 
lens with an external pupil employing the principles of this invention. 
External aperture stop 66 is at the left of the optical axis 67. Next to 
the left along the optical axis is lens group 68 that may contain both 
refractive and diffractive elements. In this example, lens group 68 
contains only refractive optical elements with overall positive optical 
power. Next to the left is lens group 70 that contains both refractive and 
diffractive optical elements with overall positive optical power. In this 
example, the right-most element 72 of lens group 70 is diffractive. It is 
understood that detailed arrangements and locations of individual optical 
elements within lens groups 68 and 70 other than those described in this 
example are consistent with the spirit of this invention. Field lens group 
74 is at the right end of the optical axis and contains refractive and 
diffractive optical elements. In this schematic example, of the two 
elements shown in the field lens, right element 76 is diffractive. Image 
80 is formed to the right of the field lens group at the right end of the 
optical axis. 
Comparison of the two lens structures of FIG. 6 reveals substantial 
advantage from the use of this invention are shown with the structure of 
FIG. 6b as follows. No special optical glass is needed. Spherochromatism, 
secondary color, secondary lateral color, and chromatic coma can be well 
corrected simultaneoulsy when employing diffractive optical elements 
alternatively in lens group 68 or lens group 70, or diffractive elements 
may be employed in both lens groups. The obtainable aperture size is 
larger than that for the conventional structure of FIG. 6a. Employing one 
or more diffractive elements in the field lens group allows field 
curvature and lateral color to be corrected simultaneously. A larger field 
of view is achieved as a result of better correction of lateral color and 
field curvature. Because fewer optical elements are used, the overall 
structure is smaller and lighter. 
FIG. 7 includes general schematic diagrams for two telephoto lenses that 
contain an internal aperture stop. Each of these structures employs two 
lens groups. FIG. 7a shows a typical conventional structure, and FIG. 7b 
shows a comparable structure employing the principles of this invention. 
In the conventional structure, input lens group 82 at the left end of 
optical axis 83 contains refractive elements. In this example, the central 
element 84 of three is made of special optical glass. Next to the right is 
aperture stop 86. Lens group 88 to the right of the aperture stop has 
overall negative optical power and contains refractive elements. In this 
example, third element 90 from the left (out of four elements) is made of 
special optical glass. Image 92 is formed at the right end of the optical 
axis. 
Significant features of the conventional structure in FIG. 7a are 
summarized as follows. Special optical glass must be used in lens group 
82, lens group 88, or both. Aperture size is limited because otherwise it 
is difficult to correct simultaneously for spherochromotism and secondary 
color. Because more optical elements are needed than for the structure of 
FIG. 7b, the structure of FIG. 7a is larger. 
FIG. 7b shows a typical equivalent structure for a telephoto lens that 
employs the principles of this invention. Input lens group 94 has positive 
overall optical power and in the figure is located at the left end of 
optical axis 95. This lens group may contain both refractive and 
diffractive elements. Next along the optical axis is the aperture stop 96. 
Lens group 98 next to the right has negative optical power and may contain 
both refractive and diffractive optical elements. In the example of FIG. 
7b, two elements are refractive, and the third 100 on the right is 
diffractive. It is understood that detailed arrangements and locations of 
such refractive and diffractive optical elements within lens group 98 
other than those described in this example are consistent with the spirit 
of this invention. Image 102 is formed at the right end of the optical 
axis. 
Comparison of the two telephoto lens structures in FIG. 7 demonstrates 
substantial advantages obtained from the use of this invention. The 
glass-diffractive structure of FIG. 7b, is smaller and lighter because 
fewer optical elements are required. No special optical glass is employed. 
Spherochromatism and secondary color can be corrected simultaneously 
through the use of diffractive optical elements in lens group 94, lens 
group 98, or both. Aperture size is larger than that obtainable in the 
conventional structure of FIG. 7a. 
To illustrate the principles of this invention in a more specific manner, 
FIG. 8 shows two fully designed optical structures, each for a 
representative Petzval lens with an external pupil. This example was 
chosen because while an external pupil is mechanically convenient, it also 
involves a more difficult optical design. Both structures have the same 
f-number (f/3.2), the same EFL (3 inches), and the same field of view (10 
degrees). FIG. 8a shows a well designed Petzval lens structure with 
conventional refractive optical elements. FIG. 8b shows a comparable 
structure employing the principles of this invention. 
In FIG. 8a, entrance pupil 104 is followed by lens group 106 having overall 
positive optical power and containing three refractive elements. The 
central optical element 108 of this group is made of type KZFSN4 special 
optical glass. Next along the optical axis is lens group 110 with overall 
positive optical power and containing five refractive optical elements. 
The fourth element from the left 112 of this group also is made of type 
KZSFN4 special optical glass. Finally, field lens group 114 contains two 
refractive elements. Ten optical elements are required in this 
glass-refractive assembly using conventional construction from the prior 
art. Image 115 is formed to the right of lens group 114. 
FIG. 8b illustrates a comparable structure employing the principles of this 
invention. After entrance pupil 116 is shown lens group 118 that contains 
two refractive elements. Next along the optical axis is lens group 120 
that contains three refractive elements plus one diffractive element 122 
formed or applied on the left-most refractive element 121. Finally, field 
lens group 124 contains one refractive element 125 plus diffractive 
element 126 applied to or formed upon the right surface of refractive 
element 125. Image 127 is formed to the right of lens group 124. 
Comparison between the conventional optical assembly of FIG. 8a and that of 
FIG. 8b, which employs the priciples of this invention, demonstrates 
substantial advantages over the prior art in actual workable optical 
structures. The conventional assembly of FIG. 8a contains a total of ten 
refractive elements including two made of special optical glass. The 
assembly of FIG. 8b contains only six refractive elements (none of which 
requires special optical glass) plus two diffractive elements, which 
occupy virtually no space. Although such advantages with respect to 
mechanical construction and lens materials are substantial in themselves, 
further improvements obtained from this invention extend into the area of 
optical performance, as will be shown. 
FIGS. 9 and 10 are employed to analyze and compare the two well-designed 
structures shown in FIG. 8 by means of H tan U optical performance curves. 
These curves, which are commonly used by those skilled in the art to 
analyze optical designs, show the tangential and sagittal aberrations 
along two designated axes. FIG. 9 shows the H tan U curves for the all 
glass structure of FIG. 8a. The optical performance of this design would 
be considered excellent in the prior art. Designations DY and DX refer to 
the geometric aberrations along the Y and X directions, respectively. 
Symbols 1, 2, and 3 respectively indicate curves for wavelengths of the 
d-line, F-line, and C-line. Horizontal axes Y.sub.REF and X.sub.REF are, 
respectively, the pupil coordinates along the Y and X axes. Conditions and 
associated locations for the six groups of curves shown in FIG. 9 are 
given in Table 1. 
TABLE 1 
______________________________________ 
Conditions for H tan U Curves in Indicated Locations 
Field of View 
Tangential Geometric 
Sagittal Geometric 
degrees Aberration Aberration 
______________________________________ 
5.0 top left top right 
3.5 middle left middle right 
0.0 bottom left bottom right 
______________________________________ 
FIG. 10 shows corresponding H tan U curves for the glassdiffraction 
structure of FIG. 8b. For FIG. 10, the axes, symbols, conditions, 
designations, and locations are same as described for FIG. 9 and as shown 
in Table 1. The glassdiffraction design is clearly superior for all 
criteria of optical performance indicated by the H tan U curves. Thus, 
with respect to chromatic aberrations, these comparative analyses with H 
tan U curves demonstrate the further advantages of this invention over the 
prior art. 
FIGS. 11 and 12 compare the two structures of FIG. 8 on the basis of 
modulation transfer function (MTF) out to 100 cycles per mm. MTF curves 
show the degradation of modulation with increasing spatial frequency and 
are an additional basis for evaluating optical performance. FIG. 11 shows 
typical MTF curves for the all glass structure of FIG. 8a. Such 
performance would be considered excellent in the prior art. Letter 
notations are employed on the curves in FIG. 11 to indicate type of 
geometric aberration and field of view; particular meanings of the letters 
are given in Table 2. 
TABLE 2 
______________________________________ 
Notations for MTF Curves 
Field of View Geometric Letter 
degrees Aberration 
Designation 
______________________________________ 
0.0 A 
3.5 tangential 
B 
3.5 sagittal C 
4.5 tangential 
D 
4.5 sagittal E 
______________________________________ 
FIG. 12 shows corresponding MTF curves for the glass-diffractive structure 
of FIG. 8b. Letter notations for the curves in FIG. 12 are the same as 
those given in Table 2. Modulation is substantially better for the 
glass-diffraction structure at all spatial frequencies. On the basis of 
the MTF criterion, additional advantages in superior performance obtained 
from the use of this invention are evident. 
FIG. 13 illustrates an optical structure that is similar to the 
glass-diffraction structure of FIG. 8b but for which f-number has been 
reduced from f/3.2 to f/2.5. This greatly improved specification provides 
an additional basis of comparison between the optical performance of the 
typical all glass structure of FIG. 8a with that obtained from the use of 
this invention, as will be shown. 
Entrance pupil 128 is shown at the left of FIG. 13. Lens group 129 with 
positive overall optical power contains two refractive elements. Lens 
group 130 with overall positive optical power contains three refractive 
elements plus a diffractive element 132 applied or formed on the left-most 
diffractive element 131. Field lens group 134 contains one refractive 
element 135 plus a diffractive element 136 applied or attached to element 
135. Image 137 is formed to the right of lens group 134. 
FIG. 14 shows H tan U performance curves for the glass-diffractive 
structure of FIG. 13. For FIG. 14, the axes, symbols, conditons, 
designations, and locations are the same as described for FIG. 9 and as 
shown in Table 1. Comparing FIG. 14 with FIG. 10 shows the expected 
degradation of optical performance that reflects the significant burden of 
reducing the f-number from f/3.2 to f/2.5. Comparing FIG. 14 with FIG. 9, 
however, provides further indication of the superiority of this invention. 
These H tan U curves demonstrate that optical performance of the f/2.5 
glass-diffraction structure of FIG. 13 is still superior to the comparable 
f/3.2 glass-refractive structure of FIG. 8a.