PROJECTION OBJECTIVE OF A MICROLITHOGRAPHIC PROJECTION EXPOSURE APPARATUS

FIELD

The disclosure relates to a projection objective of a microlithographic projection exposure apparatus, as well as a related microlithographic projection exposure apparatus and method.

BACKGROUND

Microlithographic projection exposure apparatuses can be used for the production of microstructured components such as for example integrated circuits or LCDs. Such a projection exposure apparatus typically has an illumination system and a projection objective. In the microlithography process, the image of a mask (=reticle) illuminated by the illumination system is projected by the projection objective onto a substrate (for example silicon wafer) which is coated with a light-sensitive layer (photoresist) and arranged in the image plane of the projection objective to transfer the mask structure onto the light-sensitive layer.

In microlithography objectives, such as immersion objectives with a value with respect to the numerical aperture (NA) of more than 1.5, it can be desirable to use materials with a high refractive index, in particular for the last optical element at the image side. The term “high refractive index” is used herein to denote a refractive index if its value at the given wavelength exceeds that of quartz, with a value of about 1.56 at a wavelength of 193 nm. An example of such a materialis lutetium aluminum garnet (Lu₃Al₅O₁₂, LuAG), which has a refractive index at 193 nm is about 2.14. In some cases, such materials, due to their cubic crystal structure, have intrinsic birefringence (═IBR) which rises with a low wavelength. For example, measurements for lutetium aluminum garnet have given a maximum IBR-induced retardation of 30.1 nm/cm. The term “retardation” is used herein to denote the difference in the optical paths of two orthogonal (mutually perpendicular) polarization states.

SUMMARY

In some embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, which permits the use of high-refraction crystal materials while limiting an undesirable influence of intrinsic birefringence.

In certain embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, which is configured to project a mask which can be positioned in an object plane of the projection objective onto a light-sensitive layer which can be positioned in an image plane of the projection objective. The projection objective includes at least one lens of a cubically crystalline material whose [110] crystal orientation is oriented at an angle of at most 15° relative to the optical axis of the projection objective. The projection objective also includes at least one polarization correction element which has at least two subelements of birefringent, optically uniaxial material and having at least one respective aspheric surface. The polarization correction element at least partially compensates for an intrinsic birefringence of the at least one lens.

Reference to the optical axis denotes a straight line or a succession of straight line portions, which extends through the centers of curvature of the rotationally symmetrical optical components of the projection objective.

In some embodiments, the [110] crystal orientation of the at least one lens of cubically crystalline material is oriented at an angle of at most 10° (e.g., at most 5°, at most 3°) relative to the optical axis of the projection objective.

The disclosure is based, in part at least, on the realization that the field-dependent residual retardation remaining in the case of polarization-optical compensation of an intrinsically birefringent lens (and in particular a lens which is the last at the image plane side) by a polarization correction element depends on the crystal orientation of that lens. The disclosure makes use of the realization that a reduction in that residual retardation can be achieved if the crystal orientation of the lens to be compensated with respect to its intrinsic birefringence is so selected that the maximum retardation values in the field distribution of that lens occur on or in the proximity of the optical lens of the projection objective.

The [110] crystal orientation that is selected for the lens to be compensated with respect to its intrinsic birefringence has the property that light beams which pass in axis-parallel relationship through the [110] lens experience the maximum retardation (in contrast, for example, to the situation with a [100] lens which does not have any retardation for light beams passing thereto in axis-parallel relationship). In addition the disclosure makes use of the fact that, by using a suitable polarization correction element, it is possible to completely compensate for the intrinsic birefringence for any field point (for example a field point on the optical axis) while that compensation only takes place partially for the other field points.

When designing the polarization correction element for optimum polarization-optical compensation of the retardation of the lens to be compensated with respect to its intrinsic birefringence, in the field center, it is possible by the combination of a polarization correction element on the one hand and a lens with [110] crystal orientation which is to be compensated with respect to its intrinsic birefringence on the other hand, to create a situation in which the maximum retardation of the [110] lens is optimized for axis-parallel beams in the field center.

In some embodiments, the polarization correction element includes a crystal material with a non-cubic crystal structure. For example, the polarization correction element can include an optically uniaxial crystal material, such as magnesium fluoride (MgF₂), lanthanum fluoride (LaF₃), sapphire (Al₂O₃) or crystalline quartz (SiO₂).

In certain embodiments, the polarization correction element can have at least three subelements (optionally, precisely three subelements) of birefringent material and with at least one respective aspheric surface. With such a polarization correction element it is possible to achieve at least almost complete compensation of intrinsic birefringence for any field point (for example the field center).

More generally, the polarization correction element can have at least two subelements of birefringent material, with each sublement having at least one aspheric surface.

In some embodiments, the birefringent material of the subelements of the polarization correction element is an optically uniaxial crystal material. The birefringent material of the subelements of the polarization correction element can be, for example, magnesium fluoride (MgF₂), lanthanum fluoride (LaF₃), sapphire (Al₂O₃) or crystalline quartz (SiO₂).

In certain embodiments, the lens is the last lens of the projection objective on the image plane side of the projection objective. For the field center, it is possible to minimize a field-dependent residual error with respect to polarization-optical compensation, that is caused by the typically planoconvex geometry of the last lens on the image plane side, as (in contrast to the situation for example in the case of the coma rays or edge rays of the different field beams) the principal rays which are in axis-parallel relationship in the image plane and which are near the axis pass through substantially the same optical travel length in the last lens on the image plane side.

In some embodiments, the projection objective has precisely one lens of a cubically crystalline material whose [110] crystal orientation is oriented at an angle of at most 15° relative to the optical axis of the projection objective. The disclosure makes use of the fact that the combination of a polarization correction element on the one hand and a lens with [110] crystal orientation on the other hand, in regard to the polarization-optical compensation which can be achieved, possibly makes the presence of further [110] lenses with lens clocking dispensable.

In certain embodiments, the optical crystal axes of all three subelements are oriented differently from each other.

In some embodiments, the optical crystal axes of at least two subelements of the polarization correction element are oriented in a plane perpendicular to the optical axis of the projection objective.

In certain embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, for projecting a mask which can be positioned in an object plane onto a light-sensitive layer which can be positioned in an image plane. The projection objective includes precisely one lens of a cubically crystalline material that has its [110] crystal orientation oriented at an angle of at most of 15° relative to the optical axis the projection objective. The projection objective also includes a polarization correction element which has an optically uniaxial crystal material and at least partially compensates for an intrinsic birefringence of the lens.

The disclosure makes use of the realization that the combination of a polarization correction element on the one hand and a lens with [110] crystal orientation on the other hand, in regard to the polarization-optical compensation which can be achieved, possibly makes the presence of further [110] lenses with lens clocking dispensable.

In some embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, for projecting a mask which can be positioned in an object plane onto a light-sensitive layer which can be positioned in an image plane. All lenses of cubically crystalline material in the projection objective have their [110] crystal orientation oriented at an angle of at most 15° relative to the optical axis of the projection objective. The projection objective also includes a polarization correction element which has an optically uniaxial crystal material and at least partially compensates for an intrinsic birefringence of the one or more lenses.

The disclosure also relates to a microlithographic projection exposure apparatus, a process for the production of microlithographic components, and a microlithographic component.

Further configurations of the disclosure are to be found in the description and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an overall meridional section through a complete catadioptric projection objective;

FIGS. 2
a-b show a diagrammatic view of the typical configuration of partial rays of different beams in a first lens on the object plane side and a last lens on the image plane side of a projection objective;

FIG. 3 shows an overall meridional section through a complete catadioptric projection objective;

FIGS. 4
a-b show the residual retardation (in nm) obtained for the projection objective of FIG. 1 without polarization correction element in the case of a [100] crystal orientation of the last lens on the image plane side (FIG. 4a) and for the case of a [110] crystal orientation of the last lens on the image plane side (FIG. 4b);

FIGS. 5
a-c show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [100] crystal orientation;

FIGS. 6
a-b show the residual retardation (in nm) obtained with a polarization correction element as shown in FIGS. 5a-c for the field center (FIG. 6a) and the field edge (FIG. 6b);

FIGS. 7
a-c show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [110] crystal orientation;

FIGS. 8
a-b show the residual retardation (in nm) obtained with a polarization correction element as shown in FIGS. 7a-c for the field center (FIG. 8a) and the field edge (FIG. 8b);

FIGS. 9
a-b show the residual retardation (in nm) obtained for the projection objective of FIG. 3 without polarization correction element in the case of a [100] crystal orientation of the last lens on the image plane side (FIG. 9a) and for the case of a [110] crystal orientation of the last lens on the image plane side (FIG. 9b);

FIGS. 10
a-c show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [100] crystal orientation;

FIGS. 11
a-b show the residual retardation (in nm) obtained with a polarization correction element as shown in FIGS. 10a-c for the field center (FIG. 11a) and the field edge (FIG. 11b),

FIGS. 12
a-c show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [110] crystal orientation; and

FIGS. 13
a-b show the residual retardation (in nm) obtained with a polarization correction element as shown in FIGS. 12a-c for the field center (FIG. 13a) and the field edge (FIG. 13b).

DETAILED DESCRIPTION

FIG. 1 shows an exemplary projection objective 100. The design data of exemplary projection objective 100 are set out in Table 1, where column 1 represents the number of the respective refracting or in some other fashion distinguished optical surface, column 2 specifies the radius r of that surface (in mm), column 3 gives a reference to an asphere present on that surface, column 4 specifies the spacing, identified as thickness, of that surface relative to the following surface (in mm), column 5 specifies the material following the respective surface, column 6 specifies the refractive index of that material at λ=193 nm and column 7 specifies the optically useable free half diameter of the optical component. The radii, thicknesses and half diameters are specified in millimeters.

The surfaces identified by thick dots in FIG. 1 and specified in Tables 1 and 2 are aspherically curved, wherein the curvature of those surfaces is given by the following asphere formula:

$\begin{matrix} P (h) = \frac{(1 / r) \cdot h^{2}}{1 + \sqrt{1 - (1 + cc) {(1 / r)}^{2} h^{2}}} + C_{1} h^{4} + C_{2} h^{6} + \dots & (1) \end{matrix}$

P denotes the camber height of the surface in question parallel to the optical axis, h denotes the radial spacing from the optical axis, r denotes the radius of curvature of the surface in question, cc denotes the conical constant (identified by K in Table 2) and C1, C2, . . . denote the asphere constants set out in Table 2.

Referring to FIG. 1 the projection objective 100 has a catadioptric structure with a first optical subsystem 110, a second optical subsystem 120 and a third optical subsystem 130. As used herein, “subsystem” always denotes such an arrangement of optical elements, by which a real object is projected into a real image or intermediate image. In other words each subsystem, starting from a given object or intermediate image plane, always includes all optical elements to the next real image or intermediate image.

The first optical subsystem 110 includes an arrangement of refractive lenses 111-118 and reproduces the object plane “OP” in a first intermediate image IMI1, the approximate position of which is indicated in FIG. 1 by an arrow. That first intermediate image IMI1 is reproduced by the second optical subsystem 120 in a second intermediate image IMI2, the approximate position of which is also indicated in FIG. 1 by an arrow.

The second optical subsystem 120 includes a first concave mirror 121 and a second concave mirror 122 which are each “cut off” in a direction perpendicular to the optical axis in such a way that light propagation can occur from the respective reflecting surfaces of the concave mirrors 121, 122 to the image plane “IP”. The second intermediate image IMI2 is reproduced in the image plane IP by the third optical subsystem 130.

The third optical subsystem 130 includes an arrangement of refractive lenses 131-143. In regard to the last lens 143 at the image plane side this involves a planoconvex lens with a lens surface which is convexly curved on the object plane side. Lens 143 is a [110] lens with its [110] crystal orientation that is oriented at an angle of at most 15° relative to the optical axis (OA).

Between the light exit surface of the lens 143 and the light-sensitive layer arranged in the image plane IP in the region of the projection objective 100 is an immersion liquid which in the illustrated embodiment, at a working wavelength of 193 nm, has a refractive index of n_Imm≈1.65. An immersion liquid which is suitable for example for that purpose bears the designation “Dekalin”. A further suitable immersion liquid is cyclohexane (n_Imm≈11.57 at 193 nm).

Disposed in the pupil plane PP1 is a polarization correction element 105, the structure of which is described in greater detail hereinafter with reference to FIGS. 4 through 8.

The reduction or minimization achieved with respect to the field-dependent residual retardation as a consequence of the combination of a polarization correction element with a lens which is last on the image plane side with [110] crystal orientation is described in greater detail hereinafter with reference to FIGS. 2a-b.

FIGS. 2
a and 2b diagrammatically show the typical configuration of three respective subrays of three individual light beams in a lens which is first on the object plane side (FIG. 2a) and the lens which is last on the image plane side (FIG. 2b) on an enlarged scale. The coma rays of those beams A, B and C are denoted in FIGS. 2a and 2b by A1, A3, B1, B3, C1 and C3. The principal rays of the beams A, B and C are denoted in FIGS. 2a and 2b by A2, B2 and C2. Those principal rays extend substantially parallel to the optical axis OA with double-side (and thus in particular image-side) telecentry of the projection objective within the last lens on the image plane side. As is further apparent from FIG. 2b the optical travel lengths of those principal rays A2, B2 and C2 within the last lens on the image plane side are almost equal so that those subrays also experience substantially the same retardation and can be equally well compensated by a polarization correction element.

In contrast for example the subray C3 of the beam C within the last lens on the image plane side as shown in FIG. 2b covers a substantially greater optical distance than the subray C1 of the same beam C. That difference is responsible for the above-mentioned field-dependent residual error of the polarization-optical compensation effect which can be achieved by a polarization correction element, or the residual retardation achieved, and is correspondingly greater, the greater the spread angle of the individual beams.

It follows from the foregoing description that the polarization-optical compensation which can be achieved by the polarization correction element with respect to the last lens on the image plane side is particularly effective, in the field center. The fact that the last lens is in the [110] crystal orientation means that the particular effectiveness of a polarization correction element which is optimized for the field center is advantageously combined with a maximum retardation in the intrinsically birefringent [110] crystal material of that last lens.

The effect of that advantageous combination is clear from a comparison of FIGS. 4 through 8.

FIGS. 4
a and b show the residual retardation (in nm) obtained for the projection objective of FIG. 1 without polarization correction element, more specifically in the case of a [100] crystal orientation of the last lens on the image plane side (FIG. 4a) and for the case of a [110] crystal orientation of the last lens on the image plane side (FIG. 4b). It will be seen that the residual retardations are respectively approximately at 200 nm, wherein the maximum residual retardation is achieved in the case of the [100] crystal orientation at the field edge and in the case of the [110] crystal orientation in the field center. In this respect, here and hereinafter the respective axes are specified in the diagrams for representing the residual retardation, in pupil coordinates, that is to say in the value range of −NA through +NA (NA=numerical aperture).

FIG. 5
a-c show the height profiles (in μm) of three subelements of a polarization correction element for IBR compensation in the case of the [100] lens of FIG. 4a. In this case, here and hereinafter, the respective axes are specified in mm in the diagrams for representing height profiles.

The three subelements are respectively made from sapphire (Al₂O₃). The optical crystal axes in those three subelements are respectively disposed in a plane perpendicular to the optical axis OA of the projection objective and are so oriented that the optical crystal axis of the second subelement in the light propagation direction is arranged rotated through 45° about the optical axis OA with respect to the optical crystal axis of the first subelement while the optical crystal axis of the third subelement in the light propagation direction is again arranged parallel to the optical crystal axis of the first subelement. In some embodiments, the third subelement can also be arranged rotated for example through an angle of 90° about the optical axis OA with respect to the optical crystal axis of the first subelement (and through 45° about the optical axis OA with respect to the optical crystal axis of the second subelement) so that then the optical crystal axes of all three subelements are differently oriented.

The positive or negative height data contained in the height profiles of FIGS. 5a-c of the three subelements are respectively specified relative to the thickness of a plane plate with an effective retardation of a wavelength (or generally an integral multiple of the wavelength, that is to say relative to a plane plate of the thickness D=N*λ/Δn with Δn=n_e−n_o).

A further quantitative description of the height profiles of the three subelements is shown in Table 5 which contains the Zernike coefficients of the surfaces so scaled that a respective height profile in micrometers is afforded, more specifically in accordance with the relationship:

$\begin{matrix} height profile = \sum_{i} (C_{i} * Z_{i} (r / r_{\max}, phi) & (2) \end{matrix}$

C_idenotes the Zernike coefficients in Table 5, phi denotes the azimuth angle, r/r_maxdenotes the standardized radial coordinate and Z_idenotes the i-th standard Zernike polynomial, where the maximum radii r_maxin the projection objective 100 are 55.47800 mm for the first subelement, 55.48200 mm for the second subelement and 55.48500 mm for the third subelement.

The residual retardation achieved by that polarization correction element is shown in FIG. 6a for the field center and in FIG. 6b for the field edge. While FIG. 6a shows almost complete compensation for the field center, FIG. 6b shows that there is still a maximum residual retardation of 24 nm for the field edge.

Similarly FIGS. 7a-c show the height profiles (in μm) of the subelements of a polarization correction element used for IBR compensation of the [110] lens as shown in FIG. 4b, where Table 6 contains the corresponding Zernike coefficients in accordance with the foregoing description. FIG. 8a shows the residual polarization obtained by that polarization correction element for the field center (FIG. 8a) and the residual retardation obtained for the field edge (FIG. 8b). While in FIG. 8a optimum compensation is still obtained for the field center the residual retardation for the field edge is only still a maximum of 18 nm as shown in FIG. 8b.

Of the subelements of the polarization correction element two or more (in particular all) of those subelements can also be assembled seamlessly (for example by wringing). In addition compensation elements (for example of optically isotropic material) for compensation of a beam deflection can also be associated with one or more (in particular all) of those subelements.

FIG. 3 shows a complete projection objective 300 in meridional section in accordance. The design data of that projection objective 300 are set out in Table 3 (in a similar fashion to Table 1) and the aspheric constants are to be found in Table 4.

The projection objective 300 includes a first refractive subsystem 310, a second catadioptric subsystem 320 and a third refractive subsystem 330 and is therefore also referred as a “RCR system”.

The first refractive subsystem 310 includes refractive lenses 311 through 319, after which a first intermediate image IMI1 is produced in the beam path. The second subsystem 320 includes a double-folding mirror with two mirror surfaces 321 and 322 arranged at an angle relative to each other, where light incident from the first subsystem is reflected firstly at the mirror surface 321 in the direction towards lenses 323 and 324 and a subsequent concave mirror 325. The light reflected at the concave mirror 325 is reflected after again passing through the lenses 323 and 324 at the second mirror surface 322 of the double-fold mirror so that as the outcome the optical axis OA is folded twice through 90°. The second subsystem 320 produces a second intermediate image IMI2 and the light from that intermediate image IMI2 is incident on the third refractive subsystem 330 which includes refractive lenses 331 through 345. The second intermediate image IMI2 is reproduced on the image plane IP by the third refractive subsystem 330.

The concave mirror 325 of the second catadioptric subsystem permits in per se known manner effective compensation of the image field curvature produced by the subsystems 310 and 330.

A polarization correction element 305 is disposed in the first pupil plane PP1 of the projection objective 300. The structure of the element 305 is described in greater detail hereinafter with reference to FIGS. 9 through 13.

FIGS. 9
a and 9b show residual retardation (in nm) obtained for the projection objective 300 of FIG. 3 without polarization correction element, in the case of a [100] crystal orientation of the last lens on the image plane side (FIG. 9a) and in the case of a [110] crystal orientation of the last lens on the image plane side (FIG. 9b).

The optical crystal axes in those three subelements are again respectively disposed in a plane perpendicularly to the optical axis OA of the projection objective and are oriented similarly to the optical crystal axes in the three subelements of the polarization correction element in the exemplary embodiment of FIG. 1 and FIGS. 4 through 8, respectively.

FIGS. 10
a-c show the height profiles (in μm) of three subelements of a polarization correction element for IBR compensation in the case of the [100] lens of FIG. 9a.

A further quantitative description of the height profiles of the three subelements is set forth in Table 7 which contains the Zernike coefficients of the surfaces so scaled that a respective height profile in micrometers is afforded, in accordance with foregoing relationship (2). In that case the maximum radii r_maxin the projection objective 300 are 10.50640 mm for the first subelement, 10.51220 mm for the second subelement and 10.51810 mm for the third subelement.

The residual retardation obtained by that polarization correction element is shown in FIG. 11a for the field center and in FIG. 11b for the field edge. While FIG. 11a shows almost complete compensation for the field center, FIG. 11b shows that there is still a maximum residual retardation of 16 nm for the field edge.

Similarly FIGS. 12a-c show the height profiles (in μm) of the subelements of a polarization correction element used for IBR compensation of the [110] lens shown in FIG. 9b, where Table 8 contains the corresponding Zernike coefficients in accordance with the foregoing description. FIGS. 13a and 13b show the residual polarization obtained by that polarization correction element for the field center (FIG. 13a) and the residual retardation obtained for the field edge FIG. 13b). While an optimum compensation is still obtained in FIG. 13a for the field center, the residual retardation for the field edge is only still a maximum of 12 nm.

Although the disclosure has been described certain embodiments, numerous variations and alternative embodiments will be apparent to one man skilled in the art, for example by combination and/or exchange of features of individual embodiments. Accordingly, it will be appreciated that such variations and alternative embodiments are also embraced by the present disclosure and the scope of the disclosure is limited only in the sense of the accompanying claims and equivalents thereof.

TABLE 1

(DESIGN DATA for FIG. 1):

(NA = 1.55; field size 26 mm * 5.5 mm; wavelength 193 nm)

REFRACTIVE
HALF

SURFACE
RADIUS

THICKNESS
MATERIAL
INDEX
DIAMETER

0
0.000000

29.999023

1.00000000
63.700

1
0.000000

−0.293904

1.00000000
76.311

2
116.967388
AS
33.971623
SIO2V
1.56078570
93.710

3
268.858710

45.405733

1.00000000
92.342

4
−252.724978
AS
58.607153
SIO2V
1.56078570
92.157

5
−152.905212

0.986967

1.00000000
102.264

6
100.588881

94.936165
SIO2V
1.56078570
89.748

7
480.541211
AS
22.683526

1.00000000
61.038

8
−151.461922

9.967307
SIO2V
1.56078570
58.676

9
−1104.178549
AS
2.998283

1.00000000
54.598

10
0.000000

0.000000

1.00000000
53.972

11
0.000000

26.000000

1.00000000
53.972

12
−4615.634680

9.983258
SIO2V
1.56078570
77.043

13
−7648.187834

9.234701

1.00000000
82.010

14
−625.750713

48.866298
SIO2V
1.56078570
85.509

15
−110.073136
AS
47.938753

1.00000000
90.434

16
693.459276

15.566986
SIO2V
1.56078570
114.997

17
2225.036283

111.995402

1.00000000
115.765

18
−209.012550

24.611839
SIO2V
1.56078570
126.681

19
−181.333947
AS
37.469604

1.00000000
129.924

20
0.000000

238.315935

1.00000000
129.948

21
−214.798316
AS
−238.315935
REFL
1.00000000
151.231

22
186.831531
AS
238.315935
REFL
1.00000000
153.712

23
0.000000

37.462671

1.00000000
111.274

24
297.174670

29.574318
SIO2V
1.56078570
123.808

25
1191.420870

35.484494

1.00000000
123.384

26
4081.914442

22.323161
SIO2V
1.56078570
122.901

27
273.503277
AS
0.998916

1.00000000
122.715

28
231.074591
AS
9.994721
SIO2V
1.56078570
108.656

29
162.434674

7.329878

1.00000000
100.728

30
173.924185

9.996236
SIO2V
1.56078570
100.278

31
147.324038

39.865421

1.00000000
96.038

32
517.833939
AS
9.994259
SIO2V
1.56078570
95.918

33
418.975568

18.691694

1.00000000
97.853

34
402.609022

9.991838
SIO2V
1.56078570
103.816

35
225.169608
AS
18.474719

1.00000000
105.756

36
350.705440
AS
25.452147
SIO2V
1.56078570
107.818

37
−3388.791523

12.488356

1.00000000
110.250

38
1008.270218
AS
41.022442
SIO2V
1.56078570
119.521

39
−314.632041

3.943706

1.00000000
121.832

40
1442.963243
AS
12.476333
SIO2V
1.56078570
126.022

41
−1002.829857

14.096377

1.00000000
126.891

42
194.591039

81.128704
SIO2V
1.56078570
132.890

43
−264.895277
AS
−22.880987

1.00000000
131.108

44
0.000000

−0.362185

1.00000000
132.343

45
0.000000

24.001275

1.00000000
132.533

46
159.644367

50.327970
SIO2V
1.56078570
109.736

47
494.742901
AS
0.961215

1.00000000
105.155

48
328.066727

14.868291
SIO2V
1.56078570
92.427

49
−3072.231603
AS
0.927658

1.00000000
86.384

50
84.317525

69.022697
LuAG
2.15000000
64.842

51
0.000000

3.100000
HINDLIQ
1.65002317
24.540

52
0.000000

0.000000

15.928

TABLE 2

(ASPHERIC CONSTANTS for FIG. 1):

Surface

2
4
7
9
15

K
0
0
0
0
0

C1
−4.353148e−08
−9.800573e−08
2.666231e−07
1.295769e−07
1.774606e−08

C2
−1.948518e−13
5.499401e−13
−1.471516e−11
1.032347e−11
1.042043e−13

C3
−3.477204e−16
−1.499103e−16
−1.385474e−15
5.718200e−15
2.794961e−17

C4
2.346643e−20
−1.967686e−20
2.138176e−18
−4.988183e−18
−3.892158e−21

C5
−2.078112e−24
4.517642e−24
−1.482225e−22
1.949505e−21
4.464755e−25

C6
−8.347999e−31
−2.738209e−28
−8.304062e−27
−2.335999e−25
4.773462e−30

C7
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C8
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C9
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

Surface

19
21
22
27
28

K
0
−2.01691
−1.35588
0
0

C1
−1.294881e−08
−1.791441e−08
1.799581e−08
−2.305522e−07
−5.364751e−08

C2
2.960445e−14
1.393731e−13
6.604119e−14
−2.977863e−12
2.985313e−12

C3
−3.744673e−18
−1.959652e−18
1.091967e−18
1.067601e−15
1.185542e−16

C4
3.872183e−22
3.972150e−23
3.177716e−23
−7.036742e−20
−5.029250e−20

C5
−1.724706e−26
−6.577183e−28
−5.281159e−28
2.314154e−24
3.896020e−24

C6
4.346424e−31
6.141114e−33
1.575655e−32
−3.151486e−29
−1.479810e−28

C7
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C8
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C9
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

Surface

32
35
36
38
40

K
0
0
0
0
0

C1
2.753990e−08
1.438723e−07
4.030346e−08
4.491651e−08
−9.637167e−08

C2
−2.426854e−11
−2.226044e−11
−6.610222e−12
−5.791619e−12
3.256893e−12

C3
1.360579e−15
1.482620e−15
2.501723e−16
5.024169e−16
−9.241857e−17

C4
−1.150640e−19
−5.040252e−20
−2.574681e−21
−3.768862e−20
9.112235e−21

C5
7.525459e−24
1.831772e−24
−7.619628e−25
1.711080e−24
9.519978e−26

C6
−2.203312e−30
−8.726413e−29
1.815817e−29
−3.990765e−29
−1.423818e−29

C7
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C8
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C9
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

Surface

43
47
49

K
0
0
0

C1
5.213696e−08
−1.687244e−07
1.276858e−07

C2
−2.852489e−13
1.277072e−11
1.143276e−12

C3
6.349974e−17
−5.376139e−16
−2.525252e−16

C4
−4.223029e−21
1.564911e−20
9.197266e−20

C5
1.155960e−25
−3.759137e−25
−8.401499e−24

C6
−1.415349e−30
1.266337e−29
6.171793e−28

C7
0.000000e+00
0.000000e+00
0.000000e+00

C8
0.000000e+00
0.000000e+00
0.000000e+00

C9
0.000000e+00
0.000000e+00
0.000000e+00

TABLE 3

(DESIGN DATA for FIG. 3):

REFRACTIVE
HALF

SURFACE
RADIUS

THICKNESS
MATERIAL
INDEX
DIAMETER

0
0.000000

56.505360

1.00000000
61.600

1
0.000000

0.628593

1.00000000
84.411

2
0.000000

9.999465
SIO2V
1.56078570
84.665

3
0.000000

1.018383

1.00000000
87.136

4
267.687560

23.051668
SIO2V
1.56078570
94.506

5
2076.339784

3.011269

1.00000000
95.214

6
195.468828

118.243767
SIO2V
1.56078570
99.907

7
213.465552

65.301393

1.00000000
87.739

8
233.154018

24.923341
SIO2V
1.56078570
92.865

9
−1992.179958
AS
1.169743

1.00000000
91.232

10
397.921478

69.915906
SIO2V
1.56078570
91.709

11
505.661172

17.194249

1.00000000
95.812

12
−735.689494

9.999732
SIO2V
1.56078570
96.173

13
887.983169

8.242783

1.00000000
100.163

14
0.000000

0.000000

1.00000000
101.571

15
0.000000

42.782393

1.00000000
101.571

16
−410.552179
AS
78.848881
SIO2V
1.56078570
128.012

17
−163.270786

336.654237

1.00000000
134.938

18
237.665945

66.291266
SIO2V
1.56078570
153.690

19
−1317.124240
AS
86.415659

1.00000000
152.243

20
222.206724

27.565105
SIO2V
1.56078570
112.997

21
921.104852
AS
68.984477

1.00000000
110.393

22
0.000000

0.000000

1.00000000
82.262

23
0.000000

−223.984401
REFL
1.00000000
82.262

24
112.393927
AS
−9.995120
SIO2V
1.56078570
93.383

25
618.177768

−30.194887

1.00000000
110.198

26
180.843143

−9.993434
SIO2V
1.56078570
111.320

27
459.728303

−49.418013

1.00000000
131.268

28
166.364160

49.418013
REFL
1.00000000
133.173

29
459.728303

9.993434
SIO2V
1.56078570
130.248

30
180.843143

30.194887

1.00000000
106.184

31
618.177768

9.995120
SIO2V
1.56078570
102.211

32
112.393927
AS
223.984401

1.00000000
87.128

33
0.000000

0.000000

1.00000000
69.972

34
0.000000

−63.976352
REFL
1.00000000
69.972

35
412.103957

−20.679211
SIO2V
1.56078570
92.437

36
203.153828

−0.998595

1.00000000
95.263

37
−1996.505583

−25.026685
SIO2V
1.56078570
104.114

38
387.517974

−0.999117

1.00000000
105.544

39
−217.409028

−35.834400
SIO2V
1.56078570
112.665

40
−1732.046627

−89.753105

1.00000000
111.738

41
−432.227186

−24.454670
SIO2V
1.56078570
100.002

42
−429.393785
AS
−61.820584

1.00000000
96.269

43
127.267221
AS
−9.998963
SIO2V
1.56078570
96.639

44
−354.132669

−7.868044

1.00000000
110.880

45
−523.720649

−14.975470
SIO2V
1.56078570
112.701

46
−341.520890
AS
−0.997791

1.00000000
118.281

47
−411.353502

−48.777625
SIO2V
1.56078570
120.957

48
342.083102

−8.810353

1.00000000
122.794

49
514.961229
AS
−14.987375
SIO2V
1.56078570
123.090

50
291.403757

−79.216652

1.00000000
128.222

51
826.480933
AS
−24.931069
SIO2V
1.56078570
151.976

52
388.289534

−1.073107

1.00000000
155.772

53
1460.275628

−24.262791
SIO2V
1.56078570
162.233

54
543.277065

−0.999651

1.00000000
163.887

55
−4320.460965

−27.112870
SIO2V
1.56078570
168.245

56
901.554468

−0.999423

1.00000000
168.871

57
−227.624376

−78.149238
SIO2V
1.56078570
170.522

58
−2243.544699

−9.897025

1.00000000
167.855

59
0.000000

0.000000

1.00000000
165.919

60
0.000000

−43.822974

1.00000000
165.919

61
−193.437748

−56.826827
SIO2V
1.56078570
128.975

62
4852.914186
AS
−1.258966

1.00000000
124.642

63
−126.542916

−25.022273
SIO2V
1.56078570
89.797

64
−202.284936
AS
−0.996510

1.00000000
78.587

65
−95.520347

−72.724717
LUAG
2.10000000
70.909

66
0.000000

−6.000000
HIINDLIQ
1.64000000
28.915

67
0.000000

0.000000

15.401

TABLE 4

(ASPHERIC CONSTANTS for FIG. 3):

Surface

9
16
19
21
24

K
0
0
0
0
0

C1
1.993155e−07
7.648792e−08
1.310449e−08
1.499407e−08
−1.140413e−07

C2
−2.965837e−11
−1.147476e−12
−1.473288e−13
4.898569e−13
−1.405657e−12

C3
7.084938e−15
−1.620016e−16
1.789597e−18
−4.831673e−18
−6.422308e−16

C4
−1.108567e−18
1.291519e−20
−3.347563e−23
5.603761e−22
9.595133e−20

C5
1.294384e−22
−4.536509e−25
7.855804e−28
1.107164e−28
−1.651690e−23

C6
−8.666805e−27
8.063130e−30
−1.561895e−32
−1.720748e−31
1.285598e−27

C7
2.821071e−31
−5.992411e−35
1.565488e−37
3.402783e−35
−5.054656e−32

C8
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C9
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

Surface

32
42
43
46
49

K
0
0
0
0
0

C1
−1.140413e−07
−4.189168e−08
−1.685701e−07
6.336319e−09
5.280703e−08

C2
−1.405657e−12
−3.147936e−13
9.635698e−12
4.071242e−12
1.157060e−12

C3
−6.422308e−16
−1.294082e−18
−1.217963e−15
−3.577670e−16
−7.824880e−17

C4
9.595133e−20
−2.828644e−22
1.012583e−19
2.732048e−20
7.171704e−21

C5
−1.651690e−23
4.489648e−26
−8.858422e−24
−1.655966e−24
−3.888551e−26

C6
1.285598e−27
−1.468171e−29
4.866371e−28
6.535740e−29
−2.007284e−29

C7
−5.054656e−32
1.147294e−33
−1.337836e−32
−1.353076e−33
4.237726e−34

C8
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

C9
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00
0.000000e+00

Surface

51
62
64

K
0
0
0

C1
−6.339317e−09
4.857833e−08
−2.139384e−07

C2
9.839286e−13
−8.830803e−12
1.525695e−11

C3
−3.557535e−17
7.521403e−16
−4.799207e−15

C4
2.050828e−21
−4.932093e−20
1.286852e−18

C5
−7.703006e−26
2.223792e−24
−3.670356e−22

C6
2.045013e−30
−5.700404e−29
7.133596e−26

C7
−2.770838e−35
−3.566708e−35
−9.239454e−30

C8
0.000000e+00
4.807714e−38
6.969720e−34

C9
0.000000e+00
−1.056980e−42
−2.499170e−38

TABLE 5

Zernike coefficients for FIG. 1 with [100] lens:

Zernike
Element 1
Element 2
Element 3

1
8.28E−02
−3.48E−03
8.15E−02

2
−1.12E−02
1.62E−01
−1.16E−02

3
3.22E−01
1.50E−02
3.21E−01

4
4.08E−03
−3.98E−03
−3.13E−05

5
−1.19E+01
−1.64E−03
−1.19E+01

6
1.48E−02
−5.22E+00
1.47E−02

7
1.53E−03
4.36E−03
1.00E−03

8
1.65E−01
−2.19E−03
1.29E−01

9
1.58E−02
2.05E−03
8.85E−03

10
1.43E−02
5.89E−02
1.38E−02

11
−4.02E−01
2.37E−02
−3.74E−01

12
3.61E+00
9.78E−05
3.54E+00

13
−1.11E−02
3.62E+00
−1.12E−02

14
4.76E−03
−8.69E−02
4.05E−03

15
8.91E−02
−5.32E−03
5.26E−02

16
2.96E−02
1.58E−03
1.98E−02

17
−1.37E−02
1.56E−02
−2.85E−02

18
−3.63E−03
−4.99E−02
−3.67E−03

19
−9.41E−03
−3.82E−03
−1.04E−02

20
−8.93E−02
−1.38E−02
−6.41E−02

21
6.83E−01
8.84E−05
5.92E−01

22
2.80E−04
−7.95E−01
1.24E−05

23
−1.02E−04
−6.01E−02
−1.04E−03

24
1.99E−01
4.05E−04
1.56E−01

25
3.86E−02
5.00E−04
2.58E−02

26
7.30E−03
1.39E−01
6.66E−03

27
−5.21E−02
−9.22E−03
−5.42E−02

28
3.64E−02
−7.62E−03
1.65E−02

29
2.39E−03
3.00E−02
2.45E−03

30
−1.57E−04
1.53E−01
−1.37E−03

31
−2.10E−01
1.63E−03
−1.81E−01

32
5.43E−01
1.08E−04
4.37E−01

33
−3.73E−04
3.08E−01
−6.85E−04

34
4.18E−04
−7.80E−02
−6.80E−04

35
2.37E−01
−1.77E−03
1.89E−01

36
4.47E−02
1.06E−03
2.88E−02

37
6.12E−01
3.30E−04
6.10E−01

38
−6.88E−03
2.32E+00
−7.15E−03

39
−6.13E−03
−9.59E−02
−7.05E−03

40
4.76E−02
6.55E−03
4.83E−02

41
4.20E−02
−1.60E−03
1.70E−02

42
−4.14E−04
4.15E−03
−4.74E−04

43
−2.68E−04
4.10E−02
−1.70E−03

44
−2.32E−01
−2.25E−03
−2.01E−01

45
6.83E−01
3.67E−04
5.68E−01

46
−9.34E−04
2.81E−01
−1.27E−03

47
7.97E−04
−9.23E−02
−4.25E−04

48
2.45E−01
−1.38E−03
1.97E−01

49
5.38E−02
9.61E−04
3.49E−02

50
−7.00E−03
−2.09E−01
−7.84E−03

51
5.02E−02
−1.02E−02
3.60E−02

52
−9.15E−01
−1.47E−04
−9.20E−01

53
8.34E−03
−2.09E+00
8.02E−03

54
4.16E−04
6.56E−02
−6.87E−04

55
−3.27E−02
6.41E−04
−3.93E−02

56
4.80E−02
−1.64E−03
1.91E−02

57
3.82E−04
7.56E−03
3.41E−04

58
−8.37E−04
6.39E−02
−2.40E−03

59
−2.43E−01
−2.07E−03
−2.14E−01

60
7.38E−01
3.59E−04
6.21E−01

61
−1.01E−03
1.48E−01
−1.37E−03

62
8.11E−04
−9.84E−02
−4.80E−04

63
2.57E−01
−1.20E−03
2.12E−01

64
6.27E−02
9.17E−04
4.10E−02

65
5.29E−03
−4.88E−03
−9.60E−03

66
2.19E−03
2.67E−02
1.29E−03

67
7.61E−03
7.87E−02
6.75E−03

68
−3.80E−02
9.28E−03
−4.76E−02

69
4.11E−01
−3.66E−04
4.02E−01

70
−2.97E−03
6.57E−01
−3.24E−03

71
4.34E−04
2.99E−02
−7.66E−04

72
−1.37E−02
2.47E−04
−1.92E−02

73
5.73E−02
−1.79E−03
2.55E−02

74
3.79E−04
1.46E−02
3.16E−04

75
−9.06E−04
7.68E−02
−2.54E−03

76
−2.51E−01
−1.72E−03
−2.27E−01

77
7.47E−01
3.78E−04
6.34E−01

78
−9.70E−04
1.98E−01
−1.32E−03

79
7.88E−04
−9.81E−02
−5.24E−04

80
2.55E−01
−1.31E−03
2.17E−01

81
7.13E−02
9.31E−04
4.71E−02

82
−2.47E−03
−4.91E−02
−4.14E−03

83
3.09E−02
8.09E−04
3.79E−02

84
−1.89E−02
4.93E−03
−3.54E−02

85
−2.05E−03
−3.05E−02
−3.11E−03

86
−2.42E−03
−6.97E−02
−3.48E−03

87
3.88E−02
−1.76E−03
2.53E−02

88
−1.16E−01
−3.49E−04
−1.24E−01

89
9.09E−04
−2.37E−01
5.50E−04

90
−5.29E−04
3.01E−02
−1.82E−03

91
−6.03E−03
8.78E−04
−1.50E−02

92
6.45E−02
−1.69E−03
3.08E−02

93
2.82E−04
1.48E−02
1.95E−04

94
−8.48E−04
6.89E−02
−2.47E−03

95
−2.44E−01
−1.88E−03
−2.27E−01

96
7.69E−01
3.82E−04
6.69E−01

97
−9.48E−04
2.10E−01
−1.27E−03

98
7.56E−04
−9.46E−02
−5.20E−04

99
2.40E−01
−1.28E−03
2.12E−01

100
7.96E−02
8.77E−04
5.34E−02

TABLE 6

Zernike coefficients for FIG. 1 with [110] lens:

Zernike
Element 1
Element 2
Element 3

1
1.23E+00
7.07E−03
1.23E+00

2
1.51E−02
3.33E−01
1.50E−02

3
−3.38E−01
−2.41E−02
−3.41E−01

4
−6.89E+00
6.38E−03
−6.91E+00

5
−1.71E+00
1.19E−03
−1.71E+00

6
−1.67E−02
6.23E+00
−1.66E−02

7
−5.77E−04
8.01E−02
−4.05E−04

8
−3.40E−01
−6.04E−04
−3.11E−01

9
1.12E+00
−2.82E−03
1.08E+00

10
−1.20E−02
1.14E−01
−1.21E−02

11
−3.64E−01
−3.74E−02
−3.63E−01

12
−6.80E−01
4.97E−04
−7.01E−01

13
1.18E−02
−3.47E+00
1.15E−02

14
−1.12E−02
−1.59E−01
−1.10E−02

15
−2.66E−02
1.27E−02
1.93E−03

16
7.67E−01
−3.42E−03
7.17E−01

17
3.27E+00
−1.44E−02
3.29E+00

18
2.25E−03
2.15E+00
2.41E−03

19
1.04E−02
2.14E−02
1.02E−02

20
−1.53E−01
1.86E−02
−1.34E−01

21
2.99E−01
−1.18E−04
2.68E−01

22
7.32E−03
−1.98E+00
7.10E−03

23
−1.36E−03
4.31E−03
−1.31E−03

24
−5.88E−02
1.53E−03
−2.90E−02

25
6.73E−01
1.02E−04
6.19E−01

26
−6.31E−03
2.36E−01
−6.29E−03

27
1.68E−02
−1.50E−02
−1.09E−02

28
−2.91E−01
8.19E−03
−2.56E−01

29
5.01E−04
−1.26E+00
4.32E−04

30
2.47E−03
−4.86E−02
2.46E−03

31
5.65E−03
7.46E−03
2.64E−02

32
4.69E−01
2.57E−04
4.35E−01

33
−4.78E−03
1.21E+00
−4.78E−03

34
4.70E−03
1.89E−01
4.78E−03

35
−1.64E−01
−2.44E−03
−1.36E−01

36
1.10E−01
1.82E−04
5.24E−02

37
1.10E+00
−4.48E−03
1.10E+00

38
3.80E−03
9.45E−01
3.89E−03

39
8.83E−03
4.43E−02
8.72E−03

40
4.85E−02
4.99E−03
2.12E−02

41
−1.01E+00
1.56E−03
−9.75E−01

42
−9.55E−04
−1.55E−01
−9.21E−04

43
−3.48E−03
−9.44E−02
−3.51E−03

44
−8.20E−02
−4.91E−03
−6.76E−02

45
1.83E−01
4.28E−04
1.46E−01

46
−2.21E−03
2.08E−01
−2.29E−03

47
4.48E−04
7.32E−02
6.45E−04

48
−2.40E−01
1.43E−03
−2.10E−01

49
1.54E−01
−8.40E−04
9.17E−02

50
3.42E−04
1.70E−01
4.41E−04

51
2.23E−03
−1.11E−02
−8.28E−03

52
−3.83E−01
2.41E−03
−3.77E−01

53
−3.97E−03
−1.09E−01
−3.90E−03

54
−2.13E−03
−1.04E−01
−2.08E−03

55
1.09E−01
1.24E−03
8.29E−02

56
−4.97E−02
−1.62E−03
−1.63E−02

57
−1.52E−03
3.20E−01
−1.41E−03

58
−9.75E−05
−3.73E−02
−2.30E−04

59
−2.32E−01
7.66E−05
−2.19E−01

60
8.14E−02
3.06E−04
4.00E−02

61
2.64E−03
−4.45E−01
2.42E−03

62
−3.50E−03
1.32E−02
−3.29E−03

63
−1.91E−01
2.70E−03
−1.65E−01

64
4.63E−01
−1.03E−03
4.03E−01

65
3.09E−01
−2.72E−03
3.00E−01

66
−7.11E−04
1.42E+00
−7.17E−04

67
8.68E−04
1.23E−02
8.75E−04

68
−5.05E−02
8.70E−04
−5.85E−02

69
−4.86E−01
−4.72E−04
−4.82E−01

70
2.16E−03
−4.33E−01
2.18E−03

71
−4.26E−03
−8.66E−02
−4.26E−03

72
1.07E−01
−8.27E−04
7.51E−02

73
1.86E−01
3.73E−04
2.23E−01

74
−7.72E−05
−1.07E−01
−3.66E−05

75
2.02E−03
−2.59E−02
1.91E−03

76
−1.94E−01
3.12E−03
−1.82E−01

77
2.46E−01
1.31E−04
2.02E−01

78
2.75E−03
−3.73E−01
2.59E−03

79
−2.22E−03
4.60E−02
−2.10E−03

80
−1.25E−01
2.12E−03
−1.08E−01

81
5.09E−01
−8.99E−04
4.56E−01

82
−3.15E−03
−4.73E−02
−3.14E−03

83
−2.38E−02
−8.56E−03
−1.34E−02

84
5.25E−02
5.96E−04
4.59E−02

85
−7.38E−04
−2.87E−01
−7.86E−04

86
−3.16E−05
−2.48E−02
4.81E−05

87
5.58E−02
2.82E−03
5.17E−02

88
1.95E−01
−8.12E−04
1.99E−01

89
6.58E−04
−5.77E−02
7.71E−04

90
1.62E−03
−1.03E−02
1.51E−03

91
7.50E−02
1.40E−04
4.29E−02

92
−2.87E−01
1.00E−03
−2.51E−01

93
7.64E−04
−2.63E−01
7.62E−04

94
9.85E−04
−5.21E−02
9.45E−04

95
−8.10E−02
2.64E−03
−7.63E−02

96
3.40E−01
9.13E−05
2.98E−01

97
1.27E−04
−1.69E−01
1.02E−04

98
3.25E−04
7.54E−02
3.96E−04

99
−1.33E−01
1.66E−03
−1.28E−01

100
3.68E−01
−8.69E−04
3.25E−01

TABLE 7

Zernike coefficients for FIG. 3 with [100] lens:

Zernike
Element 1
Element 2
Element 3

1
−5.20E−02
−1.98E−02
−5.16E−02

2
−1.15E−02
1.82E−01
−1.15E−02

3
1.50E−01
1.16E−02
1.51E−01

4
−1.07E−01
−2.20E−02
−1.06E−01

5
−1.34E+01
−2.71E−03
−1.34E+01

6
1.41E−03
−5.60E+00
1.45E−03

7
1.47E−03
−2.81E−02
1.43E−03

8
1.08E−01
−4.12E−03
9.92E−02

9
−4.27E−02
5.85E−04
−4.05E−02

10
1.41E−02
8.59E−02
1.42E−02

11
−4.65E−01
2.26E−02
−4.60E−01

12
4.58E+00
−6.33E−04
4.57E+00

13
−3.52E−03
3.65E+00
−3.43E−03

14
3.28E−03
−2.67E−02
3.21E−03

15
−1.29E−03
−3.64E−03
−8.29E−03

16
−2.37E−02
1.69E−03
−2.09E−02

17
−1.58E−01
9.09E−02
−1.56E−01

18
−1.67E−02
−1.31E−01
−1.68E−02

19
−9.00E−03
−9.34E−03
−8.96E−03

20
3.17E−02
−1.15E−02
3.42E−02

21
−3.46E−01
−3.18E−04
−3.60E−01

22
8.48E−04
−1.59E+00
9.43E−04

23
−1.25E−03
−3.60E−02
−1.36E−03

24
1.27E−01
7.76E−04
1.17E−01

25
−3.31E−02
9.62E−04
−2.98E−02

26
9.70E−03
7.57E−02
9.79E−03

27
−4.80E−02
−3.29E−04
−4.88E−02

28
−3.12E−02
−1.76E−02
−2.89E−02

29
5.07E−03
7.34E−03
5.09E−03

30
1.77E−03
1.11E−01
1.89E−03

31
−1.16E−01
4.07E−03
−1.12E−01

32
8.53E−02
8.68E−05
7.06E−02

33
−4.51E−04
5.63E−01
−3.42E−04

34
1.74E−04
−3.33E−02
5.81E−05

35
1.33E−01
−2.08E−03
1.21E−01

36
−3.65E−02
2.91E−03
−3.29E−02

37
6.20E−01
4.55E−03
6.26E−01

38
−5.12E−04
2.56E+00
−5.97E−04

39
−6.99E−03
−4.66E−02
−6.93E−03

40
2.52E−02
6.82E−03
2.53E−02

41
−2.95E−02
1.05E−03
−2.69E−02

42
−3.08E−03
−2.54E−02
−3.17E−03

43
−1.83E−04
−1.04E−02
−7.27E−05

44
−1.15E−01
−2.59E−03
−1.11E−01

45
2.88E−01
3.57E−04
2.71E−01

46
−3.54E−04
7.37E−02
−2.30E−04

47
4.01E−04
−4.84E−02
2.74E−04

48
1.37E−01
−1.15E−03
1.24E−01

49
−3.79E−02
2.15E−03
−3.42E−02

50
−7.02E−03
−2.04E−01
−7.08E−03

51
5.09E−02
−9.05E−03
5.25E−02

52
−1.00E+00
−8.40E−05
−9.93E−01

53
1.17E−03
−2.40E+00
1.05E−03

54
2.77E−03
3.21E−02
2.88E−03

55
−2.37E−02
−4.55E−04
−2.56E−02

56
−2.73E−02
−3.95E−03
−2.44E−02

57
1.73E−03
−4.84E−03
1.70E−03

58
−6.60E−04
4.85E−02
−5.38E−04

59
−1.20E−01
−1.33E−03
−1.15E−01

60
2.82E−01
3.92E−04
2.62E−01

61
−2.60E−04
1.81E−02
−1.14E−04

62
2.84E−04
−5.74E−02
1.50E−04

63
1.63E−01
−1.49E−03
1.50E−01

64
−4.08E−02
2.56E−03
−3.74E−02

65
2.14E−02
−3.63E−02
2.58E−02

66
1.53E−02
1.19E−01
1.53E−02

67
7.88E−03
1.32E−01
7.81E−03

68
−4.64E−02
7.68E−03
−4.27E−02

69
6.28E−01
−5.30E−05
6.37E−01

70
−1.17E−03
1.28E+00
−1.28E−03

71
1.20E−04
1.27E−02
2.28E−04

72
−1.17E−02
6.03E−04
−1.24E−02

73
−3.05E−02
−4.10E−03
−2.74E−02

74
5.12E−04
−5.97E−03
4.65E−04

75
−5.85E−04
5.53E−02
−4.59E−04

76
−1.46E−01
−1.44E−03
−1.42E−01

77
2.91E−01
4.82E−04
2.70E−01

78
−2.85E−04
1.42E−01
−1.21E−04

79
2.54E−04
−5.57E−02
1.01E−04

80
1.71E−01
−1.65E−03
1.57E−01

81
−4.08E−02
2.91E−03
−3.78E−02

82
−5.64E−03
−4.41E−02
−5.71E−03

83
2.45E−03
−4.80E−03
1.97E−03

84
−5.55E−04
2.12E−02
4.58E−03

85
−8.43E−03
−3.86E−02
−8.41E−03

86
−4.36E−03
−9.15E−02
−4.46E−03

87
5.15E−02
−4.47E−03
5.44E−02

88
−3.55E−01
−4.58E−04
−3.45E−01

89
7.27E−04
−5.43E−01
5.93E−04

90
−3.63E−04
5.57E−03
−2.48E−04

91
−5.94E−03
1.26E−03
−7.76E−03

92
−3.39E−02
−4.09E−03
−3.06E−02

93
4.93E−04
−9.61E−03
4.45E−04

94
−5.44E−04
4.51E−02
−4.06E−04

95
−1.54E−01
−1.82E−03
−1.50E−01

96
3.42E−01
5.55E−04
3.20E−01

97
−3.27E−04
1.19E−01
−1.64E−04

98
2.87E−04
−6.36E−02
1.12E−04

99
1.80E−01
−1.60E−03
1.66E−01

100
−3.94E−02
3.04E−03
−3.71E−02

TABLE 8

Zernike coefficients for FIG. 3 with [110] lens:

Zernike
Element 1
Element 2
Element 3

1
4.83E−01
2.93E−02
4.79E−01

2
1.68E−02
1.92E−01
1.67E−02

3
−2.79E−01
−1.85E−02
−2.81E−01

4
−7.03E+00
3.27E−02
−7.04E+00

5
−2.49E+00
1.79E−02
−2.49E+00

6
1.19E−02
5.86E+00
1.15E−02

7
−2.46E−03
6.03E−03
−2.48E−03

8
−2.78E−01
2.94E−03
−2.72E−01

9
2.13E+00
−6.50E−03
2.13E+00

10
−7.36E−03
6.11E−02
−7.31E−03

11
−3.00E−01
−3.06E−02
−3.01E−01

12
−6.65E−01
4.38E−03
−6.67E−01

13
3.12E−03
−4.56E+00
1.95E−03

14
−1.08E−02
−1.30E−01
−1.08E−02

15
1.17E−01
8.74E−03
1.19E−01

16
5.53E−01
−7.61E−03
5.45E−01

17
3.72E+00
−4.84E−02
3.73E+00

18
5.10E−02
2.15E+00
5.14E−02

19
1.11E−02
8.31E−02
1.12E−02

20
−3.69E−02
1.90E−02
−3.38E−02

21
4.46E−01
−1.55E−03
4.43E−01

22
−3.18E−03
−6.97E−01
−4.58E−03

23
3.97E−03
5.38E−02
3.92E−03

24
−2.50E−02
−2.92E−03
−2.22E−02

25
1.07E−01
5.30E−03
9.70E−02

26
−5.33E−03
1.78E−01
−5.35E−03

27
7.08E−02
−1.94E−02
6.51E−02

28
−9.66E−01
3.20E−02
−9.62E−01

29
−1.98E−02
−1.48E+00
−1.96E−02

30
−1.14E−03
−2.60E−02
−1.04E−03

31
5.01E−02
2.29E−04
5.19E−02

32
2.07E−01
1.67E−03
2.02E−01

33
3.24E−03
1.98E+00
1.69E−03

34
5.34E−03
1.25E−01
5.24E−03

35
−1.14E−01
−6.94E−04
−1.10E−01

36
−3.41E−01
3.97E−04
−3.51E−01

37
1.29E+00
−8.80E−03
1.29E+00

38
3.27E−02
1.20E+00
3.41E−02

39
1.08E−02
1.17E−02
1.07E−02

40
−3.49E−03
8.00E−03
−7.33E−03

41
−7.60E−01
−3.03E−03
−7.52E−01

42
−5.82E−04
4.20E−01
−8.98E−05

43
−2.67E−03
−7.35E−02
−2.53E−03

44
−8.45E−02
−5.13E−03
−8.43E−02

45
−1.73E−01
1.31E−03
−1.79E−01

46
4.18E−03
−5.21E−01
2.16E−03

47
−4.32E−03
−3.76E−02
−4.48E−03

48
−1.04E−01
3.54E−03
−9.82E−02

49
1.92E−01
−4.14E−03
1.82E−01

50
−7.42E−04
5.07E−02
−8.61E−04

51
9.49E−03
−1.09E−02
9.43E−03

52
−6.69E−01
9.88E−03
−6.68E−01

53
−9.34E−03
−3.79E−01
−7.65E−03

54
−6.83E−03
−7.66E−02
−6.92E−03

55
3.19E−02
−1.12E−03
2.73E−02

56
5.60E−01
−6.94E−03
5.68E−01

57
7.43E−03
3.40E−01
8.02E−03

58
3.67E−03
3.54E−02
3.86E−03

59
−1.35E−01
3.56E−03
−1.33E−01

60
−1.47E−03
−9.18E−04
−7.85E−03

61
−1.72E−03
−5.02E−01
−4.13E−03

62
−4.12E−03
6.37E−03
−4.32E−03

63
−3.67E−02
2.06E−03
−3.14E−02

64
3.71E−01
−2.01E−03
3.59E−01

65
3.96E−01
−1.31E−02
3.99E−01

66
1.62E−02
1.66E+00
1.55E−02

67
1.53E−03
1.38E−03
1.27E−03

68
−5.96E−02
3.90E−03
−5.77E−02

69
−1.56E−01
−5.63E−03
−1.52E−01

70
2.32E−04
−3.04E−01
2.23E−03

71
−1.51E−03
−5.28E−03
−1.57E−03

72
4.45E−02
−1.84E−03
3.75E−02

73
4.54E−02
4.67E−03
5.26E−02

74
−3.69E−03
−3.03E−01
−3.14E−03

75
2.66E−03
−2.61E−03
2.93E−03

76
−2.91E−02
2.51E−03
−2.63E−02

77
2.11E−01
−6.93E−04
2.03E−01

78
−6.88E−04
9.83E−02
−3.22E−03

79
1.83E−03
6.74E−02
1.56E−03

80
−5.99E−02
1.58E−03
−5.59E−02

81
8.73E−02
−1.09E−03
7.31E−02

82
−4.97E−03
−9.09E−02
−4.70E−03

83
−8.53E−03
−9.63E−03
−4.26E−03

84
−5.39E−02
4.49E−03
−5.13E−02

85
7.83E−04
−6.40E−01
−1.20E−04

86
−3.20E−03
−5.82E−04
−3.52E−03

87
4.35E−02
1.13E−03
4.60E−02

88
4.54E−01
−1.08E−03
4.57E−01

89
9.66E−04
2.35E−01
3.33E−03

90
6.07E−03
3.56E−02
6.01E−03

91
1.33E−02
5.63E−04
6.51E−03

92
−5.06E−01
2.07E−03
−4.97E−01

93
−4.84E−03
−8.16E−02
−4.19E−03

94
2.11E−05
−3.62E−02
4.06E−04

95
−2.61E−02
7.66E−04
−2.55E−02

96
9.27E−02
1.12E−04
8.33E−02

97
3.17E−03
9.43E−02
5.00E−04

98
1.19E−03
4.57E−02
7.97E−04

99
−1.26E−01
2.23E−03
−1.22E−01

100
3.55E−02
−2.26E−03
2.17E−02

	Number	Date	Country
Parent	PCT/EP2008/052736	Mar 2008	US
Child	12539136		US

PROJECTION OBJECTIVE OF A MICROLITHOGRAPHIC PROJECTION EXPOSURE APPARATUS

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CPC

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Abstract

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CROSS-REFERENCE TO RELATED APPLICATIONS

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