JP7614962B2 - PROJECTION OPTICAL SYSTEM, EXPOSURE APPARATUS, AND METHOD FOR MANUFACTURING ARTICLE - Google Patents

Description

The present invention relates to a projection optical system, an exposure apparatus, and a method for manufacturing an article.

In the lithography process, which is a manufacturing process for semiconductor devices and flat panel displays (FPDs) such as liquid crystal or organic EL display devices, an exposure apparatus having a projection optical system can be used. In the exposure apparatus, the pattern of an original (reticle, mask) is projected via a projection optical system onto a substrate (wafer, glass plate, etc.) coated with a photosensitive material (resist), thereby transferring the pattern of the original onto the substrate.

A known example of the projection optical system of an exposure apparatus is a telecentric catadioptric optical system that uses a concave mirror and a convex mirror to reflect light a total of three times. In such a projection optical system, aspheric surfaces are used for the lenses and/or mirrors that make up the system, and an image of an illumination area (e.g., an arc-shaped area) on an original plate placed on the object plane can be projected onto the substrate at the same magnification or at a magnified magnification.

Patent Document 1 proposes a configuration of a projection optical system that can improve throughput by expanding the width (slit width) of an arc-shaped illumination area on the original. Patent Document 2 proposes a configuration of a projection optical system that can increase the imaging magnification (projection magnification) of the projection optical system. Patent Document 3 proposes a configuration of a projection optical system that has a magnification ratio to suppress the increase in size of the original due to the increase in size of the device.

JP 2006-78631 A JP 2006-78592 A JP 2008-89832 A

Akiyoshi Suzuki, "Analysis of a 1:1 Two-Mirror System," Optics, Vol. 14, No. 5, October 1985

Changes in market demand for exposure tools include higher definition, larger screens, and improved production efficiency. To meet these demands, it is necessary to improve the resolution of the projection optical system and expand the exposure range. In other words, there is a demand for even higher specifications for the projection optical system of exposure tools, such as higher NA, shorter wavelengths, and an expanded projection area on the image plane.

In the configurations of the projection optical systems described in Patent Documents 1 and 2, two lenses and an aspheric surface are placed near a convex mirror, but the optical performance (particularly the correction of the sagittal and meridional color image planes and the color halo of the lateral aberration) is insufficient. Therefore, it is not suitable for further increasing the NA or expanding the projection area. In the configuration of the projection optical system described in Patent Document 3, a single lens with aspheric surfaces on both sides is placed near a convex mirror, but the optical performance (particularly the correction of the image height difference of the sagittal halo, the chromatic aberration, and the lateral aberration) is insufficient. Therefore, it is not suitable for further increasing the NA or expanding the projection area.

Therefore, the present invention aims to provide a projection optical system that can achieve both high specifications and good optical performance.

In order to achieve the above object, one aspect of the present invention provides a projection optical system that has a concave mirror and a convex mirror, and projects an image of a pattern of an illumination area located off an optical axis on an object surface onto an image surface by reflecting the image on the concave mirror, the convex mirror, and the concave mirror in that order, the projection optical system further comprises a lens group arranged on an optical path between the concave mirror and the convex mirror , the concave mirror being aspherical, the lens group including a first lens having a first aspherical surface, and a second lens arranged between the first lens and the convex mirror and having a second aspherical surface, the first aspherical surface of the first lens being a first aspherical surface of a line at which a meridian plane that bisects the illumination area intersects the illumination area, the end point closer to the optical axis being Yi and the end point farther from the optical axis being Ya, the first aspherical surface of the first lens being a line at which a chief ray from the end point Yi is incident The second aspheric surface of the second lens is characterized in that, when a position of the aspheric surface is Pcr, a position of the first aspheric surface where a sagittal marginal ray from the end point Ya is incident is Psm, and powers at the position Pcr and the position Psm are φcr and φsm, respectively, φsm < φcr is satisfied, and as a power change from the position Pcr to the position Psm, the power changes in a negative direction from the power φcr to the power φsm, and in order to compensate for the power change from the position Pcr to the position Psm on the first aspheric surface, the second aspheric surface of the second lens has a region where the power changes in a positive direction from a position where a light ray that has passed through the position Pcr of the first aspheric surface is incident toward a position where a light ray that has passed through the position Psm of the first aspheric surface is incident.

Further objects and other aspects of the present invention will become apparent from the following description of preferred embodiments thereof with reference to the accompanying drawings.

The present invention can provide, for example, a projection optical system that can achieve both high specifications and good optical performance.

FIG. 1 is a schematic diagram showing a configuration of a projection optical system according to a first embodiment. FIG. 1 shows an illumination area on an object plane. FIG. 1 is a diagram for explaining the configuration of a lens group according to the first embodiment; FIG. 13 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the first embodiment. FIG. 1 is a longitudinal aberration diagram of the projection optical system according to the first embodiment. FIG. 1 is a diagram showing lateral aberration and wavefront aberration at the i-line in the projection optical system of Example 1. FIG. 13 is a schematic diagram showing the configuration of a projection optical system according to a second embodiment. FIG. 13 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the second embodiment. FIG. 13 is a longitudinal aberration diagram of the projection optical system according to the second embodiment. FIG. 13 is a diagram showing lateral aberration and wavefront aberration at the i-line in the projection optical system of the second embodiment. FIG. 13 is a schematic diagram showing the configuration of a projection optical system according to a third embodiment. FIG. 13 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the third embodiment. FIG. 13 is a longitudinal aberration diagram of the projection optical system according to the third embodiment. FIG. 13 is a diagram showing lateral aberration and wavefront aberration at the i-line in the projection optical system of Example 3. FIG. 13 is a schematic diagram showing the configuration of a projection optical system according to a fourth embodiment. FIG. 13 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the fourth embodiment. FIG. 13 is a longitudinal aberration diagram of the projection optical system according to the fourth embodiment. FIG. 13 is a diagram showing lateral aberration and wavefront aberration at i-line in the projection optical system of Example 4. FIG. 13 is a schematic diagram showing the configuration of a projection optical system according to a fifth embodiment. FIG. 13 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the fifth embodiment. FIG. 13 is a longitudinal aberration diagram of the projection optical system according to the fifth embodiment. FIG. 13 is a diagram showing lateral aberration and wavefront aberration at a wavelength of 320 nm in the projection optical system of Example 5. FIG. 13 is a schematic diagram showing the configuration of a projection optical system according to a sixth embodiment. FIG. 13 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the sixth embodiment. FIG. 13 is a longitudinal aberration diagram of the projection optical system according to the sixth embodiment. FIG. 13 is a diagram showing lateral aberration and wavefront aberration at a wavelength of 320 nm in the projection optical system of Example 6. FIG. 13 is a schematic diagram showing the configuration of a projection optical system according to a seventh embodiment. FIG. 13 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the seventh embodiment. FIG. 13 is a longitudinal aberration diagram of the projection optical system according to the seventh embodiment. FIG. 13 is a diagram showing lateral aberration and wavefront aberration at i-line in the projection optical system of Example 7. FIG. 13 is a schematic diagram showing the configuration of a projection optical system according to an eighth embodiment of the present invention. FIG. 23 is a diagram showing a change in local power of an aspheric surface in the projection optical system according to the eighth embodiment. FIG. 13 is a longitudinal aberration diagram of the projection optical system according to the eighth embodiment. FIG. 13 is a diagram showing lateral aberration and wavefront aberration at i-line in the projection optical system of Example 8. Schematic diagram showing an example of the configuration of an exposure apparatus A diagram for explaining the basic parameters of a 1:1 two-mirror system. Schematic diagram of a conventional projection optical system Longitudinal aberration diagram in a conventional projection optical system 1 is a diagram showing a lateral aberration diagram and a wavefront aberration diagram for the i-line in a projection optical system having a conventional configuration. FIG. 13 is a diagram showing a change in local power of an aspheric surface in a projection optical system having a conventional configuration. FIG. 1 is a diagram showing a change in local power of an aspheric surface in the projection optical system of Patent Document 1. FIG. 1 is a diagram showing a change in local power of an aspheric surface in the projection optical system of Patent Document 1. FIG. 1 is a diagram showing a change in local power of an aspheric surface in the projection optical system of Patent Document 1. Diagram to explain the causes of ghosts and flares

The following embodiments are described in detail with reference to the attached drawings. Note that the following embodiments do not limit the invention according to the claims. Although the embodiments describe multiple features, not all of these multiple features are necessarily essential to the invention, and multiple features may be combined in any manner. Furthermore, in the attached drawings, the same reference numbers are used for the same or similar configurations, and duplicate explanations are omitted.

First, the reason why it is not easy to achieve high specifications such as high NA, short wavelength, expansion of the projection area (effective area) on the image plane, and compactness in a projection optical system used in an exposure apparatus and good optical performance at the same time, which are the objectives of the present invention, will be explained using the above-mentioned non-patent document 1. According to non-patent document 1, for example, from equation (21) in non-patent document 1, it can be seen that the transverse aberration is proportional to the fourth power of θ and the third power of NA (φ), and the residual wavefront aberration is proportional to h× ^NA7. As shown in FIG. 27 (corresponding to FIG. 1 in non-patent document 1), h, φ, and θ respectively represent parameters related to the object height, NA, and chief ray angle. In other words, if h and θ are also increased while φ is increased to ensure the distance between the convex mirror and the light rays above and below it, a high NA can be achieved, if h and θ are increased, an expansion of the projection area can be achieved, and if θ is increased, the diameter of the concave mirror is reduced, so a compact design can be achieved. However, in this case, the amount of the above-mentioned aberrations can be enormous. Furthermore, when shortening the wavelength, since the glass material used is almost limited to quartz, it becomes difficult to correct field curvature, astigmatism, and lateral aberration, particularly including color, and if h is increased to expand the projection area, the correction becomes even more difficult. Therefore, the present inventors have conducted extensive research and found a configuration of a projection optical system that can achieve both high specifications and good optical performance. Below, an embodiment of the projection optical system according to the present invention will be described.

[Example 1]
A first embodiment of the projection optical system according to the present invention will be described. FIG. 1 is a schematic diagram showing the configuration of a projection optical system PO1 according to the first embodiment of the present invention. The projection optical system PO1 has a concave mirror M1 and a convex mirror M2, and projects an image of a pattern in an illumination area located off the optical axis on an object surface onto an image surface by reflecting the image of the pattern on the concave mirror M1, the convex mirror M2, and the concave mirror M1 in that order. In FIG. 1, OA represents the optical axis, OP represents the object surface, IP represents the image surface, L1 represents the first aspheric lens, SG represents the refractive optical element, and LG represents the lens group. When the projection optical system PO1 is applied to an exposure apparatus, an original may be placed on the object surface OP of the projection optical system PO1, and a substrate may be placed on the image surface IP of the projection optical system PO2. The light beam emitted from the object plane OP with NA 0.1 passes through or is reflected by each optical element in the order of the optical path from the object plane OP: L1 → SG → M1 → LG → M2 → LG → M1 → SG → L1, and is imaged at the image plane IP at the same magnification. That is, the projection optical system PO1 of the first embodiment is a life-size system that projects the image of the illumination area IR at the object plane OP (specifically, the image of the pattern provided in the illumination area IR) at the same magnification onto the image plane IP. The pupil position (pupil plane) of the projection optical system PO1 is the convex mirror M2, and an aperture stop may be disposed near the convex mirror M2. The refractive optical member SG can also be used to adjust the imaging magnification or distortion.

In the configuration example shown in FIG. 1, the lens group LG is disposed on the optical path between the concave mirror M1 and the convex mirror M2, and may include a lens L2 and a lens L3. It may be understood that the lens L2 is a first lens having a first aspheric surface, and the lens L3 is a second lens disposed between the lens L2 (first lens) and the convex mirror M2 and having a second aspheric surface. In this embodiment 1, the lens L2 is a meniscus lens with its convex surface facing the concave mirror, and the surface of the lens L2 facing the concave mirror is an aspheric surface (first aspheric surface). In addition, the surface of the lens L3 facing the convex mirror is an aspheric surface (second aspheric surface).

Figure 2A shows the illumination area IR on the object plane OP. The illumination area IR may be understood as an area where the original placed on the object plane OP is illuminated by slit light, and may be called an effective area. The illumination area IR is located outside the optical axis (outside the optical axis OA) on the object plane OP so that the optical axis OA is not included. In this embodiment 1, an arc-shaped illumination area IR is described, but the shape of the illumination area IR is not limited to an arc shape and may be a rectangular shape. Also, in this embodiment 1, as shown in Figure 2A, the length in the Y-axis direction, which is the short side direction of the illumination area IR, is represented as the slit width Sw, the length in the X-axis direction, which is the long side direction, is represented as the illumination width (exposure width) W, the minimum object height in the meridian plane in the illumination area IR is represented as the lower limit Yi, and the maximum object height is represented as the upper limit Ya. The meridional plane can be defined as a surface (meridional surface) that includes the optical axis OP and the chief ray that passes through the center of gravity of the illumination area IR as an object point, that is, as a surface that includes the optical axis OP and bisects the illumination area IR. The lower limit Yi may be understood as the end point closer to the optical axis OP of the two end points of the line where the illumination area IR intersects with the meridional plane, and the upper limit Ya may be understood as the end point farther from the optical axis OP of the two end points. In the projection optical system PO1, the larger the illumination width W, the larger the screen size that can be achieved during one-shot exposure, and the larger the slit width Sw, the higher the exposure illuminance can be, which can improve throughput (i.e., production efficiency).

Figure 2B shows the configuration of the lens group LG in this embodiment 1. Figure 2B (a) shows an enlarged view of the lens group LG (lenses L2, L3) and the convex mirror M2, Figure 2B (b) shows the light beam position on the aspheric surface L2R1 (surface on the concave mirror side) of lens L2, and Figure 2B (c) shows the change in local power on each aspheric surface. As described above, the lens group LG in this embodiment 1 includes lens L2, which is a meniscus lens arranged closest to the concave mirror M1 and with its convex surface facing the concave mirror M1 side, and lens L3 arranged between lens L2 and the convex mirror M2. The surface L2R1 of lens L2 on the concave mirror M2 side and the surface L3R2 of lens L3 on the convex mirror M2 side are aspheric surfaces, and these surfaces may be referred to as aspheric surfaces L2R1 and L3R2 below.

Figure 2B(a) shows the upper ray, chief ray, and lower ray with the lower limit Yi (end point Yi) and the upper limit Ya (end point Ya) as object points, respectively, and indicates the position Pcr on the aspheric surface L2R1 where the chief ray from the lower limit Yi is incident with an x mark. In Figure 2B(b), the beam diameter from the lower limit Yi is indicated with a dashed line (Yi beam diameter), and the beam diameter from the upper limit Ya is indicated with a short dotted line (Ya beam diameter). The position Pcr on the aspheric surface L2R1 where the chief ray from the lower limit Yi is incident is indicated with an x mark, and the position Psm on the aspheric surface L2R1 where the sagittal marginal ray from the upper limit Ya is incident is indicated with a circle mark. In addition, in FIG. 2B(b), circles with radii extending from the optical axis OA to positions Pcr and Psm are shown by long dotted lines, and in this embodiment 1, the aspheric local power shape is defined within the area surrounded by the dotted lines. Here, the sagittal marginal ray from the upper limit Ya may be understood as a marginal ray within the sagittal plane from the upper limit Ya, or as a marginal ray (peripheral ray) among the sagittal rays from the upper limit Ya.

Figure 2B(c) shows the change in local power for each aspheric surface, with the vertical axis representing the position (height) in the radial direction of the aspheric surface, and the horizontal axis representing the local power of each aspheric surface (hereinafter sometimes referred to as aspheric surface local power). The numbers on the horizontal axis represent the numbers of the aspheric surfaces arranged in the order of the optical path from the object surface OP, with the third being aspheric surface L2R1 and the fourth being aspheric surface L3R2. The aspheric surface local power shown on the horizontal axis is positive in the right direction on the paper and negative in the left direction on the paper. In Figure 2B(c), the positions Pcr and Psm on the aspheric surface L2R1 are indicated by x marks and o marks, respectively, and the positions (heights) on the aspheric surface L3R2 where the light rays that have passed through the positions Pcr and Psm on the aspheric surface L2R1 are incident are also indicated by x marks and o marks.

Here, in order to achieve both high specifications and good optical performance, the projection optical system according to the present invention is configured so that the first aspheric surface of the first lens satisfies formula (1) when the aspheric local powers at positions Pcr and Psm on the first aspheric surface are φcr and φsm, respectively. φoa in formula (1) indicates the power on the optical axis of the first aspheric surface. The second aspheric surface of the second lens includes a region for compensating for the power change from position Pcr to position Psm on the first aspheric surface (change from power φcr to power φsm).
(φsm−φcr)/｜φoa｜< 0...(1)

In the case of the projection optical system PO1 of the present embodiment 1, as described above, the first lens is the lens L2, the first aspheric surface is the aspheric surface L2R1, the second lens is the lens L3, and the second aspheric surface is the aspheric surface L3R2. Referring to FIG. 2B(c), in the aspheric surface L2R1 (the third aspheric surface) as the first aspheric surface, the aspheric local power changes monotonically from φcr to φsm in the negative direction from position Pcr (marked with an x) to position Psm (marked with an o), and the above formula (1) is satisfied. In addition, the aspheric surface L3R2 (the fourth aspheric surface) as the second aspheric surface has a region in which the aspheric local power changes in the positive direction so as to compensate (preferably cancel) the change in the negative aspheric local power in the aspheric surface L2R1 as the first aspheric surface. Specifically, in aspheric surface L3R2, the local aspheric power changes monotonically in the positive direction from the position (x mark) where the light ray that passed through position Pcr of aspheric surface L2R1 is incident to the position (circle mark) where the light ray that passed through position Psm of aspheric surface L2R1 is incident.

Next, to clarify the effect of the configuration of the projection optical system according to the present invention compared to a conventional projection optical system (difference in correction mechanism), the results of an attempt to design a conventional projection optical system POc will be described. The conventional projection optical system POc has the same optical specifications (configuration, design freedom) as the projection optical system PO1 of Example 1 shown in FIG. 1, except that the lens group LG includes only one lens L2 that is aspherical on both sides. The optical specifications of the conventional projection optical system POc are NA 0.1, illumination width W = 1100 mm, and slit width Sw = 100 mm (object height 519-619 mm), as shown in Table 1 below. Tables 2 and 3 below show examples of numerical values of various parameters used in the design of the conventional projection optical system POc (explanation conforms to paragraph 0038). Also, a schematic diagram of a conventional projection optical system POc is shown in Figure 28, a longitudinal aberration diagram of the conventional projection optical system POc is shown in Figure 29A, and a transverse aberration diagram and the wavefront aberration RMS of the i-line are shown in Figure 29B. Figure 30 shows the change in local aspheric power in the conventional projection optical system POc, where the position (height) of each aspheric surface is normalized by the effective radius.

Usually, in an aberration diagram, the meridional upper ray, lower ray, and sagittal ray are displayed interchangeably depending on the sign of the entrance pupil position based on the object plane, but here, in all aberration diagrams, the upper and lower rays on the optical path diagram have been corrected to correspond to the aberration diagram. Also, in the numerical examples of various parameters shown in Tables 2 and 3, a mirror is inserted just before the image plane so that the image field has a positive spacing and a positive refractive index in the longitudinal aberration diagram, and the number of mirrors is an even number. The above settings are used in common in all embodiments of the present invention described below.

In the projection optical system POc of the conventional configuration, the design results show that the dominant wavelength is 365 nm (i-line) as shown in FIGS. 29A-29B, and it has been confirmed that the following aberrations remain, as can be seen from the lateral aberration, for example.
(Aberration 1) The meridional curvature of color field is corrected at intermediate image heights, but the tendency is reversed at the upper and lower image height ends (short wavelengths are under-corrected and long wavelengths are over-corrected toward higher image heights).
(Aberration 2) Meridional off-axis spherical aberration (halo) including color tends to be under-corrected. (Aberration 3) Sagittal off-axis spherical aberration (halo) including color tends to be under-corrected toward higher image heights. (Aberration 4) The spherical aberration that governs the sagittal halo at low image heights tends to be over-corrected. As a result, it was confirmed that the wavefront aberration RMS for the i-line was small at intermediate object heights, but increased to approximately 40 mλ and 50 mλ at the object heights at both ends of the slit width.

The reason for this is that for both surface R1 on the concave mirror side of lens L2 and surface R2 on the convex mirror side, the change in surface power is negative for correcting aberrations 1 to 3, but positive for correcting aberration 4, so a single surface alone cannot correct all of aberrations 1 to 4. Furthermore, even when considering aberration correction at two surfaces, surfaces R1 and R2, the Petzval sum correction for the entire system is carried out by the power of the concave and convex mirrors, so the power of the meniscus lens is close to zero, and surfaces R1 and R2 move in a bending manner. In other words, because the sensitivity of aberration correction is similar, surfaces R1 and R2 cannot each perform aberration correction independently. As a result, in Figure 30, the change in power between the aspheric local powers at the positions of lens L2 in the conventional configuration corresponding to positions Pcr and Psm of the aspheric surface L2R1 in this embodiment 1 is extremely small, as shown by φcr (marked with an x) and φsm (marked with an o), respectively. Therefore, in the projection optical system described in Patent Document 3, in which only one lens with aspheric surfaces on both sides is placed near the convex mirror, as in the above-mentioned conventional configuration, aberrations may be undercorrected, as described above.

In contrast, according to the configuration of the projection optical system PO1 of the present embodiment 1 of the present invention, the occurrence of spherical aberration can be suppressed by making the lens L2 of the lens group LG a meniscus lens with the convex surface facing the concave mirror side. In other words, the aberration 4 can be reduced (suppressed). And, the aspheric surface L2R1 located closest to the concave mirror among the aspheric surfaces in the lens group LG is far from the convex mirror which is the pupil position, and the position difference through which the light rays pass for each image height is large. Therefore, by changing the aspheric local power change in the aspheric surface L2R1 from φcr to φsm in the negative direction, it is possible to simultaneously correct aberrations 1 to 3 caused by the image height difference. On the other hand, the aspheric surface L2R1 alone can increase the aberration 4, but the aberration 4 is reduced by using the aspheric surface L3R2 of the lens L3. Specifically, the aspheric surface L3R2 of lens L3 is placed near the convex mirror, which is the pupil position where the difference in position where the light rays pass for each image height is small, and the local power of the aspheric surface L3R2 is changed in the positive direction to compensate for the negative power change at the aspheric surface L2R1 of lens L2. This makes it possible to correct the uniform component of the aberration corrected by the aspheric surface L2R1 of lens L2 and mainly aberration 4, making it possible to correct aberrations 1 to 4 well overall. The effect of the above aberration correction can be greater because the light rays pass through lens group LG twice before and after reflection from convex mirror M2.

In addition, in the projection optical systems described in Patent Documents 1 and 2, two or more lenses are arranged near the convex mirror. In Patent Document 1, examples 1, 3, and 4 use aspheric surfaces in the lens group, and in Patent Document 2, examples 3 (same as example 3 in Patent Document 1) and 4 (same as example 4 in Patent Document 1) use aspheric surfaces in the lens group. For verification, the inventor reproduced the aspheric local powers of examples 1, 3, and 4 of Patent Document 1, and the results are shown in Figures 31, 32, and 33, respectively (the vertical axis is normalized by the effective radius). In each of Figures 31 to 33, the aspheric local powers at the positions Pcr and Psm defined above are shown by φcr (marked with an x) and φsm (marked with an o) on the aspheric surface arranged closest to the concave mirror among the aspheric surfaces in the lens group. In addition, in the subsequent aspheric surfaces, the positions where the light rays that have passed through positions Pcr and Psm are incident are shown by marks x and o, respectively. As is clear from each of Figures 31 to 33, the aspheric surface arranged on the meniscus lens closest to the concave mirror changes in the positive direction from φcr (marked with an x) to φsm (marked with an o), and it can be seen that the correction principle is different from that of the projection optical system according to the present invention. Therefore, with the configurations of the projection optical systems described in Patent Documents 1 and 2, it is difficult to achieve both high specifications and good aberration correction.

Next, more preferable configuration conditions for achieving both high specifications and good optical performance in the projection optical system according to the present invention will be described.
The projection optical system according to the present invention may be configured to satisfy the following formula (2) when the power of the second aspheric surface of the second lens (the aspheric surface L3R2 of the lens L3 in the first embodiment) is φmr and the power of the convex mirror M2 is φtm. Formula (2) is a condition for correcting spherical aberration to a good range, and sets a range including no power for the lens surface. When (φmr/φtm) is smaller than the lower limit (-0.12), the lens surface becomes convex and the positive power becomes large, so that high-order under-spherical aberration occurs. On the other hand, when it is larger than the upper limit (0.15), over-spherical aberration is likely to occur, so that the sagittal halo of a low image height also becomes over, and as a result, the sagittal halo image height difference increases.
-0.12 ≦ φmr／φtm ≦ 0.15...(2)

In addition, the projection optical system according to the present invention may be configured to satisfy the following formula (3) when the power of the entire lens group LG is φAM and the power of the second lens (lens L3 in the first embodiment) is φTL. Formula (3) specifies the power of the lens that is located closest to the convex mirror among the lenses in the lens group LG. Since the Petzval sum in the entire optical system is determined by the powers of the concave mirror M1 and the convex mirror M2, the power φAM of the lens group LG is close to no power, and the sign can be both positive and negative. Therefore, the ratio between the absolute value of the power φAM and the power φTL of the second lens is specified. In the projection optical system PO1 of the first embodiment, the power of the lens L3 that is located closest to the convex mirror has a positive value. In addition, since the power of the surface of the lens L3 facing the convex mirror is defined by the above formula (2), when (|φAM|/φTL) is smaller than the lower limit (0.08), the power of the surface of the lens L3 facing the concave mirror becomes large in the positive direction. In this case, the effect of correcting the above-mentioned aberrations 1 to 3, which is achieved by configuring the first spherical surface of the first lens to satisfy the above formula (1), is reduced (cancelled), which is undesirable. On the other hand, the upper limit automatically becomes no power, which is equal to the power φAM of the lens group LG, so that it can be defined as 1.0 (the preferred upper limit is 0.95).
0.08 ≦ ｜φAM｜/φTL ≦ 0.95 ・・・(3)

In addition, the projection optical system according to the present invention may be configured such that the first aspheric surface of the first lens (aspheric surface L2R1 of lens L2 in Example 1) satisfies the following formula (4). If ((φsm-φcr)/|φoa|) is smaller than the lower limit (-0.95), the aberrations 1 to 3 are overcorrected. Therefore, the positive aspheric local power change caused by the lens L2 having the aspheric surface L2R1 arranged closest to the concave mirror and the aspheric surface L3R2 of the lens L3 arranged between the lens L2 and the convex mirror M2 cannot maintain the balance of the aberrations. As a result, the meri field curvature of short wavelengths remains over (long wavelengths are under), and the sagittal and meridional halo high-order components including color remain over. On the other hand, if it is larger than the upper limit (-0.055), the correction effect of the above-mentioned aberrations 1 to 3 is insufficient, so the aberrations 1 to 3 remain.
-0.95 ≦ (φsm－φcr)／｜φoa｜ ≦ -0.055 ・・・(4)

In addition, the projection optical system according to the present invention may be configured to satisfy the following formula (5) when the radius of curvature of the convex mirror M2 is Rt, the radius of curvature of the surface of the second lens (lens L3 in Example 1) on the concave mirror side is Rm1, and the radius of curvature of the surface of the second lens on the convex mirror side is Rm2. In the projection optical system PO1 of Example 1, the surface of the second lens on the concave mirror side is the surface of the lens L3 on the opposite side to the aspheric surface L3R2, and the surface of the second lens on the convex mirror side is the aspheric surface L3R2 of the lens L3. Formula (5) is a condition for suppressing unnecessary light generated by multiple reflections between the convex mirror M2 and the lens surface arranged closest to the convex mirror in the lens group LG. When the radius of curvature of the lens surface arranged close to the convex mirror M2 is close to the radius of curvature of the convex mirror M2, the paraxial back position of the unnecessary light, which acts as a reflecting surface, is close to the image plane, which may cause ghosts and flares. The optical path in this case is shown in FIG. 34. The solid arrows indicate the light rays incident on the lens, and the light rays reflected by each lens surface are represented by the representative dotted line patterns. One of the measures to suppress unnecessary light is to reduce the reflectance of the anti-reflection film on the lens surface. However, instead of or in addition to this, it is preferable to consider the radius of curvature of the lens surface that generates the unnecessary light when designing the projection optical system, and to move the paraxial back position away from the image surface. When the value of (Rt/Rm1) or (Rt/Rm2) in formula (5) is 1, the radius of curvature of the convex mirror and the radius of curvature of the lens surface are the same, so the paraxial back position of the unnecessary light is closest to the image surface, which is not preferable. In formula (5), the upper limit value of (Rt/Rm1) or (Rt/Rm2) is set to 0.31, and the radius of curvature of the lens surface is larger than the radius of curvature of the convex mirror. Furthermore, if the value is negative, the paraxial back position of the unnecessary light is significantly separated from the image surface, which is preferable. When the upper limit value is 0.31, the paraxial back position of the unwanted light is approximately 1300 mm, and at NA 0.1, the light beam diameter on the image plane becomes large at 260 mm, so that the illuminance of the unwanted light can be reduced (suppressed).
Rt/Rm1≦0.31 and Rt/Rm2≦0.31 (5)

In addition, the projection optical system according to the present invention may be configured so that the angle 2θ at which the chief ray from the maximum object height is incident on the lens group LG from the concave mirror M1 is greater than 30 degrees, as shown in the following formula (6). For the angle 2θ, see FIG. 27 described above. Formula (6) is a condition for achieving a compact projection optical system. In the projection optical system according to the present invention, the aberration correction capability is improved by appropriately setting the shape (local power change) of the aspheric surface in the lens group LG, and therefore the power arrangement of the concave mirror M1 and the convex mirror M2 can be shortened. Therefore, the effective diameter of the concave mirror M1 can also be shortened, and compactness can be achieved. For comparison, in Examples 1, 2, and 4 of Patent Document 1, the angle 2θ is small, 19.9°, 19.2°, and 26.8°, respectively, so that when the NA is increased and the illumination area is expanded, the projection optical system becomes large.
2θ > 30°...(6)

Next, a specific example of the configuration of the projection optical system PO1 of the first embodiment will be described. The configuration of the projection optical system PO1 of the first embodiment has been described above with reference to FIG. 1. Table 4 below shows the optical specifications of the projection optical system PO1 of the first embodiment, and also includes the specifications shown in FIG. 2A. The projection optical system PO1 of the first embodiment has a NA of 0.1, but achieves a specification that allows a large screen with an illumination width of 1100 mm and an improvement in production efficiency with a slit width of 100 mm. Tables 5 to 6 below show examples of numerical values of various parameters in the projection optical system PO1 of the first embodiment. In Table 5, "surface number" indicates the number given to the multiple surfaces provided in the projection optical system PO1 in the order of the optical path from the object surface OP. "Aspheric setting" indicates whether each surface is aspheric or not, and surfaces marked with "ASP" are aspheric. "R" indicates the radius of curvature (mm), "D" indicates the surface spacing (mm), and "glass" indicates the glass material. However, the refractive index of air is 1, the parts where "glass" is multiplied by "-1" indicate reflection, and the parts where it is "SiO2" indicate that the glass material is synthetic quartz. Table 5 also shows the refractive index for each wavelength. Furthermore, "asp_data" shown in Table 6 is an aspheric coefficient, and all aspheric surfaces in the projection optical system PO1 of this embodiment 1 can be defined by the aspheric equation expressed by the following equation (7). The projection optical system PO1 of the embodiment 1 configured in this way satisfies all of the configuration conditions of the above equations (1) to (6), as shown in the following Table 7.
z=(1/R)h ² /(1+(1-(1+k)(1/R) ² h ² ) ^1/2 )
+Ah ⁴ +Bh ⁶ +Ch ⁸ +Dh ¹⁰ +Eh ¹²
+Fh ¹⁴ +Gh ¹⁶ +Hh ¹⁸ +Jh ²⁰ ...(7)

Figure 3 shows the change in aspheric local power in the projection optical system PO1 of Example 1, where the position (height) of each aspheric surface is normalized by the effective radius. The vertical axis of Figure 3 shows the value of the position (height) of each aspheric surface normalized by the effective radius. The numbers on the horizontal axis of Figure 3 indicate the numbers of the aspheric surfaces arranged in the order of the optical path from the object surface OP, and the aspheric local power shown on the horizontal axis indicates the positive direction to the right of the page and the negative direction to the left of the page. The vertical and horizontal axes of Figure 3 are the same in Figures 6, 9, 12, 15, 18, 21, and 24 described later.

On the horizontal axis of FIG. 3, the first aspheric surface is the aspheric surface of the first aspheric lens L1, the second aspheric surface is the aspheric surface of the concave mirror M1, and these aspheric surfaces can be used mainly to correct the field curvature, astigmatism, and telecentricity that depend on the height of the chief ray. The third aspheric surface is the aspheric surface L2R1 of the lens L2, and the fourth aspheric surface is the aspheric surface L3R2 of the lens L3, which correspond to the seventh and tenth surfaces in Table 5, respectively. Note that since the projection optical system PO1 of this embodiment 1 is a symmetrical system, the aspheric surfaces on the optical path from the object surface OP to the convex mirror M2 will be described here, and the aspheric surfaces on the optical path from the convex mirror M2 to the image surface IP, which have a similar tendency, will not be described.

In FIG. 3, the positions Pcr and Psm of the aspheric surface L2R1 are indicated by an x and a circle on the third aspheric surface, respectively, and the positions of the aspheric surface L3R2, into which the light rays passing through the positions Pcr and Psm of the aspheric surface L2R1 are incident, are also indicated by an x and a circle on the fourth aspheric surface. As shown in FIG. 3, in the third aspheric surface L2R1 (surface 7 in Table 5), the aspheric local power changes monotonically in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with a circle), and the configuration condition of the above formula (1) or formula (4) is satisfied. On the other hand, in the fourth aspheric surface L3R2 (surface 10 in Table 5), the aspheric local power changes monotonically in the positive direction from the x mark to the circle mark so as to compensate for the power change of the third aspheric surface L2R1. This maximizes the effect of aberration correction and achieves high specifications. In addition, the maximum effective diameter of concave mirror M1 is 1550 mm, making it possible to achieve compact size.

Figure 4A shows the longitudinal aberration diagram of the projection optical system PO1 of this embodiment 1, and Figure 4B shows the transverse aberration diagram and the wavefront aberration RMS of the i-line. It is clear from a comparison with the aberration diagram and wavefront aberration RMS of the conventional projection optical system POc shown in Figures 29A and 29B that the illumination area on the object plane is well corrected for both meridional and sagittal aberrations, including chromatic aberration. In addition, the wavefront aberration RMS of the i-line (365 nm) is a maximum of 13.9 mλ, demonstrating good performance.

[Example 2]
A projection optical system according to a second embodiment of the present invention will be described. The second embodiment basically inherits the contents described in the first embodiment, and is the same as that described in the first embodiment except for what will be mentioned below. For example, the configuration conditions and various definitions shown in formulas (1) to (6) are the same as those described in the first embodiment.

FIG. 5 is a schematic diagram showing the configuration of a projection optical system PO2 according to a second embodiment of the present invention. The projection optical system PO2 according to the second embodiment has a different configuration of the lens group LG compared to the projection optical system PO1 according to the first embodiment, but otherwise has a similar configuration. The lens group LG according to the second embodiment may include a lens L2 and a lens L3. The lens L2 may be understood as a first lens having a first aspheric surface, and the lens L3 may be understood as a second lens disposed between the lens L2 (first lens) and the convex mirror M2 and having a second aspheric surface. In the second embodiment, the lens L2 is a meniscus lens with a convex surface facing the concave mirror side, and the surface of the lens L2 on the concave mirror side is an aspheric surface (first aspheric surface). In addition, the surface of the lens L3 on the concave mirror side is an aspheric surface (second aspheric surface). The difference is that the surface of the lens L3 on the convex mirror side is an aspheric surface in the first embodiment, whereas the surface of the lens L3 on the concave mirror side is an aspheric surface in the second embodiment.

Table 8 below shows the optical specifications of the projection optical system PO2 of this embodiment, including the specifications shown in FIG. 2A. The projection optical system PO2 of this embodiment has a NA of 0.1, but achieves a large screen with an illumination width of 1100 mm and a slit width of 100 mm, which improves production efficiency. Tables 9 and 10 below show examples of the numerical values of various parameters in the projection optical system PO2 of this embodiment. The explanations in the table and the aspheric expressions are the same as in the first embodiment. The projection optical system PO2 of the second embodiment thus configured satisfies all of the above formulas (1) to (6) except for formula (5), as shown in Table 11 below. The reason that formula (5) is not satisfied is because the main countermeasure against ghosts and flares is the anti-reflection coating.

Figure 6 shows the change in aspheric local power in the projection optical system PO2 of Example 2, where the position (height) of each aspheric surface is normalized by the effective radius. On the horizontal axis of Figure 6, the first aspheric surface is the aspheric surface of the first aspheric lens L1, and the second aspheric surface is the aspheric surface of the concave mirror M1. These aspheric surfaces can be used mainly to correct the field curvature, astigmatism, and telecentricity that depend on the height of the chief ray. The third aspheric surface is the aspheric surface on the concave mirror side of lens L2, and the fourth aspheric surface is the aspheric surface on the concave mirror side of lens L3, which correspond to the seventh and ninth surfaces in Table 9, respectively. Note that since the projection optical system PO2 of Example 2 is a symmetrical system, the aspheric surfaces on the optical path from the object surface OP to the convex mirror M2 will be described here, and the aspheric surfaces on the optical path from the convex mirror M2 to the image surface IP, which have a similar tendency, will not be described.

As shown in Figure 6, in the third aspheric surface (surface 7 in Table 9), the aspheric local power changes monotonically in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with a circle), and the configuration conditions of formula (1) or (4) above are satisfied. On the other hand, in the fourth aspheric surface (surface 9 in Table 9), the aspheric local power changes monotonically in the positive direction from the x mark to the circle mark so as to compensate for the change in power of the third aspheric surface. This maximizes the effect of aberration correction and achieves high specifications. In addition, the maximum effective diameter is 1550 mm for concave mirror M1, making it possible to achieve compactness.

Figure 7A shows the longitudinal aberration diagram for the projection optical system PO2 of this embodiment, and Figure 7B shows the transverse aberration diagram and the wavefront aberration RMS for the i-line. It is immediately clear when compared with the aberration diagram and wavefront aberration RMS for the projection optical system POc of the conventional configuration shown in Figures 29A and 29B, that the illumination area on the object plane is well corrected for both meridional and sagittal aberrations, including chromatic aberration. In addition, the wavefront aberration RMS for the i-line (365 nm) is a maximum of 5.6 mλ, demonstrating good performance.

[Example 3]
A projection optical system according to a third embodiment of the present invention will be described. The third embodiment basically inherits the contents described in the first embodiment, and is the same as that described in the first embodiment except for what will be mentioned below. For example, the configuration conditions and various definitions shown in formulas (1) to (6) are the same as those described in the first embodiment.

Figure 8 is a schematic diagram showing the configuration of a projection optical system PO3 of Example 3 according to the present invention. The projection optical system PO3 of Example 3 has a different configuration of the lens group LG compared to the projection optical system PO1 of Example 1, but otherwise has a similar configuration. The lens group LG of Example 3 can include lenses L2, L3, and L4. It may be understood that lens L2 is a first lens having a first aspheric surface, and lens L3 and/or lens L4 are second lenses each having a second aspheric surface. In Example 3, lens L2 is a meniscus lens with a convex surface facing the concave mirror side, and the surface of lens L2 facing the convex mirror side is an aspheric surface (first aspheric surface). In addition, the surface of lens L3 facing the concave mirror side and/or the surface of lens L4 facing the convex mirror side are each aspheric surfaces (second aspheric surfaces).

Table 12 below shows the optical specifications of the projection optical system PO3 of this embodiment, including the specifications shown in FIG. 2A. The projection optical system PO3 of this embodiment achieves specifications that enable a large screen with an illumination width of 1100 mm and improved production efficiency with a slit width of 100 mm, despite having an NA of 0.1. Tables 13 and 14 below show examples of the numerical values of various parameters in the projection optical system PO3 of this embodiment. The table explanations and aspheric formulas are the same as those in the first embodiment. The projection optical system PO3 of the third embodiment, configured in this manner, satisfies all of the configuration conditions of the above formulas (1) to (6), as shown in Table 15 below.

Figure 9 shows the change in aspheric local power in the projection optical system PO3 of Example 3, where the position (height) of each aspheric surface is normalized by the effective radius. On the horizontal axis of Figure 9, the first aspheric surface is the aspheric surface of the first aspheric lens L1, the second aspheric surface is the aspheric surface of the concave mirror M1, and these aspheric surfaces can be used mainly to correct the field curvature, astigmatism, and telecentricity that depend on the height of the chief ray. The third aspheric surface is the aspheric surface on the convex mirror side of lens L2, the fourth aspheric surface is the aspheric surface on the concave mirror side of lens L3, and the fifth aspheric surface is the aspheric surface on the convex mirror side of lens L4, which correspond to the 8th, 9th, and 12th surfaces in Table 13, respectively. In addition, since the projection optical system PO3 in this embodiment 3 is a symmetric system, we will explain here the aspheric surfaces on the optical path from the object plane OP to the convex mirror M2, and will omit a description of the aspheric surfaces on the optical path from the convex mirror M2 to the image plane IP, which have a similar tendency.

As shown in FIG. 9, in the third aspheric surface (surface 8 in Table 13), the aspheric local power changes monotonically in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with an o), and the configuration conditions of formula (1) or (4) above are satisfied. On the other hand, in the fourth aspheric surface (surface 9 in Table 13) and/or the fifth aspheric surface (surface 12 in Table 13), the aspheric local power changes monotonically in the positive direction from the x mark to the o mark so as to compensate for the change in power of the third aspheric surface. This maximizes the effect of aberration correction, achieving high specifications. In addition, the maximum effective diameter is 1550 mm for the concave mirror M1, making it possible to achieve compactness.

The longitudinal aberration diagram of the projection optical system PO3 of this embodiment 3 is shown in FIG. 10A, and the transverse aberration diagram and the wavefront aberration RMS of the i-line are shown in FIG. 10B. When compared with the aberration diagram and wavefront aberration RMS of the projection optical system POc of the conventional configuration shown in FIG. 29A-FIG. 29B, it is immediately apparent that the illumination area on the object plane is well corrected for both meridional and sagittal aberrations, including chromatic aberration. In addition, the wavefront aberration RMS of the i-line (365 nm) is a maximum of 3.5 mλ, demonstrating good performance.

[Example 4]
A fourth embodiment of the projection optical system according to the present invention will be described. The fourth embodiment basically inherits the contents described in the first embodiment, and is the same as that described in the first embodiment except for what will be mentioned below. For example, the configuration conditions and various definitions shown in formulas (1) to (6) are the same as those described in the first embodiment.

Figure 11 is a schematic diagram showing the configuration of a projection optical system PO4 according to a fourth embodiment of the present invention. The projection optical system PO4 of this embodiment has a different configuration of the lens group LG compared to the projection optical system PO1 of the first embodiment, but otherwise has a similar configuration. The lens group LG of this embodiment can include a lens L2, a lens L3, and a lens L4. It may be understood that the lens L2 and/or the lens L3 are first lenses having a first aspheric surface, and the lens L4 is a second lens having a second aspheric surface. In this embodiment, the lens L2 and the lens L3 are meniscus lenses with a convex surface facing the concave mirror side, and the surface of the lens L2 and/or the lens L3 on the concave mirror side is an aspheric surface (first aspheric surface). In addition, the surface of the lens L4 on the convex mirror side is an aspheric surface (second aspheric surface).

Table 16 below shows the optical specifications of the projection optical system PO4 of this embodiment 4, including the specifications shown in FIG. 2A. The projection optical system PO4 of this embodiment 4 achieves specifications that enable a large screen with an illumination width of 1100 mm and improved production efficiency with a slit width of 100 mm, despite having an NA of 0.1. Tables 17 to 18 below show examples of numerical values of various parameters in the projection optical system PO4 of this embodiment 4. The table explanations and aspheric formulas are the same as those in embodiment 1. The projection optical system PO4 of embodiment 4 configured in this way satisfies all of the configuration conditions of the above formulas (1) to (6), as shown in Table 19 below.

Figure 12 shows the change in aspheric local power in the projection optical system PO4 of Example 4, where the position (height) of each aspheric surface is normalized by the effective radius. On the horizontal axis of Figure 12, the first aspheric surface is the aspheric surface of the first aspheric lens L1, the second aspheric surface is the aspheric surface of the concave mirror M1, and these aspheric surfaces can be used mainly to correct the field curvature, astigmatism, and telecentricity that depend on the height of the chief ray. The third aspheric surface is the aspheric surface on the concave mirror side of lens L2, the fourth aspheric surface is the aspheric surface on the concave mirror side of lens L3, and the fifth aspheric surface is the aspheric surface on the convex mirror side of lens L4, which correspond to the 7th, 9th, and 12th surfaces of Table 17, respectively. In addition, since the projection optical system PO4 in this embodiment 4 is a symmetric system, the aspheric surface on the optical path from the object plane OP to the convex mirror M2 will be described here, and a description of the aspheric surface on the optical path from the convex mirror M2 to the image plane IP, which has a similar tendency, will be omitted.

As shown in FIG. 12, in the third aspheric surface (surface 7 in Table 17), the aspheric local power changes in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with an o), and the above-mentioned condition of the composition of formula (1) or (4) is satisfied. In addition, in the fourth aspheric surface (surface 9 in Table 17), the aspheric local power changes in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with an o), and the above-mentioned condition of the composition of formula (1) or (4) is satisfied. On the other hand, in the fifth aspheric surface (surface 12 in Table 17), the aspheric local power changes monotonically in the positive direction from the x to the o so as to compensate for the power change of the third and/or fourth aspheric surfaces. This maximizes the effect of aberration correction and achieves high specifications. In addition, the maximum effective diameter is 1550 mm for the concave mirror M1, so that miniaturization is also possible.

The longitudinal aberration diagram of the projection optical system PO4 of this embodiment 4 is shown in FIG. 13A, and the transverse aberration diagram and the wavefront aberration RMS of the i-line are shown in FIG. 13B. When compared with the aberration diagram and wavefront aberration RMS of the projection optical system POc of the conventional configuration shown in FIG. 29A-FIG. 29B, it is immediately apparent that the illumination area on the object plane is well corrected for both meridional and sagittal aberrations, including chromatic aberration. In addition, the wavefront aberration RMS of the i-line (365 nm) is a maximum of 4.3 mλ, demonstrating good performance.

[Example 5]
A fifth embodiment of the projection optical system according to the present invention will be described. The fifth embodiment basically inherits the contents described in the first embodiment, and is the same as that described in the first embodiment except for what will be mentioned below. For example, the configuration conditions and various definitions shown in formulas (1) to (6) are the same as those described in the first embodiment.

Figure 14 is a schematic diagram showing the configuration of a projection optical system PO5 of Example 5 according to the present invention. The projection optical system PO5 of Example 5 has a different configuration of the lens group LG compared to the projection optical system PO1 of Example 1, but otherwise has a similar configuration. The lens group LG of Example 5 can include a lens L2 and a lens L3. It may be understood that the lens L2 is a first lens having a first aspheric surface, and the lens L3 is a second lens having a second aspheric surface. In Example 5, the lens L2 is a meniscus lens with a convex surface facing the concave mirror side, and the surface of the lens L2 facing the concave mirror side is an aspheric surface (first aspheric surface). In addition, the surface of the lens L3 facing the concave mirror side is an aspheric surface (second aspheric surface).

The following Table 20 shows the optical specifications of the projection optical system PO5 of this embodiment 5, including the specifications shown in FIG. 2A. The projection optical system PO5 of this embodiment 5 has a shorter wavelength than those of the first to fourth embodiments, a main wavelength of 320 nm, which is the DUV (deep ultra-violet) wavelength, and a larger NA of 0.12. The illumination width is 900 mm, and the slit width is 50 mm. In terms of the shorter wavelength, higher NA, and illumination width, specifications that enable high resolution and a larger screen are realized. In addition, the following Tables 21 to 22 show examples of the numerical values of various parameters in the projection optical system PO5 of this embodiment 5. The explanation of the table and the aspheric formula are the same as those of the first embodiment. The projection optical system PO5 of the fifth embodiment thus configured satisfies all of the configuration conditions of the above formulas (1) to (6) except for the configuration condition of formula (6), as shown in the following Table 23.

Figure 15 shows the change in aspheric local power in the projection optical system PO5 of the fifth embodiment, where the position (height) of each aspheric surface is normalized by the effective radius. On the horizontal axis of Figure 15, the first aspheric surface is the aspheric surface of the first aspheric lens L1, and the second aspheric surface is the aspheric surface of the concave mirror M1. These aspheric surfaces can be used mainly to correct the field curvature, astigmatism, and telecentricity that depend on the height of the chief ray. The third aspheric surface is the aspheric surface on the concave mirror side of the lens L2, and the fourth aspheric surface is the aspheric surface on the concave mirror side of the lens L3, which correspond to the seventh and ninth surfaces in Table 21, respectively. Note that since the projection optical system PO5 of the fifth embodiment is a symmetrical system, the aspheric surfaces on the optical path from the object surface OP to the convex mirror M2 will be described here, and the aspheric surfaces on the optical path from the convex mirror M2 to the image surface IP, which have a similar tendency, will not be described.

As shown in Figure 15, in the third aspheric surface (surface 7 in Table 21), the aspheric local power changes monotonically in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with a circle), satisfying the configuration conditions of formula (1) or (4) above. On the other hand, in the fourth aspheric surface (surface 9 in Table 21), the aspheric local power changes monotonically in the positive direction from the x to the circle so as to compensate for the change in power of the third aspheric surface. This maximizes the effect of aberration correction and achieves high specifications.

Figure 16A shows the longitudinal aberration diagram for the projection optical system PO5 of this embodiment 5, and Figure 16B shows the transverse aberration diagram and the wavefront aberration RMS at a wavelength of 320 nm. It can be seen that, despite the shorter wavelength of the illumination area on the object plane, both meridional and sagittal aberrations, including chromatic aberration, are well corrected. In addition, the wavefront aberration RMS at a wavelength of 320 nm is a maximum of 29.5 mλ, demonstrating good performance.

[Example 6]
A sixth embodiment of the projection optical system according to the present invention will be described. The sixth embodiment basically inherits the contents described in the first embodiment, and is the same as that described in the first embodiment except for what will be mentioned below. For example, the configuration conditions and various definitions shown in formulas (1) to (6) are the same as those described in the first embodiment.

Figure 17 is a schematic diagram showing the configuration of a projection optical system PO6 according to a sixth embodiment of the present invention. Compared to the projection optical system PO1 of the first embodiment, the projection optical system PO6 of the sixth embodiment has a second aspherical lens L2 between the first aspherical lens L1 and the refractive optical element SG, and may include lenses L3 and L4 in the lens group. It may be understood that lens L3 is a first lens having a first aspherical surface, and lens L4 is a second lens having a second aspherical surface. In this sixth embodiment, lens L3 is a meniscus lens with a convex surface facing the concave mirror, and the surface of lens L3 facing the concave mirror is an aspherical surface (first aspherical surface). In addition, the surface of lens L4 facing the concave mirror is an aspherical surface (second aspherical surface).

The following Table 24 shows the optical specifications of the projection optical system PO6 of this embodiment 6, and also includes the specifications shown in FIG. 2A. The projection optical system PO6 of this embodiment 6 has a shorter wavelength than the projection optical system PO6 of the first to fourth embodiments, as in the fifth embodiment, and the dominant wavelength is 320 nm, which is a DUV (deep ultra-violet) wavelength. The NA is 0.15, which is larger than that of the fifth embodiment. The illumination width is 900 mm, and the slit width is 50 mm. In terms of the shorter wavelength, higher NA, and illumination width, specifications that enable higher resolution and larger screens are realized. In addition, the following Tables 25 to 26 show examples of numerical values of various parameters in the projection optical system PO6 of this embodiment 6. The explanation of the table and the aspheric formula are the same as in the first embodiment. The projection optical system PO6 of the sixth embodiment thus configured satisfies all of the configuration conditions of the above formulas (1) to (6), as shown in the following Table 27.

Figure 18 shows the change in aspheric local power in the projection optical system PO6 of Example 6, where the position (height) of each aspheric surface is normalized by the effective radius. On the horizontal axis of Figure 18, the first and second aspheric surfaces are the aspheric surfaces of the first aspheric lens L1, the third aspheric surface is the aspheric surface of the second aspheric lens L2, and the fourth aspheric surface is the aspheric surface of the concave mirror M1. These aspheric surfaces can be used primarily to correct the curvature of field, astigmatism, and telecentricity, which depend on the height of the chief ray. The fifth aspheric surface is the aspheric surface on the concave mirror side of lens L3, and the sixth aspheric surface is the aspheric surface on the concave mirror side of lens L4, which correspond to the ninth and eleventh surfaces of Table 25, respectively. In addition, since the projection optical system PO6 in this embodiment 6 is a symmetric system, we will explain here the aspheric surfaces on the optical path from the object plane OP to the convex mirror M2, and will omit a description of the aspheric surfaces on the optical path from the convex mirror M2 to the image plane IP, which have a similar tendency.

As shown in FIG. 18, in the fifth aspheric surface (surface 9 in Table 25), the aspheric local power changes monotonically in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with an o), and the configuration conditions of formula (1) or (4) above are satisfied. On the other hand, in the sixth aspheric surface (surface 11 in Table 25), the aspheric local power changes monotonically in the positive direction from the x mark to the o mark so as to compensate for the change in power of the fifth aspheric surface. This maximizes the effect of aberration correction and achieves high specifications. In addition, since the maximum effective diameter is 1524 mm for the concave mirror M1, it is also possible to achieve a high NA (NA 0.15) and compact size.

Figure 19A shows the longitudinal aberration diagram for the projection optical system PO6 of this embodiment 6, and Figure 19B shows the transverse aberration diagram and the wavefront aberration RMS at a wavelength of 320 nm. It can be seen that, despite the shorter wavelength of the illumination area on the object plane, both meridional and sagittal aberrations, including chromatic aberration, are well corrected. In addition, the wavefront aberration RMS at a wavelength of 320 nm is a maximum of 10.7 mλ, demonstrating good performance.

[Example 7]
A seventh embodiment of the projection optical system according to the present invention will be described. The seventh embodiment basically inherits the contents described in the first embodiment, and is the same as that described in the first embodiment except for what will be mentioned below. For example, the configuration conditions and various definitions shown in formulas (1) to (6) are the same as those described in the first embodiment.

Figure 20 is a schematic diagram showing the configuration of a projection optical system PO7 according to a seventh embodiment of the present invention. The projection optical system PO7 according to the seventh embodiment is a magnifying system that magnifies and projects an image of an illumination area IR (specifically, an image of a pattern provided in the illumination area IR) on an object surface OP onto an image surface IP. In the example of Figure 20, L1 represents a first aspheric lens, L2 represents a second aspheric lens, M1 represents a first concave mirror, LG represents a lens group, M2 represents a convex mirror, M3 represents a second concave mirror, L5 represents a third aspheric lens, and L6 represents a fourth aspheric lens. OA represents the optical axis, OP represents the object surface, and IP represents the image surface. The light beam emitted from the object surface OP with NA 0.12 passes through or is reflected by each optical element in the order of the optical path from the object surface OP: L1 → L2 → M1 → LG → M2 → LG → M3 → L5 → L6, and is magnified (1.2 times) and imaged on the image surface IP. The pupil position (pupil plane) of the projection optical system PO7 is the convex mirror M2, and the aperture stop may be located near the convex mirror M2.

The lens group LG of this embodiment 7 may include a lens L3 and a lens L4. It may be understood that lens L3 is a first lens having a first aspheric surface, and lens L4 is a second lens having a second aspheric surface. In this embodiment 7, lens L3 is a meniscus lens with its convex surface facing the concave mirror, and the surface of lens L3 facing the concave mirror is an aspheric surface (first aspheric surface). In addition, the surface of lens L4 facing the concave mirror is an aspheric surface (second aspheric surface).

The following Table 28 shows the optical specifications of the projection optical system PO7 of this embodiment, including the specifications shown in FIG. 2A. In the projection optical system PO7 of this embodiment, the dominant wavelength is 365.5 nm, and the NA is 0.1 (image surface side). The illumination width is 875 mm, and the slit width is 67 mm, but the illumination width converted at the image surface is 1050 mm, and the slit width is 80 mm. In such a magnification system configuration (i.e., a configuration having a magnification), the illumination width can be increased to realize a large screen, and the size of the original placed on the object surface OP can be reduced. In other words, there is an advantage that the original can be produced inexpensively. In addition, the following Tables 29 to 30 show examples of the numerical values of various parameters in the projection optical system PO7 of this embodiment. The explanation of the table and the aspheric formula are the same as those in the first embodiment. The projection optical system PO7 of Example 7 configured in this manner satisfies all of the configuration conditions of the above formulas (1) to (6) except for the configuration condition of formula (6), as shown in Table 31 below.

Figure 21 shows the change in aspheric local power in the projection optical system PO7 of Example 7, where the position (height) of each aspheric surface is normalized by the effective radius. On the horizontal axis of Figure 21, the first aspheric surface is the aspheric surface of the first aspheric lens L1, the second aspheric surface is the aspheric surface of the second aspheric lens L2, and the third aspheric surface is the aspheric surface of the first concave mirror M1. The eighth aspheric surface is the aspheric surface of the second concave mirror M3, the ninth aspheric surface is the aspheric surface of the third aspheric lens L5, and the tenth aspheric surface is the aspheric surface of the fourth aspheric lens L6. These aspheric surfaces can be used mainly to correct field curvature, astigmatism, distortion, coma, and telecentricity, which depend on the height of the chief ray. Additionally, the fourth aspheric surface is the aspheric surface on the concave mirror side of lens L3, and the fifth aspheric surface is the aspheric surface on the concave mirror side of lens L4, which correspond to the seventh and ninth surfaces, respectively, on Table 29. Note that here, we will only explain the aspheric surfaces on the optical path from object plane OP to convex mirror M2, and will omit a description of the aspheric surfaces on the optical path from convex mirror M2 to image plane IP, which have a similar tendency.

As shown in Figure 21, in the fourth aspheric surface (surface 7 in Table 29), the aspheric local power changes monotonically in the negative direction from φcr to φsm from position Pcr (marked with an x) to position Psm (marked with a circle), satisfying the configuration conditions of formula (1) or (4) above. On the other hand, in the fifth aspheric surface (surface 9 in Table 29), the aspheric local power changes monotonically in the positive direction from the x to the circle so as to compensate for the change in power of the fourth aspheric surface. This maximizes the effect of aberration correction and achieves high specifications.

Figure 22A shows the longitudinal aberration diagram of the projection optical system PO7 of this embodiment 7, and Figure 22B shows the transverse aberration diagram and the wavefront aberration RMS of the i-line (wavelength 365.5 nm). It can be seen that the illumination area on the object plane is well corrected for both meridional and sagittal aberrations, including chromatic aberration. In addition, the wavefront aberration RMS of the i-line (wavelength 365.5 nm) is a maximum of 19.6 mλ, demonstrating good performance.

[Example 8]
Example 8 of the projection optical system according to the present invention will be described. Example 8 basically inherits the contents explained in Examples 1 and 7, and is the same as explained in Examples 1 and 7 except for what will be mentioned below. For example, the configuration conditions and various definitions shown in formulas (1) to (6) are the same as explained in Example 1.

Figure 23 is a schematic diagram showing the configuration of a projection optical system PO8 of Example 8 according to the present invention. The projection optical system PO8 of Example 8 has a different configuration of the lens group LG compared to the projection optical system PO7 of Example 7, but otherwise has a similar configuration. The lens group of Example 8 may include a lens L3 and a lens L4. The lens L3 may be understood to be a first lens having a first aspheric surface, and the lens L4 may be understood to be a second lens having a second aspheric surface. In Example 8, the lens L3 is a meniscus lens with a convex surface facing the concave mirror side, and both the surface of the lens L3 on the concave mirror side and/or the surface of the lens L3 on the convex mirror side are aspheric (first aspheric). In addition, the surface of the lens L4 on the concave mirror side is aspheric (second aspheric). The difference is that in Example 7, only the surface of the lens L3 on the concave mirror side is aspheric, whereas in Example 8, both the surface of the lens L3 on the concave mirror side and the surface of the lens L3 on the convex mirror side are aspheric.

The following Table 32 shows the optical specifications of the projection optical system PO8 of this embodiment 8, and also includes the specifications shown in FIG. 2A. In the projection optical system PO8 of this embodiment 8, the dominant wavelength is 365.5 nm, and the NA is 0.1 (image surface side), as in the seventh embodiment. The illumination width is 875 mm, and the slit width is 67 mm, but the illumination width converted at the image surface is 1050 mm, and the slit width is 80 mm. In such a magnification system configuration (i.e., a configuration having a magnification), the illumination width can be increased to realize a large screen, and the size of the original placed on the object surface OP can be reduced. In other words, there is an advantage that the original can be manufactured inexpensively. In addition, the following Tables 33 to 34 show examples of numerical values of various parameters in the projection optical system PO8 of this embodiment 8. The explanation of the table and the aspheric formula are the same as in the first embodiment. The projection optical system PO7 of the seventh embodiment configured in this way satisfies all of the configuration conditions of the above formulas (1) to (6), as shown in the following Table 35.

Figure 24 shows the change in aspheric local power in the projection optical system PO8 of Example 8, where the position (height) of each aspheric surface is normalized by the effective radius. On the horizontal axis of Figure 24, the first aspheric surface is the aspheric surface of the first aspheric lens L1, the second aspheric surface is the aspheric surface of the second aspheric lens L2, and the third aspheric surface is the aspheric surface of the first concave mirror M1. The tenth aspheric surface is the aspheric surface of the second concave mirror M3, the eleventh aspheric surface is the aspheric surface of the third aspheric lens L5, and the twelfth aspheric surface is the aspheric surface of the fourth aspheric lens L6. These aspheric surfaces can be used mainly to correct field curvature, astigmatism, distortion, coma, and telecentricity, which depend on the height of the chief ray. Additionally, the fourth aspheric surface is the aspheric surface on the concave mirror side of lens L3, the fifth aspheric surface is the aspheric surface on the convex mirror side of lens L3, and the sixth aspheric surface is the aspheric surface on the concave mirror side of lens L4, which correspond to the seventh, eighth, and ninth surfaces on table 33. Note that here, only the aspheric surfaces on the optical path from object plane OP to convex mirror M2 will be described, and a description of the aspheric surfaces on the optical path from convex mirror M2 to image plane IP, which have a similar tendency, will be omitted.

As shown in FIG. 24, in the fourth aspheric surface (surface 7 in Table 33), the aspheric local power changes monotonically from φcr to φsm in the negative direction from position Pcr (marked with an x) to position Psm (marked with an o), and the above-mentioned condition of the composition of formula (1) or (4) is satisfied. In addition, in the fifth aspheric surface (surface 8 in Table 33), the aspheric local power changes monotonically from φcr to φsm in the negative direction from position Pcr (marked with an x) to position Psm (marked with an o), and the above-mentioned condition of the composition of formula (1) or (4) is satisfied. On the other hand, in the sixth aspheric surface (surface 9 in Table 33), the aspheric local power changes monotonically in the positive direction from the x to the o so that the power change of the fourth aspheric surface and/or the power change of the fifth aspheric surface is compensated. This maximizes the effect of aberration correction and achieves high specifications. In addition, the maximum effective diameter of the second concave mirror M3 is 1658 mm, making it possible to achieve compact size.

Figure 25A shows the longitudinal aberration diagram of the projection optical system PO8 of this embodiment 8, and Figure 25B shows the transverse aberration diagram and the wavefront aberration RMS of the i-line (wavelength 365.5 nm). It can be seen that the illumination area on the object plane is well corrected for both meridional and sagittal aberrations, including chromatic aberration. In addition, the wavefront aberration RMS of the i-line (wavelength 365.5 nm) has good performance, with a maximum of 17.4 mλ.

<Embodiments of Exposure Apparatus>
An embodiment of an exposure apparatus having a projection optical system according to the present invention will be described. FIG. 26 is a schematic diagram showing an example of the configuration of an exposure apparatus EA of this embodiment. The exposure apparatus EA of this embodiment is, for example, a scanning exposure apparatus that transfers a pattern of an original 9 onto a substrate 20 while scanning the original 9 and the substrate 20 relatively, and can include an illumination optical system IL, a projection optical system PO, and a controller CNT. The controller CNT is configured by a computer having, for example, a CPU (Central Processing Unit) and a memory, and controls each part of the exposure apparatus EA to control the exposure of the substrate 20. In addition, the original 9 and the substrate 20 are held and driven by an original driving mechanism (original stage) and a substrate driving mechanism (substrate stage), respectively, not shown.

The illumination optical system IL may include, for example, a light source LS, a first condenser lens 3, an optical integrator 4 (fly-eye lens), a second condenser lens 5, a slit definition member 6, an imaging optical system 7, and a plane mirror 8. The light source LS may include, for example, a mercury lamp 1 and an elliptical mirror 2. The slit definition member 6 defines the illumination area of the original 9 (i.e., the cross-sectional shape of the slit light that illuminates the original 9). The imaging optical system 7 is configured to image the slit light defined by the slit definition member 6 on the object plane OP of the projection optical system PO. The plane mirror 8 bends the optical path in the illumination optical system IL. Note that, in the exposure apparatus EA shown in FIG. 26, the light source LS is provided as a component of the illumination optical system IL, but this is not limiting, and the light source LS does not have to be a component of the illumination optical system IL.

The projection optical system PO projects the pattern of the original 9 placed on the object plane OP onto the substrate 20 placed on the image plane IP. This exposes the substrate 20, and the pattern of the original 9 can be transferred onto the substrate. The projection optical system PO can be configured as any of an equal-magnification imaging optical system (equal-magnification system), a magnification imaging optical system (magnification system), and a reduction imaging optical system (reduction system), but in this embodiment it can be configured as an equal-magnification imaging optical system or a magnification imaging optical system. In addition, any of the projection optical systems PO1 to PO8 of the above-mentioned Examples 1 to 8 can be used as the projection optical system PO.

The projection optical system PO may include, in order from the object surface OP, a first aspherical lens 10, a first plane mirror 12, a first concave mirror 13, a convex mirror 15, a second concave mirror 16, a second plane mirror 17, and a second aspherical lens 19 on an optical path from the object surface OP to the image surface. In addition, a first refracting member 11 may be disposed between the first aspherical lens 10 and the first plane mirror 12, and a second refracting member 18 may be disposed between the second plane mirror 17 and the second aspherical lens 19. The first refracting member 11 and the second refracting member 18 may be used to adjust the imaging magnification and/or distortion. Furthermore, in the projection optical system PO of this embodiment, a lens group 14 is provided between the concave mirror (first concave mirror 13, second concave mirror 16) and the convex mirror 15. The lens group 14 may be any of the lens groups LG in the above-mentioned Examples 1 to 8. In addition, the plane including the mirror surface (reflecting surface) of the first plane mirror 12 and the plane including the mirror surface (reflecting surface) of the second plane mirror 17 should form an angle of 90 degrees with each other. The first plane mirror 12 and the second plane mirror 17 may be configured integrally (i.e., as a single structure). Also, the first concave mirror 13 and the second concave mirror 16 may be configured integrally (i.e., as a single structure).

<Embodiments of a method for manufacturing an article>
The method for manufacturing an article according to an embodiment of the present invention is suitable for manufacturing an article such as a microdevice such as a semiconductor device or an element having a fine structure. The method for manufacturing an article according to the present embodiment includes a step of forming a latent image pattern on a photosensitive agent applied to a substrate using the above-mentioned exposure apparatus (a step of exposing the substrate), and a step of developing (processing) the substrate on which the latent image pattern has been formed in the step. Furthermore, the manufacturing method includes other well-known steps (oxidation, film formation, deposition, doping, planarization, etching, resist stripping, dicing, bonding, packaging, etc.). The method for manufacturing an article according to the present embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article compared to conventional methods.

The invention is not limited to the above-described embodiment, and various modifications and variations are possible without departing from the spirit and scope of the invention. Therefore, the following claims are appended to disclose the scope of the invention.

PO: Projection optical system, OP: Object plane, IP: Image plane, LG: Lens group, M1, M3: Concave mirror, M2: Convex mirror

Claims (17)

1. A projection optical system having a concave mirror and a convex mirror, the projection optical system projects an image of a pattern of an illumination area located off an optical axis on an object plane onto an image plane by reflecting the image on the concave mirror, the convex mirror, and the concave mirror in this order,
a lens group disposed on an optical path between the concave mirror and the convex mirror,
the concave mirror is aspheric;
the lens group includes a first lens having a first aspheric surface, and a second lens disposed between the first lens and the convex mirror and having a second aspheric surface;
Regarding the first aspheric surface of the first lens, when one of two end points of a line at which a meridional plane that bisects the illumination area intersects with the illumination area is defined as Yi, and the other end point is defined as Ya, a position on the first aspheric surface at which a principal ray from the end point Yi is incident is defined as Pcr, a position on the first aspheric surface at which a sagittal marginal ray from the end point Ya is incident is defined as Psm, and powers at the positions Pcr and Psm are defined as φcr and φsm, respectively,
φsm＜φcr
and the power is changed in a negative direction from the power φ to the power φ as a change in power from the position P to the position P,
the second aspheric surface of the second lens has a region in which power changes in a positive direction from a position where a light ray that has passed through the position Pcr on the first aspheric surface is incident to a position where a light ray that has passed through the position Psm on the first aspheric surface is incident, in order to compensate for a power change from the position Pcr to the position Psm on the first aspheric surface . When the power of the second aspheric surface of the second lens is φmr and the power of the convex mirror is φtm,
-0.12 ≦ φmr／φtm ≦ 0.15
2. The projection optical system according to claim 1, wherein the following expression is satisfied: When the power of the entire lens group is φAM and the power of the second lens is φTL,
0.08 ≦ ｜φAM｜／φTL ≦ 0.95
3. The projection optical system according to claim 1, wherein the following is satisfied: When the power on the optical axis of the first aspheric surface is φoa,
-0.95 ≦ (φsm－φcr)／｜φoa｜≦ -0.055
4. The projection optical system according to claim 1, wherein the following is satisfied: 5. The projection optical system according to claim 1, wherein the first lens is a lens in the lens group that is disposed closest to the concave mirror. 6. The projection optical system according to claim 1, wherein the first lens is a meniscus lens having a convex surface facing the concave mirror side. 7. The projection optical system according to claim 1, wherein the second lens is a lens in the lens group that is disposed closest to the convex mirror. 8. The projection optical system according to claim 1, wherein the second lens has a positive power. When the radius of curvature of the convex mirror is Rt, the radius of curvature of the surface of the second lens facing the concave mirror is Rm1, and the radius of curvature of the surface of the second lens facing the convex mirror is Rm2,
Rt/Rm1≦0.31 and Rt/Rm2 ≦0.31
Fulfilling
9. The projection optical system according to claim 1, wherein at least one of a surface of the second lens facing the concave mirror and a surface of the second lens facing the convex mirror is the second aspheric surface. 10. The projection optical system according to claim 1, wherein an angle at which a chief ray from a maximum object height enters said lens group from said concave mirror is greater than 30 degrees. 11. The projection optical system according to claim 1, wherein the illumination area is an arc-shaped area. 12. The projection optical system according to claim 1, further comprising an aspheric lens on an optical path between the object surface and the concave mirror and/or between the image surface and the concave mirror. 13. The projection optical system according to claim 1, wherein the projection optical system is a unity magnification system. 13. The projection optical system according to claim 1, wherein the projection optical system is a magnification system. 1. A projection optical system having a concave mirror and a convex mirror, the projection optical system projects an image of a pattern of an illumination area located off an optical axis on an object plane onto an image plane by reflecting the image on the concave mirror, the convex mirror, and the concave mirror in this order,
a lens group disposed on an optical path between the concave mirror and the convex mirror,
the lens group includes a first lens having a first aspheric surface, and a second lens disposed between the first lens and the convex mirror and having a second aspheric surface;
Regarding the first aspheric surface of the first lens, when one of two end points of a line at which a meridional plane that bisects the illumination area intersects with the illumination area is defined as Yi, and the other end point is defined as Ya, a position on the first aspheric surface at which a principal ray from the end point Yi is incident is defined as Pcr, a position on the first aspheric surface at which a sagittal marginal ray from the end point Ya is incident is defined as Psm, and powers at the positions Pcr and Psm are defined as φcr and φsm, respectively,
φsm＜φcr
Fulfilling
the second aspheric surface of the second lens has a region for compensating for a power change from the position Pcr to the position Psm on the first aspheric surface,
When the radius of curvature of the convex mirror is Rt, the radius of curvature of the surface of the second lens facing the concave mirror is Rm1, and the radius of curvature of the surface of the second lens facing the convex mirror is Rm2,
Rt/Rm1≦0.31 and Rt/Rm2≦0.31
Fulfilling
a surface of said second lens facing said concave mirror and a surface of said second lens facing said convex mirror, said surface being the second aspheric surface. An exposure apparatus for exposing a substrate, comprising:
an illumination optical system for illuminating the original;
A projection optical system according to any one of claims 1 to 15 ,
Equipped with
an exposure apparatus, wherein the projection optical system projects a pattern of the original, which is arranged on an object plane, onto the substrate, which is arranged on an image plane; an exposure step of exposing a substrate using the exposure apparatus according to claim 16 ;
a processing step of processing the substrate exposed in the exposure step,
A method for manufacturing an article, comprising the steps of: manufacturing an article from the substrate processed in the processing step.