Patent Publication Number: US-10761431-B2

Title: Spatial light modulator, method of driving same, and exposure method and apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. Ser. No. 16/032,829, filed Jul. 11, 2018, which is a continuation of U.S. Ser. No. 13/993,145, filed Aug. 7, 2013, which is a U.S. national stage application of PCT/JP2011/071575 filed Sep. 22, 2011 and claims foreign priority benefit of Japanese Application No. 2010-277530 filed Dec. 13, 2010 in the Japanese Intellectual Property Office, the contents of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a spatial light modulator having a plurality of optical elements and a method of driving the same, an exposure technology to expose an object with use of the spatial light modulator, and a device manufacturing technology using the exposure technology. 
     BACKGROUND 
     The exposure apparatus including those of a one-shot exposure type such as steppers or those of a scanning exposure type such as scanning steppers are used for forming a predetermined pattern in each shot area on a substrate such as a wafer or a glass plate via a projection optical system, for example, in a lithography process for manufacturing devices (electronic devices or microdevices) such as semiconductor devices or liquid crystal display devices. 
     There are the recently-proposed exposure apparatus of a so-called maskless method to generate a variable pattern on the object plane of the projection optical system, using spatial light modulators (SLM) having an array of many microscopic mirrors an inclination angle of each of which is variable, instead of masks, for efficiently manufacturing each of devices while suppressing an increase of manufacturing cost due to preparation of masks for respective types of devices and masks for respective layers on the substrate (e.g., cf. Patent Literature 1). There are also the proposed spatial light modulators of a type having an array of many micromirrors a height of a reflective surface of each of which is controllable, in order to control a phase distribution of incident light (e.g., cf. Non Patent Literature 1). 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: International Publication WO2009/060745 
       
    
     Non Patent Literature 
     
         
         Non Patent Literature 1: Yijian Chen et al., “Design and fabrication of tilting and piston micromirrors for maskless lithography,” Proc. of SPIE (U.S.A.) Vol. 5751, pp. 1023-1037 (2005) 
       
    
     SUMMARY 
     In use of the spatial light modulator having the array of many micromirrors, errors of height (phase) set for each micromirror include, for example, a systematic error which is an error with a predetermined tendency common to the many micromirrors, in addition to a random error. Among these errors, influence of the random error is alleviated, for example, by averaging effect. However, since influence of the systematic error is not alleviated by averaging effect, occurrence of the systematic error can cause an intensity distribution of a spatial image finally formed on the surface of the substrate to deviate from a target distribution. 
     Furthermore, when there is light passing via gap regions between the micromirrors, the light can cause the intensity distribution of the spatial image finally formed on the surface of the substrate to deviate from the target distribution. 
     In the light of the above-described circumstances, an object of the present invention is to reduce the error from the target distribution of the intensity distribution of the spatial image finally formed on the surface of the substrate, in use of the spatial light modulator having the array of optical elements. 
     A first aspect of the present invention provides a method of driving a spatial light modulator having an array of optical elements each of which is to be illuminated with light. This driving method comprises: setting, in a first region which is at least a part of the array of optical elements, an arrangement of optical elements in a first state for letting incident light pass as light with the same phase as that of the incident light or with a phase different by a first phase from that of the incident light and optical elements in a second state for letting incident light pass as light with a phase different by a second phase which is different substantially 180° from the first phase, to a first arrangement; and setting, in a second region which is at least a part of the array of optical elements, an arrangement of optical elements in the first state and optical elements in the second state to a second arrangement in which optical elements in the first state or in the second state in the first arrangement are inverted into the second state or into the first state, respectively. 
     A second aspect of the present invention provides an exposure method of exposing a substrate with exposure light via an array of optical elements in a spatial light modulator and via a projection optical system. This exposure method comprises: setting an arrangement of states of the optical elements by the method of driving the spatial light modulator according to the present invention; and implementing overlay exposure of the substrate with the exposure light from an illumination area including the first region and the second region of the array of optical elements via the projection optical system, in a state in which the optical elements are set in the first arrangement and in a state in which the optical elements are set in the second arrangement. 
     A third aspect of the present invention provides an exposure method of exposing at least a partial region on a substrate with exposure light via a first spatial light modulator with an array of optical elements and via a projection optical system, and exposing at least the partial region on the substrate with exposure light via a second spatial light modulator with an array of optical elements and the projection optical system. This exposure method comprises: setting, in a first region which is at least a part of the array of optical elements in the first spatial light modulator, an arrangement of optical elements in a first state for letting incident light pass as light with the same phase as that of the incident light or with a phase different by a first phase from that of the incident light and optical elements in a second state for letting incident light pass as light with a phase different by a second phase which is different substantially 180° from the first phase, to a first arrangement; and setting, in a second region which is at least a part of the array of optical elements in the second spatial light modulator and corresponds to the first region, an arrangement of optical elements in the first state for letting incident light pass as light with the same phase as that of the incident light or with a phase different by the first phase from that of the incident light and optical elements in the second state for letting incident light pass as light with a phase different by the second phase which is different substantially 180° from the first phase, to a second arrangement. An arrangement of optical elements in the first state in the first arrangement corresponds to an arrangement of optical elements in the second state in the second arrangement, and an arrangement of optical elements in the second state in the first arrangement corresponds to an arrangement of optical elements in the first state in the second arrangement. 
     A fourth aspect of the present invention provides a spatial light modulator having an array of optical elements each of which is to be illuminated with light. This spatial light modulator comprises: a plurality of first circuits which output a first signal for setting states of the optical elements to a first state for letting incident light pass as light with the same phase as that of the incident light or with a phase different by a first phase from that of the incident light, or a second signal for setting the states of the optical elements to a second state for letting incident light pass as light with a phase different by a second phase which is different substantially 180° from the first phase; a control circuit which controls output signals from the plurality of first circuits, in order to set, in a first region which is at least a part of the array of optical elements, an arrangement of optical elements in the first state and optical elements in the second state to a first arrangement; and a plurality of second circuits which invert the output signals from the first circuits, in order to set, in a second region which is at least a part of the array of optical elements, an arrangement of optical elements in the first state and optical elements in the second state to a second arrangement in which optical elements in the first state or in the second state in the first arrangement are inverted into the second state or into the first state, respectively. 
     A fifth aspect of the present invention provides an exposure apparatus for exposing a substrate with exposure light via a projection optical system. This exposure apparatus comprises: an illumination system which emits the exposure light; a spatial light modulator which is arranged on the object plane side of the projection optical system and which has an array of optical elements each of which can be controlled so as to guide the exposure light to the projection optical system; and a control device which controls the illumination system and the spatial light modulator, and the control device operates as follows: the control device sets, in a first region which is at least a part of the array of optical elements, an arrangement of optical elements in a first state for letting incident light pass as light with the same phase as that of the incident light or with a phase different by a first phase from that of the incident light and optical elements in a second state for letting incident light pass as light with a phase different by a second phase which is different substantially 180° from the first phase, to a first arrangement, in accordance with a spatial image formed on the substrate via the projection optical system, to expose the substrate; and the control device sets, in a second region which is at least a part of the array of optical elements, an arrangement of optical elements in the first state and optical elements in the second state to a second arrangement in which optical elements in the first state or in the second state in the first arrangement are inverted into the second state or into the first state, respectively, to implement overlay exposure of the substrate. 
     A sixth aspect of the present invention provides a device manufacturing method comprising: forming a pattern of a photosensitive layer on the substrate, using the exposure method or the exposure apparatus of the present invention; and processing the substrate with the pattern formed thereon. 
     The present invention comprises setting the optical elements in the first state and in the second state to the first arrangement in the first region of the array of optical elements and setting the optical elements in the first state and in the second state to the second arrangement which is the inversion of the first arrangement in the second region of the array of optical elements, in the spatial light modulator, and when there is the systematic error in the optical elements in the first arrangement, there is the systematic error with an opposite sign in the optical elements in the second arrangement. For this reason, for example, by overlap illumination of an illumination target surface with light from the optical elements in the first arrangement and with light from the optical elements in the second arrangement, influence of the systematic error is alleviated. Furthermore, when there is light passing via gap regions between the optical elements, influence of the light passing via the gap regions is also alleviated. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a drawing showing a schematic configuration of an exposure apparatus as an example of embodiments. 
         FIG. 2A  is an enlarged perspective view showing a part of spatial light modulator  28  in  FIG. 1 , and  FIG. 2B  a cross-sectional view along the line BB in  FIG. 2A . 
         FIG. 3A  is a drawing showing shot areas on a wafer during scanning exposure,  FIG. 3B  a drawing showing a shot area on the wafer during exposure in the step-and-repeat method, and  FIG. 3C  a drawing showing a light intensity distribution of an exposure region. 
         FIG. 4A  is a drawing showing a first phase distribution for forming a first pattern of the spatial light modulator,  FIG. 4B  an enlarged view of a part of  FIG. 4A ,  FIG. 4C  an enlarged view showing resist patterns of spatial images corresponding to the phase distribution of  FIG. 4A , and  FIG. 4D  an enlarged view showing resist patterns in the presence of the systematic error in the phase of the mirror elements  30 . 
         FIG. 5A  is an enlarged view showing reduced (shrunk) resist patterns in the presence of the systematic error in the phase of the mirror elements  30 ,  FIG. 5B  a drawing showing relations between line widths of the left patterns in  FIG. 5A  and defocus amounts, and  FIG. 5C  a drawing showing relations between line widths of the right patterns in  FIG. 5A  and defocus amounts 
         FIG. 6A  is a drawing showing a first phase distribution including the systematic error of the spatial light modulator,  FIG. 6B  an enlarged view showing reduced resist patterns corresponding to the phase distribution of  FIG. 6A ,  FIG. 6C  a drawing showing a second phase distribution which is an inversion of the phase distribution of  FIG. 6A ,  FIG. 6D  an enlarged view showing reduced resist patterns corresponding to the phase distribution of  FIG. 6C , and  FIG. 6E  an enlarged view showing reduced resist patterns after double exposure. 
         FIG. 7A  is a drawing showing a first phase distribution including reflection in gap regions in the spatial light modulator,  FIG. 7B  an enlarged view showing resist patterns corresponding to the phase distribution of  FIG. 7A ,  FIG. 7C  a drawing showing a second phase distribution which is an inversion of the phase distribution of  FIG. 7A ,  FIG. 7D  an enlarged view showing resist patterns corresponding to the phase distribution of  FIG. 7C , and  FIG. 7E  an enlarged view showing resist patterns after double exposure. 
         FIG. 8A  is an enlarged view showing a part of a first phase distribution including gap regions generating reflected light,  FIG. 8B  an enlarged view showing resist patterns corresponding to the first phase distribution,  FIG. 8C  a drawing showing a part of a second phase distribution which is an inversion of the first phase distribution,  FIG. 8D  an enlarged view showing resist patterns corresponding to the second phase distribution, and  FIG. 8E  an enlarged view showing resist patterns after double exposure. 
         FIG. 9A  is a drawing showing a first phase distribution for forming a second pattern of the spatial light modulator,  FIG. 9B  an enlarged view of a part of  FIG. 9A , and  FIG. 9C  an enlarged view showing resist patterns of spatial images corresponding to the phase distribution of  FIG. 9A . 
         FIG. 10A  is a drawing showing a first phase distribution for the second pattern including the systematic error of the spatial light modulator,  FIG. 10B  an enlarged view showing resist patterns corresponding to the phase distribution of  FIG. 10A ,  FIG. 10C  a drawing showing a second phase distribution which is an inversion of the phase distribution of  FIG. 10A ,  FIG. 10D  an enlarged view showing resist patterns corresponding to the phase distribution of  FIG. 10C , and  FIG. 10E  an enlarged view showing resist patterns after double exposure. 
         FIG. 11A  is a drawing showing a first phase distribution for the second pattern including reflection in gap regions in the spatial light modulator,  FIG. 11B  an enlarged view showing resist patterns corresponding to the phase distribution of  FIG. 11A ,  FIG. 11C  a drawing showing a second phase distribution which is an inversion of the phase distribution of  FIG. 11A ,  FIG. 11D  an enlarged view showing resist patterns corresponding to the phase distribution of  FIG. 11C , and  FIG. 11E  an enlarged view showing resist patterns after double exposure. 
         FIG. 12A  is an enlarged view showing a part of a first phase distribution for the second pattern including gap regions generating reflected light,  FIG. 12B  an enlarged view showing resist patterns corresponding to the first phase distribution,  FIG. 12C  a drawing showing a part of a second phase distribution which is an inversion of the first phase distribution,  FIG. 12D  an enlarged view showing resist patterns corresponding to the second phase distribution, and  FIG. 12E  an enlarged view showing resist patterns after double exposure. 
         FIG. 13A  is a drawing showing zero-order light and ±first-order light from a periodic pattern,  FIG. 13B  a drawing showing a first phase distribution, and  FIG. 13C  a drawing showing a second phase distribution which is an inversion of the first phase distribution. 
         FIG. 14A  is a drawing showing a light intensity distribution in a scanning direction of an exposure region,  FIG. 14B  an explanatory drawing of a moving method of phase distribution in the array of mirror elements  30  in the spatial light modulator, and  FIG. 14C  a drawing showing two spatial light modulators in a modification example of the embodiment. 
         FIG. 15  is a block diagram showing a configuration example of modulation control unit  48  in  FIG. 1 . 
         FIG. 16  is a flowchart showing an example of operation of implementing exposure while driving the spatial light modulator. 
         FIGS. 17A, 17B, and 17C  are drawings showing respective states of movement of phase distribution in the scanning direction on the array of mirror elements  30  in the spatial light modulator. 
         FIGS. 18A and 18B  are drawings showing respective states of movement of phase distribution in the scanning direction on the array of mirror elements  30  in the spatial light modulator, subsequent to  FIG. 17C . 
         FIG. 19A  is an enlarged view showing an arrangement of mirror elements  30  including gap regions, and  FIGS. 19B, 19C, 19D, and 19E  are enlarged views showing resist patterns after double exposure in cases where the gap phase is 0°, 90°, 180°, and 270°, respectively, with the systematic error ΔZ of 2 nm. 
         FIG. 20A  is an enlarged view showing an arrangement of mirror elements  30  including gap regions, and  FIGS. 20B, 20C, 20D, and 20E  are enlarged views showing resist patterns after double exposure in cases where the gap phase is 0°, 90°, 180°, and 270°, respectively, with the systematic error ΔZ of 4 nm. 
         FIG. 21  is a drawing showing an example of relations between systematic errors ΔZ and errors of line widths of resist patterns with different gap phases. 
         FIG. 22  is a drawing showing an example of change in errors of line widths of resist patterns with variations of the gap phase. 
         FIG. 23  is a block diagram showing a part of a modulation control unit in a modification example. 
         FIG. 24  is a drawing showing a relation of signals in  FIG. 23 . 
         FIG. 25  is a block diagram showing a part of a modulation control unit in another modification example. 
         FIG. 26  is a drawing showing a schematic configuration of an exposure apparatus of a modification example. 
         FIG. 27  is a flowchart showing an example of steps of manufacturing electronic devices. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     An example of embodiments of the present invention will be described below with reference to  FIGS. 1 to 18 . 
       FIG. 1  shows a schematic configuration of an exposure apparatus EX of the maskless method according to the present embodiment. In  FIG. 1 , the exposure apparatus EX has a light source  2  for exposure which emits pulses of light, an illumination optical system ILS which illuminates an illumination target surface with illumination light (exposure light) IL for exposure from the light source  2 , a spatial light modulator  28  with a large number of mirror elements  30  which are respective height-variable micromirrors arranged in a two-dimensional array pattern approximately on the illumination target surface or on a surface near it, and a modulation control unit  48  which drives the spatial light modulator  28 . Furthermore, the exposure apparatus EX has a projection optical system PL which receives the illumination light IL reflected by a reflective, variable, uneven pattern (mask pattern with a variable phase distribution) generated by the large number of mirror elements  30  and which projects a spatial image (device pattern) created corresponding to the uneven pattern (phase distribution), onto a surface of a wafer W (substrate), a wafer stage WST which performs positioning and movement of the wafer W, a main control system  40  consisting of a computer which generally controls the operation of the overall apparatus, various control systems, and so on. 
     The description hereinafter will be based on such a coordinate system that in  FIG. 1 , the Z-axis is set along a direction perpendicular to a bottom surface of the wafer stage WST (a plane parallel to an unrepresented guide surface), the Y-axis is set along a direction parallel to the plane of  FIG. 1  in a plane normal to the Z-axis, and the X-axis is set along a direction normal to the plane of  FIG. 1 . Angles around the X-axis, Y-axis, and Z-axis will also be called angles in θx direction, θy direction, and θz direction, respectively. In the present embodiment, the wafer W is scanned in the Y-direction (scanning direction) during exposure. 
     The light source  2  applicable herein can be a solid-state pulsed laser light source which generates a harmonic of laser light output from a YAG laser or a solid-state laser (semiconductor laser or the like). The solid-state pulsed laser light source can emit pulses of laser light, for example, with the wavelength of 193 nm (or any one of various wavelengths except for it) and with the pulse width of about 1 ns, e.g., a pulsed laser beam of linearly polarized light at the frequency of approximately 1 to 3 MHz. The light source  2  also applicable herein can be, for example, an ArF excimer laser light source which emits pulses of laser light with the wavelength of 193 nm and the pulse width of about 50 ns, at the frequency of approximately 4 to 6 kHz, a KrF excimer laser light source with the wavelength of 248 nm, or a light emitting diode which emits pulsed light. 
     In the present embodiment, a power supply  42  is connected to the light source  2 . The main control system  40  supplies to the power supply  42 , emission trigger pulses TP indicative of timing and light quantity (pulse energy) of pulse emission. In synchronism with the emission trigger pulses TP, the power supply  42  makes the light source  2  emit pulses at the indicated timing and light quantity. 
     The illumination light IL consisting of a substantially parallel beam of pulsed laser light with a rectangular sectional shape emitted from the light source  2  travels via a beam expander  4  consisting of a pair of cylindrical lenses, a polarization control optical system  6  to control a state of polarization of the illumination light IL, and a mirror  8 A, to enter a diffractive optical element (diffractive optical element  10 A in  FIG. 1 ) selected from a plurality of diffractive optical elements  10 A,  10 B, and so on, in parallel with the Y-axis. The polarization control optical system  6  is, for example, an optical system that can replaceably set one of a half wave plate to rotate the direction of polarization of the illumination light IL, a quarter wave plate to convert the illumination light IL into circularly polarized light, and a birefringent prism of a wedge shape to convert the illumination light IL into randomly polarized light (unpolarized light). 
     The diffractive optical elements  10 A,  10 B, etc. are fixed at approximately equal angle intervals to a peripheral part of a rotary plate  12 . The main control system  40  controls the angle of the rotary plate  12  through a drive unit  12   a , to set a diffractive optical element selected according to an illumination condition, on the optical path of the illumination light IL. The illumination light IL diffracted by the selected diffractive optical element is guided to an entrance plane of a microlens array  16  by a relay optical system  14  consisting of lenses  14   a ,  14   b . The illumination light IL incident into the microlens array  16  is two-dimensionally divided by a large number of microscopic lens elements forming the microlens array  16 , to form a secondary light source (surface light source) on a pupil plane (illumination pupil plane IPP) of the illumination optical system ILS which is a rear focal plane of each lens element. 
     As an example, the diffractive optical element  10 A is provided for normal illumination, the diffractive optical element  10 B for small σ illumination to generate illumination light with a small coherence factor (σ value), and other diffractive optical elements (not shown) are also provided for dipolar illumination, for quadrupolar illumination, for annular illumination, and so on. A spatial light modulator having an array of a large number of microscopic mirrors inclination angles of each of which are variable around two axes orthogonal to each other, may be used instead of the plurality of diffractive optical elements  10 A,  10 B, etc., and a fly&#39;s eye lens or the like can also be used instead of the microlens array  16 . A zoom lens may also be used in place of the relay optical system  14 . 
     The illumination light IL from the secondary light source formed on the illumination pupil plane IPP travels via a first relay lens  18 , a field stop  20 , a mirror  8 B to bend the optical path into the −Z-direction, a second relay lens  22 , a condenser optical system  24 , and a mirror  8 C, to be incident at an average incidence angle α in the θx direction onto an illumination target surface (a surface in design where a transfer pattern is arranged) parallel to the XY plane. In other words, the optical axis AXI of the illumination optical system ILS intersects at the incidence angle α in the θx direction with the illumination target surface. The incidence angle α is, for example, from several deg (°) to several ten deg. In a power-off condition, reflective surfaces of the large number of mirror elements  30  arranged in the two-dimensional array pattern in the spatial light modulator  28  are arranged on or near the illumination target surface. The illumination optical system ILS is constructed including the optical members from the beam expander  4  to the condenser optical system  24  and the mirror  8 C. 
     The illumination light IL from the illumination optical system ILS illuminates a rectangular illumination area  26 A elongated in the X-direction while covering the array of the large number of mirror elements  30  in the spatial light modulator  28 , with a substantially uniform illuminance distribution. The large number of mirror elements  30  are arranged at predetermined pitches in the X-direction and in the Y-direction in a rectangular region in the illumination area  26 A. The illumination optical system ILS and the spatial light modulator  28  are supported by a frame not shown. The field stop  20  in the illumination optical system ILS is set at a position shifted by a predetermined distance in the optical-axis direction from a plane COP conjugate with the illumination target surface (the object plane of the projection optical system PL). This makes the intensity distribution of the illumination light IL in the illumination area  26 A as a trapezoidal distribution in the Y-direction (the direction corresponding to the scanning direction of the wafer W) and the X-direction (non-scanning direction). 
       FIG. 2A  is an enlarged perspective view showing a part of the array of mirror elements  30  in the spatial light modulator  28  in  FIG. 1 , and  FIG. 2B  a cross-sectional view along the line BB in  FIG. 2A . In  FIG. 2A , the large number of mirror elements  30  are arranged at the pitches (periods) px and py in the X-direction and in the Y-direction, respectively. As an example, the X-directional and Y-directional widths of the mirror elements  30  can be considered to be equal respectively to the pitches px, py. The reflective surfaces of the mirror elements  30  are square and the pitches px, py are equal to each other. It is noted herein that the reflective surfaces of the mirror elements  30  may be rectangular or of other shape and that the pitches px, py may be different from each other. 
     Each of the mirror elements  30  is located at a position P(i, j) which is the ith position (i=1, 2, . . . , I) in the X-direction and the jth position (j=1, 2, . . . , J) in the Y-direction. As an example, the number J of mirror elements  30  arranged in the Y-direction (direction corresponding to the scanning direction) is from several hundred to several thousand, and the number I of mirror elements  30  arranged in the X-direction is from several times to several ten times the number J. Furthermore, the pitch px of arrangement of the mirror elements  30  is, for example, approximately from 10 μm to 1 μm. 
     The spatial light modulator  28  has the large number of mirror elements  30 , and a base member  32  which supports each of the mirror elements  30  through hinge portions  35  (cf.  FIG. 2B ) each with flexibility (elasticity). 
     In  FIG. 2B , the base member  32  is composed of a substrate  32 A of a flat plate shape which is, for example, comprised of silicon, and an insulating layer  32 B of silicon nitride (e.g., Si 3 N 4 ) or the like formed on a surface of the substrate  32 A. Support portions  34  are formed at predetermined pitches in the X-direction and in the Y-direction on the surface of the base member  32  and a back-side projection of each mirror element  30  is supported through a pair of two-stage hinge portions  35  with flexibility in the Z-direction by elastic deformation, between adjacent Y-directional support portions  34 . The support portions  34 , hinge portions  35 , and mirror elements  30  are integrally formed, for example, of polysilicon. A reflective film  31  comprised of a thin film of metal (e.g., aluminum or the like) to enhance reflectivity is formed on the reflective surface (front surface) of each mirror element  30 . 
     Furthermore, electrodes  36 A are formed on the surface of the base member  32  on the bottom side of mirror elements  30  and electrodes  36 B are formed on the bottom faces of the hinge portions  35  so as to be opposed to the electrodes  36 A. Signal lines (not shown) for applying a predetermined voltage between corresponding electrodes  36 A,  36 B for each mirror element  30  are provided in a matrix on the surface of the base member  32  and on the side faces of the support portions  34 . The signal lines may be routed through through-holes (not shown) provided in the base member  32 . In the present embodiment, in a state without application of the voltage between the electrodes  36 A,  36 B in a power-off condition or even in a power-on condition (first state), the reflective surface of the mirror element  30  agrees with a reference plane A 1  which is a plane parallel to the XY plane, as indicated by the mirror element  30  at the position P(i, j−1) onto which the illumination light IL 2  is incident. On the other hand, in a state with application of the predetermined voltage between the electrodes  36 A,  36 B in the power-on condition (second state), the reflective surface of the mirror element  30  agrees with a plane A 2  displaced by a distance d 1  in the Z-direction from the reference plane A 1  in parallel with the XY plane, as indicated by the mirror element  30  at the position P(i, j) onto which the illumination light IL 1  is incident. Each mirror element  30  in the spatial light modulator  28  is set either in the first state or in the second state. 
     The spatial light modulator  28  of this microscopic three-dimensional structure can be manufactured by use of the MEMS (Microelectromechanical Systems) technology, for example, as described in Non Patent Literature 1 cited in the Background Art. Since each mirror element  30  of the spatial light modulator  28  needs only to be set in the first state or in the second state by parallel displacement, it is easy to achieve downsizing of the mirror elements  30  and increase in the number of arrangement of mirror elements  30 . 
     In  FIG. 2B , in the state in which the reflective surface of each mirror element  30  agrees with the reference plane A 1  (the first state), let us define a change amount of the phase of the illumination light IL reflected by the mirror element  30 , as a first phase δ 1 ; in the present embodiment the phase δ 1  is 0°. Namely, in the present embodiment, the phase of the incident light is the same as the phase of the reflected light in the first state. In the state in which the reflective surface of each mirror element  30  agrees with the plane A 2  displaced by the distance d 1  from the reference plane A 1  (the second state), let us define a change amount of the phase of the illumination light IL reflected by the mirror element  30 , as a second phase δ 2 ; then the phase δ 2  is different by 180° (π (rad)) from the phase δ 1 . Specifically, the relations below hold.
 
δ1=0°  (1A),
 
δ2=180°=π (rad)  (1B)
 
     In the description hereinafter the phases without unit refer to phases in rad. The second phase δ 2  is a difference between the change amount of the phase of the wavefront of reflected beam B 1  indicated by a dashed line with the reflective surface of the mirror element at the position P(i, j) agreeing with the reference plane A 1  and the change amount of the phase of the wavefront of reflected beam B 2  with the reflective surface agreeing with the plane A 2  at the distance d 1 . As an example, when it is assumed that the angle of incidence α is approximately 0° and that the wavelength of the illumination light IL 1  incident to the reflective surfaces of the mirror elements  30  is λ (λ=193 nm herein), the distance d 1  is given as follows.
 
 d 1=λ/4  (2A)
 
     The distance between the reflective surface of the mirror element  30  in the second state and the reference plane A 1  includes, in addition to the designed distance d 1 , a manufacturing error and/or a random error due to a driving error or the like and/or a systematic error ΔZ (an error with a predetermined tendency occurring in common to almost all the mirror elements  30 ) in fact. 
     When the angle of incidence α of the illumination light IL 1  is approximately 0, an error Δϕ of the phase of reflected light B 2  corresponding to the systematic error ΔZ of the height of the reflective surface is given as follows, using the wavelength λ of the illumination light IL 1 .
 
Δϕ=(4π/λ)Δ Z   (2B)
 
     For this reason, the change amount (the second phase δ 2 ) of the phase of the illumination light IL reflected by a certain mirror element  30  in the second state is approximately 180°. A change amount of the phase δ 2  due to the random error and the systematic error is about ±10° as an example. Influence of the random error is alleviated, for example, by exposing each point on the wafer W with multiple pulses. 
     Portions that reflect the illumination light IL in the surfaces of the support portions  34  between the mirror elements  30  will be referred to as gap regions  34   a . The phase of reflected light on the gap regions  34   a  is changed by a Z-directional distance d 2  between the surfaces of the gap regions  34   a  and the reference reflective surface A 1 . As an example, no consideration is given for the reflected light on the gap regions  34   a , but influence thereof in the case of the width of the gap regions  34   a  being relatively wide will be described later. 
     In the description below, the mirror element  30  set in the first state to reflect the incident illumination light with the phase change of 0° will also be called a mirror element of phase 0 and the mirror element  30  set in the second state to reflect the incident illumination light with the phase change of 180° as a design value will also be called a mirror element of phase π. The modulation control unit  48  in  FIG. 1  controls the voltage between the electrodes  36 A,  36 B of the mirror element  30  at each position P(i, j), according to information of a phase distribution (an uneven pattern of the array of mirror elements  30 ) of the illumination light IL set from the main control system  40 , to set the mirror element  30  in the first state (phase 0) or in the second state (phase π). 
       FIG. 2B  shows flip-flops  60 A,  60 B connected to each other and selection circuits  62 A,  62 B for selecting a first output of the flip-flop  60 A,  60 B or a second output as an inversion of the first output, which are a part of the modulation control unit  48  in  FIG. 1 . When the first output of the flip-flop  60 A or the like is at low level (or at high level), the second output is at high level (or at low level). Outputs of the selection circuits  62 A,  62 B are connected to the respective electrodes  36 A for driving two mirror elements arranged next to each other in the Y-direction, and the electrodes  36 B opposed to them are connected, for example, to a ground line (not shown). As an example, when the output of the selection circuit  62 A or the like is at low level (or at high level), the corresponding mirror element  30  is set in the first state (or in the second state). 
     The first output of the preceding-stage flip-flop (not shown) is supplied to an input part of the flip-flop  60 A, the first output of the flip-flop  60 B is supplied to the input part of the subsequent-stage flip-flop (not shown), and a control unit (not shown) outputs clock pulses CKP and selection signals SELS. The flip-flops  60 A,  60 B, etc. shift their outputs in synchronism with the clock pulses CKP. A group of flip-flops connected in this manner is called a shift register. The selection circuit  62 A and other selection circuits are connected respectively to all the flip-flop  60 A and other flip-flops. As an example, each of the selection circuit  62 A and others selects and outputs the first output of the corresponding flip-fop  60 A or other flip-flop with the selection signal SELS being in a high-level duration, and selects and outputs the second output of the corresponding flip-flop  60 A with the selection signal SELS being in a low-level duration. Each of the flip-flop  60 A and others has outputs of multiple bits in practice. The flip-flops  60 A,  60 B and selection circuits  62 A,  62 B and others may be formed in a region near the region of the array of mirror elements  30 , for example, on the back surface of the substrate  32 A or on the front surface of the base member  32 . An overall configuration example of the modulation control unit  48  will be described later. 
     The flip-flops  60 A,  60 B, etc. in  FIG. 2B  are circuits for moving the phase distribution of the mirror elements  30  in the +Y-direction and there are also a group of flip-flops (not shown) provided for moving the phase distribution in the −Y-direction. Each of the selection circuits  62 A,  62 B, etc. selects one output of the two set of flip-flops in accordance with the scanning direction of the wafer W. 
     In  FIG. 1 , the illumination light IL, after reflected by the array of many mirror elements  30  in the illumination area  26 A of the spatial light modulator  28 , is incident at the average incidence angle α into the projection optical system PL. The projection optical system PL with the optical axis AXW supported by an unrepresented column is a reduction projection optical system which is non-telecentric on the spatial light modulator  28  (object plane) side and telecentric on the wafer W (image plane) side. The projection optical system PL forms a demagnified image of a spatial image according to a phase distribution of the illumination light IL set by the spatial light modulator  28 , on an exposure region  26 B (which is a region optically conjugate with the illumination area  26 A) in one shot area on the wafer W. 
     Since the light intensity distribution in the illumination area  26 A is of the trapezoidal shape in the Y-direction and the X-direction as described above, a light intensity distribution in the exposure region  26 B is also of a trapezoidal shape in the Y-direction (the scanning direction of the wafer W) and the X-direction, as shown in the enlarged view of  FIG. 3C . In  FIG. 3C , intensity profiles EPY and EPX indicate intensity profiles of the illumination light IL on straight lines passing the center of the exposure region  26 B in parallel with the Y-axis and the X-axis, respectively. As seen from the intensity profiles EPY, EPX, the intensity decreases approximately linearly outward in slant portions  26 Ba,  26 Bb of a predetermined width at the Y-directional ends of the exposure region  26 B and the intensity also decreases approximately linearly outward in joint portions  26 Bc,  26 Bd of a predetermined width at the X-directional ends of the exposure region  26 B. The slant portions  26 Ba,  26 Bb are provided for alleviating influence of unintended phase imaging which can occur at the edges of the spatial light modulator  28 . The joint portions  26 Bc,  26 Bd are provided for alleviating the influence of unintended phase imaging occurring at the edges of the spatial light modulator  28  and for alleviating joint errors to adjacent partial regions. 
     A projection magnification β of the projection optical system PL is, for example, approximately from 1/10 to 1/100. The resolution of the projection optical system PL is, for example, approximately from one to several times a width (β·px) of an image of the mirror element  30  in the spatial light modulator  28 . For example, if the size of the mirror element  30  (the pitch of arrangement) is about several μm and the projection magnification β of the projection optical system PL is approximately 1/100, the resolution Re is approximately from several ten nm to several times it. The wafer W (substrate) includes, for example, one obtained by coating a surface of a base member of a circular flat shape of silicon or SOI (silicon on insulator) with a photoresist (photosensitive material) in the thickness of approximately several ten nm to 200 nm. 
     With the use of the projection optical system PL non-telecentric on the object side as in the present embodiment, the reflective surfaces of the large number of mirror elements  30  in the spatial light modulator  28  and the exposure surface of the wafer W (the surface of the photoresist) can be arranged approximately in parallel with each other. Therefore, it is easy to design and manufacture the exposure apparatus. When the exposure apparatus EX is the immersion lithography type, it is provided with a local liquid immersion device to supply and collect a liquid (e.g., pure water) which transmits the illumination light IL, between an optical member at the tip of the projection optical system PL and the wafer W, for example, as disclosed in U.S. Pat. Published Application No. 2007/242247. The resolution can be further increased in the case of the immersion lithography type because the numerical aperture NA can be made larger than 1. 
     In  FIG. 1 , the wafer W is sucked and held on the top surface of the wafer stage WST through a wafer holder (not shown) and the wafer stage WST is configured to implement step movement in the X-direction and the Y-direction on an unillustrated guide surface and movement at a constant speed in the Y-direction. X-directional and Y-directional positions, an angle of rotation in the θz direction, etc. of the wafer stage WST are measured by a laser interferometer  45  and this measurement information is supplied to a stage control system  44 . The stage control system  44  controls the position and speed of the wafer stage WST through a driving system  46  such as a linear motor, based on the control information from the main control system  40  and the measurement information from the laser interferometer  45 . The apparatus is also provided with an alignment system (not shown) to detect positions of alignment marks on the wafer W, for carrying out alignment of the wafer W. 
     For carrying out exposure of the wafer W, the alignment of the wafer W is first carried out as a basic operation and thereafter an illumination condition of the illumination optical system ILS is set. The main control system  40  supplies information of a phase distribution (uneven pattern) corresponding to a pattern to be formed in a plurality of partial regions in each shot area on the wafer W, to the modulation control unit  48 . Then the wafer W is positioned at a scan start position, for example, for carrying out exposure in shot areas SA 21 , SA 22 , . . . aligned on a line in the Y-direction on the surface of the wafer W shown in  FIG. 3A . Thereafter, scan is started at a constant speed in the +Y-direction on the wafer W. Arrows in the shot areas SA 22  and others in  FIG. 3A  indicate directions of movement of the exposure region  26 B relative to the wafer W. 
     During the exposure, the main control system  40  supplies to the power supply  42 , the emission trigger pulses TP, for example, according to a relative position of a first partial area SA 22   a  of the shot area SA 22  on the wafer W relative to the exposure region  26 B, to cause the illumination light to be emitted as pulsed light. Furthermore, the main control system  40  supplies the control signal at a frequency of several times to several ten times that of the emission trigger pulses TP to the modulation control unit  48 . In synchronism with the control signal, the modulation control unit  48  controls the phase distribution (uneven pattern) of the array of optical elements in the spatial light modulator  28  so as to gradually move the phase distribution of a transfer object in the Y-direction. Through this process, the partial region SA 22   a  is subjected to scanning exposure with the exposure region  26 B where the internal spatial image moves gradually. 
     Thereafter, for exposure of the first partial region of the shot area SA 23  adjacent to the shot area SA 22  on the wafer W, while the wafer W is kept scanned in the same direction, the modulation control unit  48  moves the phase distribution of the array of optical elements in the spatial light modulator  28  in the Y-direction in synchronism with the pulse emission of the illumination light IL as in case of the exposure of the shot area SA 22 . In this manner, the exposure can be continuously carried out from the shot area SA 21  to the first partial region of SA 22 . Thereafter, the wafer stage WST is actuated to implement step movement of the wafer W in the X-direction (non-scanning direction). Then, the scanning direction of the wafer W relative to the exposure region  26 B indicated by a dotted line is set to the opposite −Y-direction, and the modulation control unit  48  moves the phase distribution (uneven pattern) of the array of optical elements in the spatial light modulator  28  in the opposite direction to that during the exposure of the first region SA 22   a  and others of the shot area SA 22  and others in synchronism with the pulse emission of the illumination light IL. By this operation, the exposure can be continuously carried out from the shot area SA 23  to the second partial region SA 22   b  and others of SA 21 . On this occasion, double exposure is implemented in the joint portions  26 Bd and  26 Bc of the exposure region  26 B in  FIG. 3C  at the boundary portions of the first partial region SA 22   a  and the second partial region SA 22   b , in order to reduce the joint error. 
     In this manner, a predetermined spatial image can be efficiently transferred by exposure in each of the shot area SA 21  to SA 23  and others on the wafer W by the maskless method. Thereafter, the photoresist on the wafer W is developed to form a resist pattern (circuit pattern) corresponding to the spatial image in each shot area on the wafer W. It is noted that the shot areas SA 21  to SA 23  may be exposed while each area is divided into three or more partial regions in the X-direction. Furthermore, because of the maskless method, it is also possible to expose the shot areas SA 21  to SA 23  with spatial images different from each other. 
     The below will describe a method of driving the spatial light modulator  28  in the case where the systematic error ΔZ is included in the distance between the reference plane A 1  and the reflective surface of the mirror element  30  in  FIG. 2B  set in the aforementioned second state (phase π) in the spatial light modulator  28  and where the error Δϕ of Expression (2B) is thus included in the phase of the reflected light. 
     First, let us suppose that resist patterns to be formed on the surface of the wafer W after development are a pair of nearly square targets  38 A,  38 B in axial symmetry each having approximately the X-directional width of 40 nm and the Y-directional length of 48 nm and arranged with the X-directional spacing of 40 nm, as shown in  FIGS. 4C and 4D  as an example. In  FIG. 4C  and others, the horizontal axis and the vertical axis correspond to the X-axis (nm) and the Y-axis (nm), respectively, on the image plane of the projection optical system PL.  FIG. 4A  is a perspective view showing an example of phase distribution  50 A of the illumination light IL (uneven distribution of the reflective surfaces of the mirror elements  30 ) formed by a part of the array of mirror elements  30  in the spatial light modulator  28  in  FIG. 1 , in order to form resist patterns as close to the targets  38 A,  38 B as possible, and  FIG. 4B  an enlarged view of the central part of  FIG. 4A . The phase distributions of the array of mirror elements  30  in  FIG. 6A  and others which will be described below are also respective perspective views. It is also assumed for convenience&#39; sake of description that the projection optical system PL forms an erect image. Furthermore, among the mirror elements  30 , the mirror elements  30 A in the first state (phase 0) are represented by patterns in white and the mirror elements  30 B in the second state (phase π) by hatched patterns. 
     In  FIGS. 4A and 4B , patterns  39 A,  39 B optically conjugate with the targets  38 A,  38 B are shown as imaginary patterns by dashed lines. The pitch px (=py) of the arrangement of the individual mirror elements  30  is set to be 20 nm at the stage of projected image, i.e., to satisfy β·px=20 (nm), using the projection magnification β of the projection optical system PL. The phase distribution  50 A includes: a first region  51 A, a fourth region  51 D, a fifth region  51 E, an eighth region  51 H, and a ninth region  51 I each consisting of the mirror elements  30 A in the first state (phase 0); a second region  51 B, a third region  51 C, a sixth region  51 F, a seventh region  51 G, and a tenth region  51 J each consisting of the mirror elements  30 B in the second state (phase π); and a peripheral region  51 K of a frame shape surrounding these first region  51 A to tenth region  51 J. The imaginary patterns  39 A and  39 B are arranged in the first region  51 A and in the second region  51 B, respectively. The peripheral region  51 K is a region where the mirror elements  30 A in the first state and the mirror elements  30 B in the second state are arranged in a checkered pattern. The checkered pattern can also be called a checkered grid or a checkerboard pattern. A spatial image corresponding to a phase distribution of the peripheral region  51 K includes images in a line width that is half of the width of the images of the mirror elements  30  and, because the projection optical system PL does not resolve patterns finer than the width of the images of the mirror elements  30  (or because diffracted light does not pass through an aperture stop), the spatial image corresponding to the peripheral region  51 K becomes a light shielded part. 
     Simulations were conducted to obtain intensity distributions of spatial images on image planes at the best focus position of the projection optical system PL and at defocus positions of ±40 nm, under illumination conditions that the foregoing phase distribution  50 A was used to optimize the light quantity distribution of the illumination light IL on the illumination pupil plane IPP so as to achieve a high resolution and that the illumination light IL was linearly polarized light in the Y-direction and, for comparison, under the condition that the systematic error ΔZ of the height of the reflective surfaces of the mirror elements  30  was 0. Furthermore, theoretical resist patterns obtained by slicing those spatial images by a predetermined threshold (e.g., a value with which an average of X-directional widths becomes a target value) are patterns L, R at the best focus position, patterns LP, RP with the defocus of +40 nm, and patterns LM, RM with the defocus of −40 nm in  FIG. 4C . In this case, the left patterns L, LM, LP correspond to the target  38 A in the −X-direction and the right patterns R, RM, RP to the target  38 B in the +X-direction (the same also applies hereinafter). The left and right patterns L, R are elliptical against the targets  38 A,  38 B, according to the resolution of the projection optical system PL. It is found from  FIG. 4C  that when the systematic error ΔZ is 0, there is little change in the formed resist patterns even with the defocuses. It is noted hereinafter that in  FIG. 4D  and others, patterns Lj, Rj (j=0, 1, 2, . . . ) represent resist patterns at the best focus position, patterns LjP, RjP resist patterns with the defocus of +40 nm, and patterns LjM, RjM resist patterns with the defocus of −40 nm. 
     Next, simulations were conducted to obtain intensity distributions of spatial images on the image planes at the best focus position of the projection optical system PL and at the defocus positions of ±40 nm, under the same illumination conditions using the phase distribution  50 A and under the condition that the systematic error ΔZ of the height of the reflective surfaces of the mirror elements  30  was 2 nm (the phase error Δϕ of Expression (2B) was approximately 7.5°). Furthermore, theoretical resist patterns obtained from the spatial images are patterns L 0 , R 0  at the best focus position and patterns L 0 P, R 0 P, L 0 M, R 0 M with the defocuses in  FIG. 4D . It is found from  FIG. 4D  that when the systematic error ΔZ is 2 nm, ratios of sizes of the left and right resist patterns formed vary depending upon the defocuses (e.g., the pattern L 0 P is smaller than the pattern R 0 P). 
     Targets  38 AS,  38 BS and patterns L 1 , R 1 , L 1 P, R 1 P, L 1 M, R 1 M in  FIG. 5A  are resist patterns obtained by subjecting the targets  38 A,  38 B and the patterns L 0 , R 0 , L 0 P, R 0 P, L 0 M, L 0 M in  FIG. 4D  to shrink (reduction) in the width of 10 nm. Concerning the shrunk resist patterns, a CD (critical dimension) as a width in the transverse direction (the X-direction herein) of the left pattern UP or the like is defined as CD-L and the CD of the right pattern R 1 P or the like as CD-R; under this definition, the critical dimensions were calculated with various set values of the systematic error ΔZ and with various defocus amounts, in order to quantify variations of sizes of the left and right resist patterns. 
       FIGS. 5B and 5C  show CD-L and CD-R calculated as described above. In  FIGS. 5B and 5C  the horizontal axis represents defocus amounts (nm) and the vertical axis change amounts ΔCD (%) of CD with respect to the target value; the change amounts ΔCD shown are those with the systematic error ΔZ being set at 0, 0.25, 0.5, and 1 (nm). It is found from  FIGS. 5B and 5C  that with the defocus amounts of ±40 nm, the CD error of about 7% is made even with the systematic error ΔZ of about 0.5 nm. However, the signs of left CD-L and right CD-R are opposite about the defocuses and by making use of this relation, the CD error can be substantially reduced even with the defocus in the presence of the systematic error ΔZ, as described below. 
     Namely, in the present embodiment, when the systematic error ΔZ of the mirror elements  30  is 2 nm, a first phase distribution  50 A in  FIG. 6A  (which is the same as the phase distribution of  FIG. 4A ) is first set in the array of mirror elements  30  in the spatial light modulator  28  and the wafer W is exposed with a spatial image by the projection optical system PL. By imaginarily slicing and shrinking an exposure dose distribution in this exposure, it is possible to obtain resist patterns L 1 , R 1 , L 1 P, R 1 P, L 1 M, R 1 M in  FIG. 6B  which are the same as those in  FIG. 5A . Thereafter, a second phase distribution  50 B in  FIG. 6C  resulting from inversion of 0 and π of the phase distribution  50 A is set in the array of mirror elements  30  in the spatial light modulator  28  and the wafer is doubly exposed with a spatial image by the projection optical system PL. In the phase distribution  50 B of  FIG. 6C , a first region  52 A to a tenth region  52 J corresponding to the first region  51 A (phase 0) to the tenth region  51 J (phase π) in  FIG. 6A  are of the phase π to the phase 0, respectively. A peripheral region  52 K of the phase distribution  50 B corresponding to the peripheral region  51 K of the phase distribution  50 A is a checkered pattern but its phases are switched from 0 to π and vice versa from those in the peripheral region  51 K. Since the image of the peripheral region  52 K is a light shielded portion, the phase distribution of the same checkered pattern as the peripheral region  51 K may also be used instead of the peripheral region  52 K. 
     In this case, when it is assumed that the systematic error ΔZ causes, for example, the second region  51 B (phase π+Δϕ) in comparison to the first region  51 A (phase 0) to have the phase leading by Δϕ from the target value in the phase distribution  50 A, the second region  52 B (phase 0) in comparison to the corresponding first region  52 A (phase π+Δϕ) has the phase lagging by Δϕ behind the target value in the phase distribution  50 B. In other words, the second phase distribution  50 B becomes equivalent to a distribution resulting from inversion of the signs of the systematic error Δϕ (ΔZ) in the first phase distribution  50 A. For this reason, the characteristics of change against defocus of the line widths CD-L, CD-R of the left and right resist patterns in  FIG. 5A  about the second phase distribution  50 B become the characteristics of  FIGS. 5C and 5B  opposite to those about the phase distribution  50 A. 
     Accordingly, by slicing exposure dose distributions of spatial images of the phase distribution  50 B and shrinking sliced patterns, it is possible to obtain resist patterns L 2 , R 2 , L 2 P, R 2 P, L 2 M, R 2 M in  FIG. 6D . In this case, concerning the patterns with the defocus of +40 nm, the pattern L 2 P on the target  38 AS side in  FIG. 6D  is larger than the pattern R 2 P on the target  38 BS side, while the pattern UP on the target  38 AS side in  FIG. 6B  is smaller than the pattern R 1 P on the target  38 BS side. With the defocus of −40 nm, the magnitude relations between the patterns L 1 M, R 1 M in  FIG. 6B  and the patterns L 2 M, R 2 M in  FIG. 6D  are reverse to each other. 
     An exposure dose in the exposure of the spatial image of the phase distribution  50 A is equal to that in the exposure of the spatial image of the phase distribution  50 B and they are set to achieve an appropriate exposure dose after double exposure. As a result, an exposure dose distribution after the double exposure is approximately equal to that in use of the phase distribution  50 A with the systematic error ΔZ of 0. Namely, by slicing the exposure dose distributions after the double exposure, it is possible to obtain patterns L 3 , R 3  with the best focus and patterns L 3 P, R 3 P, L 3 M, R 3 M with the defocuses of ±40 nm as approximately equal patterns, as shown in  FIG. 6E . Therefore, it is confirmed that even if there are the systematic error ΔZ of 2 nm and the defocus amount from about +40 to −40 nm, the patterns nearly equal to the targets  38 AS,  38 BS can be formed after the development and shrink. 
     The inventors confirmed that when reflected light from the gap regions  34   a  in the array of mirror elements  30  was mixed in the reflected light from the mirror elements  30 , influence thereof was alleviated by implementing an overlay of the exposure with the foregoing first phase distribution and the exposure with the second phase distribution which is the inversion of the first phase distribution. Specifically, the first exposure is assumed to be carried out while the array of mirror elements  30  in the spatial light modulator  28  is set in the phase distribution  50 A of  FIG. 7A  which is the same as  FIG. 6A . It is, however, assumed that in the phase distribution  50 A of  FIG. 7A , the systematic error ΔZ of the height of the mirror elements  30  in the second state is 0 and that there are gap regions  34   a  of X-directional and Y-directional widths cx, cy (provided that cx=cy) in the arrangement of the mirror elements  30 , as shown in its partly enlarged view E 6 A. As an example, while the pitch of the arrangement of images of the mirror elements  30  is 20 nm (=β·px), the width β·ex of images of the gap regions  34   a  is 2.5 nm (12.5% of the pitch). The reflectance Rc of the gap regions  34   a  for the illumination light IL is assumed to be 10% (which is a percentage relative to the reflectance of the mirror elements  30 ). Furthermore, it is assumed that a change amount  83  of the phase of the reflected light from the gap regions  34   a  (a difference from the change amount δ 1  of the phase of the reflected light from the mirror elements  30  in the first state), which is determined according to the distance d 2  between the reference reflective surface A 1  and the surfaces of the gap regions  34   a  in  FIG. 2B , is 0°. In the description hereinafter, the change amount δ 3  of the phase of the reflected light from the gap regions  34   a  with respect to the change amount δ 1  of phase will also be referred to as gap phase. 
     In this case, simulations were also conducted under the condition that the wafer W was first exposed with the spatial image of the phase distribution  50 A in  FIG. 7A  by the projection optical system PL. The simulations of spatial images below were performed for situations where the spatial images were formed at the best focus position and at the defocus positions of ±40 nm. In resist patterns corresponding to exposure dose distributions of the spatial images obtained as the simulation results, patterns L 4 , L 4 P, L 4 M on the left target  38 A side are considerably larger than patterns R 4 , R 4 P, R 4 M on the right target  38 B side, as shown in  FIG. 7B . 
     Next, the second phase distribution  50 B in  FIG. 7C  as the inversion of 0 and π of the phase distribution  50 A is set in the array of the mirror elements  30  in the spatial light modulator  28  and the wafer W is doubly exposed with the spatial image by the projection optical system PL. In the phase distribution  50 B as well, as shown in partly enlarged view E 6 C, the reflectance Rc of the gap regions  34   a  is 10% and the change amount of the phase of the reflected light (gap phase δ 3 ) is 0°. In resist patterns corresponding to exposure dose distributions of the spatial images of the phase distribution  50 B in  FIG. 7C , as shown in  FIG. 7D , patterns L 5 , L 5 P, L 5 M on the left target  38 A side are considerably smaller than patterns R 5 , R 5 P, R 5 M on the right target  38 B side. 
     As a result, in resist patterns corresponding to exposure dose distributions after the double exposure, as shown in  FIG. 7E , patterns L 6 , R 6  with the best focus and patterns L 6 P, R 6 P, L 6 M, R 6 M with the defocuses of ±40 nm become almost equal. It is found therefore that even if the reflectance of the gap regions  34   a  in the phase 0° in the array of the mirror elements  30  is approximately 10% and there is the defocus from +40 to −40 nm, patterns nearly equivalent to the targets  38 A,  38 B can be formed after development. In  FIGS. 7B , D, and E, the slice level to determine the pattern size was determined so that the maximum of the X-directional widths of the patterns in  FIG. 7E  became approximately equal to the target, and it was also applied to  FIGS. 7B  and D. 
     Simulations were also conducted for situations where the change amount (gap phase δ 3 ) of the phase of the reflected light from the gap regions  34   a  in the array of the mirror elements  30  was 270°. It was assumed in this case that the phase distribution of the first exposure was the same as the phase distribution  50 A in  FIG. 7A  but the reflectance Rc of the gap regions  34   a  was 1%, as shown in a partly enlarged view of  FIG. 8A . In resist patterns corresponding to exposure dose distributions of spatial images of this phase distribution  50 A, as shown in  FIG. 8B , a pattern L 7 M on the target  38 A side is slightly larger than a pattern R 7 M on the target  38 B side, and a pattern L 7 P is slightly smaller than a pattern R 7 P. 
     Furthermore, the phase distribution of the second exposure is the same as the phase distribution  50 B in  FIG. 7B , but the reflectance Rc of the gap regions  34   a  is 1% and the gap phase δ 3  270°, as shown in a partly enlarged view of  FIG. 8C . In resist patterns corresponding to exposure dose distributions of spatial images of the phase distribution  50 B in  FIG. 8C , as shown in  FIG. 8D , a pattern L 8 M on the target  38 A side is slightly smaller than a pattern R 8 M on the target  38 B side and a pattern L 8 P is slightly larger than a pattern R 8 P. Therefore, in resist patterns corresponding to exposure dose distributions after the double exposure, as shown in  FIG. 8E , patterns L 9 , R 9  with the best focus and patterns L 9 P, R 9 P, L 9 M, R 9 M with the defocuses of ±40 nm become approximately equal. It is therefore found that even if the reflectance of the gap regions  34   a  with the gap phase of 270° in the array of mirror elements  30  is approximately 1% and there is the defocus from about +40 nm to −40 nm, the patterns nearly equivalent to the targets  38 A,  38 B can be formed after development. In  FIGS. 8B , D, and E, the slice level to determine the pattern size was determined so that the maximum of the X-directional widths of the patterns in  FIG. 8E  became approximately equal to the target, and it was also applied to  FIGS. 8B  and D. 
     Next, as another example, simulations were conducted for situations where resist patterns to be formed on the surface of the wafer W after development were asymmetric patterns, as shown in  FIG. 9C . The resist patterns in  FIG. 9C  are a short rectangular target  38 C approximately with the X-directional width of 40 nm and the Y-directional length of 56 nm and a long rectangular target  38 D approximately with the X-directional width of 40 nm and the Y-directional length of 96 nm arranged with the X-directional space of 80 nm from the target  38 C. 
       FIG. 9A  shows an example of phase distribution  53 A of illumination light IL formed by a part of the array of the mirror elements  30  in the spatial light modulator  28  in  FIG. 1 , in order to form resist patterns as close to the targets  38 C,  38 D as possible, and  FIG. 9B  is an enlarged view of the central part of  FIG. 9A . In  FIGS. 9A and 9B , patterns optically conjugate with the targets  38 C,  38 D are represented virtually by dashed lines. The pitch of the arrangement of the individual mirror elements  30  is set to be 20 nm at the stage of projected image. The phase distribution  53 A includes a first region  54 A, a third region  54 C, a fourth region  54 D, and a fifth region  54 E each consisting of the mirror elements  30  in the phase π, a second region  54 B consisting of the mirror elements  30  in the phase 0, and a peripheral region  54 F of a checkered pattern in a frame shape surrounding these first region  54 A to fifth region  54 E. 
     With the use of the phase distribution  53 A, simulations were conducted under the unpolarized illumination condition with the coherence factor (σ value) of 0.14 and, for comparison, under the condition that the systematic error ΔZ of the height of the reflective surfaces of the mirror elements  30  was 0, to obtain intensity distributions of spatial images on the image planes at the best focus position of the projection optical system PL and at the defocus positions of ±40 nm. Furthermore, resist patterns obtained from those spatial images are, as shown in  FIG. 9C , such that patterns LA, RA at the best focus position and patterns LAP, RAP and LAM, RAM with the defocuses of ±40 nm are approximately identical and each of them is a pattern close to the target  38 C or  38 D. 
     Next, with the use of the phase distribution  53 A in  FIG. 10A  which is the same as  FIG. 9A , simulations were conducted under the same illumination condition and the condition that the systematic error ΔZ of the height of the reflective surfaces of the mirror elements  30  was 2 nm, to obtain intensity distributions of spatial images. Furthermore, resist patterns obtained from the spatial images are, as shown in  FIG. 10B , such that patterns LA 1 , RA 1  at the best focus position are different from patterns LA 1 P, RA 1 P, LA 1 M, RA 1 M with the defocuses. 
     Thereafter, a second phase distribution  53 B including first region  55 A to fifth region  55 E and peripheral region  55 F in  FIG. 10C  which is an inversion of 0 and π of the phase distribution  53 A, is set in the array of the mirror elements  30  in the spatial light modulator  28  and the wafer W is doubly exposed with spatial images by the projection optical system PL. In this case, the systematic error in the phase distribution  53 B is also −ΔZ with respect to the systematic error ΔZ in the phase distribution  53 A. Therefore, resist patterns obtained by slicing exposure dose distributions of the spatial images of the phase distribution  53 B are, as shown in  FIG. 10D , such that patterns LA 2 , RA 2  at the best focus position and patterns LA 2 P, RA 2 P, LA 2 M, RA 2 M with the defocuses are different in characteristics opposite to those in  FIG. 10B . As a result, by slicing exposure dose distributions after the double exposure, we obtain patterns LA 3 , RA 3  with the best focus and patterns LA 3 P, RA 3 P, LA 3 M, RA 3 M with the defocuses of ±40 nm as nearly equal patterns, as shown in  FIG. 10E . It is therefore found that even if the systematic error ΔZ is 2 nm and there is the defocus from about +40 nm to −40 nm, the patterns approximately equivalent to the targets  38 C,  38 D can be formed after development. 
     It was also confirmed in this example that the influence of the reflected light from the gap regions  34   a  in the array of the mirror elements  30  was alleviated by implementing the overlay of the exposure with the first phase distribution  53 A and the exposure with the second phase distribution  53 B as the inversion thereof. Specifically, the first exposure was based on the setup where the array of mirror elements  30  in the spatial light modulator  28  was set in the phase distribution  53 A of  FIG. 11A  which is the same as  FIG. 9A  and the conditions that the systematic error ΔZ was 0 and that, as shown in its partly enlarged view E 11 A, the width β·ex of images of the gap regions  34   a  with respect to the pitch of 20 nm (=β·px) of the arrangement of images of the mirror elements  30  was 2.5 nm (12.5% of the pitch). It was further assumed that the reflectance Rc of the gap regions  34   a  was 1% and the change amount of the phase of the reflected light from the gap regions  34   a  (the difference from the change amount δ 1 ) was 0°. 
     In this case as well, exposure dose distributions of spatial images of the phase distribution  53 A in  FIG. 11A  are first obtained and resist patterns obtained from the exposure dose distributions are, as shown in  FIG. 11B , such that left patterns LA 4 , LA 4 P, LA 4 M are smaller than the target  38 C and right patterns RA 4 , RA 4 P, RA 4 M are larger than the target  38 D. 
     Next, the second phase distribution  53 B in  FIG. 11C  as an inversion of 0 and π of the phase distribution  53 A is set in the array of mirror elements  30  in the spatial light modulator  28  (where the reflectance Rc of the gap regions  34   a  is 1% and the change amount of the phase of the reflected light therefrom is 0° as shown in a partly enlarged view E 11 C) and the wafer W is doubly exposed with the spatial image thereof by the projection optical system PL. Resist patterns corresponding to exposure dose distributions of spatial images of the phase distribution  53 B in  FIG. 11C  are, as shown in  FIG. 11D , such that left patterns LA 5 , LA 5 P, LA 5 M are approximately equal to the target  38 C and right patterns RA 5 , RA 5 P, RA 5 M are smaller than the target  38 D. As a result, resist patterns corresponding to exposure dose distributions after the double exposure are, as shown in  FIG. 11E , such that patterns LA 6 , RA 6  with the best focus and patterns LA 6 P, RA 6 P, LA 6 M, RA 6 M with the defocuses of ±40 nm are approximately equal. It is therefore found that even if the reflectance of the gap regions  34   a  in the phase 0° in the array of mirror elements  30  is approximately 1% and there is the defocus from about +40 to −40 nm, the patterns nearly equivalent to the targets  38 C,  38 D can be formed after development. 
     Furthermore, simulations were also conducted under the conditions that the phase distribution of the first exposure was the same as the phase distribution  53 A in  FIG. 11A  and that, as shown in a partly enlarged view of  FIG. 12A , the reflectance Rc of the gap regions  34   a  was 1% and the change amount of the phase of the reflected light from the gap regions  34   a  was 270°. Resist patterns corresponding to exposure dose distributions of spatial images of this phase distribution  53 A are, as shown in  FIG. 12B , such that a pattern LA 7 M (LA 7 P) on the target  38 C side is slightly smaller (larger), in comparison with a pattern RA 7 M (RA 7 P) on the target  38 D side. 
     Furthermore, the phase distribution of the second exposure was the same as the phase distribution  53 B in  FIG. 11B  and, as shown in a partly enlarged view of  FIG. 12C , the reflectance Rc of the gap regions  34   a  was set to 1% and the change amount of the phase of the reflected light from the gap regions  34   a  to 270°. Resist patterns corresponding to exposure dose distributions of spatial images of the phase distribution  53 B in  FIG. 12C  are, as shown in  FIG. 12D , such that a pattern LA 8 M (LA 8 P) on the target  38 C side is slightly larger (smaller), in comparison with a pattern LA 8 M (LA 8 P) on the target  38 D side. Therefore, resist patterns corresponding to exposure dose distributions after the double exposure are, as shown in  FIG. 12E , such that patterns LA 9 , RA 9  with the best focus and patterns LA 9 P, RA 9 P, LA 9 M, RA 9 M with the defocuses of ±40 nm are approximately equal. It is therefore found that even if the reflectance of the gap regions  34   a  in the phase 270° in the array of mirror elements  30  is 1% and there is the defocus from about +40 to −40 nm, the patterns nearly equivalent to the targets  38 C,  38 D can be formed after development. 
     The below will describe situations where a periodic phase distribution is set in the array of mirror elements  30  in the spatial light modulator  28 . First, the phase distribution as an exposure object in the array of mirror elements  30  is assumed to be, as shown in  FIG. 13A , a distribution in which an arrangement of the mirror elements  30  in the first state and with the change amount of the phase of the reflected light with respect to the incident light being ϕ 1  (=0) and an arrangement of the mirror elements  30  in the second state and with the change amount of the phase of the reflected light being ϕ 2  (=π+Δϕ) are repeated at a predetermined pitch in the X-direction. The error Δϕ in the phase ϕ 2  in the second state is the phase error of Expression (2B) corresponding to the systematic error ΔZ of the height of the reflective surfaces of the mirror elements  30 . In this case, the amplitude a 0  of zero-order light and the amplitudes a 1 , a −1  of ±first-order light from the illumination light IL with the amplitude of 1 incident to the phase distribution of  FIG. 13A  are as follows.
 
 a   0 =(¼){exp( iϕ 1)+exp( iϕ 2)}  (3A)
 
 a   1   =a   −1 ={1/(2 1/2 π)}{exp( iϕ 1)−exp( iϕ 2)}  (3B)
 
     By substituting ϕ 1 =0 and ϕ 2 =π+Δϕ into these equations, we obtain the amplitudes a 0 , a 1 , and a −1  approximately as given below, under the condition that Δϕ (rad) is an infinitesimal value.
 
 a   0 =−(¼) iΔϕ   (3C)
 
 a   1   =a   −1 =(2 1/2 /π)(1+ iΔϕ/ 2)  (3D)
 
     In this case as well, a phase distribution  56 A in  FIG. 13B  which is the same as  FIG. 13A  is first coherently illuminated to expose the wafer with a spatial image thereof. The x-directional electric field E 1 (x) of the spatial image is given as below. It is noted herein that the pitch (period) of the spatial image is P.
 
 E   1 ( x )= a   0 +2 a   1  exp( i Δθ)cos(2π x/P )  (3E)
 
     The phase difference Δθ in Expression (3E) is a phase difference between the zero-order light and the first-order light due to defocus. The phase difference Δθ is given as below when δ is a defocus amount, n the refractive index of a medium between the projection optical system PL and the wafer, and λ the wavelength of the illumination light IL. 
     
       
         
           
             
               
                 
                   Δθ 
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         π 
                       
                       λ 
                     
                     ⁢ 
                     n 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     δ 
                     ⁢ 
                     
                       { 
                       
                         1 
                         - 
                         
                           
                             1 
                             - 
                             
                               ( 
                               
                                 λ 
                                 nP 
                               
                               ) 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The intensity I 1 (x) of the spatial image is expressed by the product of the electric field E 1 (x) in Expression (3E) and its complex conjugate as below. The third expression below is an expression obtained by ignoring the second-order and higher-order terms about Δϕ under the condition that Δϕ is an infinitesimal amount. The first term of the third expression below is the intensity in an ideal focus condition, and the second term the intensity dependent on the systematic error Δϕ. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               E 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                           · 
                           
                             
                               
                                 E 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
                             _ 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               4 
                               
                                 π 
                                 2 
                               
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     
                                       Δϕ 
                                       2 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                               · 
                               
                                 { 
                                 
                                   
                                     cos 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           4 
                                           ⁢ 
                                           π 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           x 
                                         
                                         P 
                                       
                                       ) 
                                     
                                   
                                   + 
                                   1 
                                 
                                 } 
                               
                             
                           
                           - 
                           
                             
                               
                                 2 
                               
                               π 
                             
                             ⁢ 
                             Δϕ 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     Δϕ 
                                     2 
                                   
                                   ⁢ 
                                   
                                     cos 
                                     ⁡ 
                                     
                                       ( 
                                       Δθ 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     Δθ 
                                     ) 
                                   
                                 
                               
                               } 
                             
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   P 
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               Δϕ 
                               2 
                             
                             16 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             = 
                             . 
                           
                           . 
                         
                         ⁢ 
                           
                         ⁢ 
                         
                           
                             
                               4 
                               
                                 π 
                                 2 
                               
                             
                             ⁢ 
                             
                               { 
                               
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         x 
                                       
                                       P 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 1 
                               
                               } 
                             
                           
                           - 
                           
                             
                               
                                 2 
                               
                               π 
                             
                             ⁢ 
                             
                               Δϕsin 
                               ⁡ 
                               
                                 ( 
                                 Δθ 
                                 ) 
                               
                             
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   P 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Next, the wafer is assumed to be subjected to overlay exposure with a spatial image of a phase distribution  56 B of  FIG. 13C , which is an inversion of the portions of phase 0 and the portions of phase π in the phase distribution  56 A of  FIG. 13B . In the phase distribution  56 B, the systematic phase error Δϕ is also added to the portions of phase π. The x-directional electric field E 2 (x) of the spatial image of the phase distribution  56 B is as follows.
 
 E   2 ( x )= a   0 −2 a   1  exp( i Δθ)cos(2π x/P )  (3F)
 
     The intensity I 2 (x) of the spatial image is expressed by the product of the electric field E 2 (x) of Expression (3F) and its complex conjugate as below. The second expression below is also obtained by ignoring the second-order and higher-order terms about Δϕ under the condition that Δϕ is an infinitesimal amount. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               4 
                               
                                 π 
                                 2 
                               
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     
                                       Δϕ 
                                       2 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                               · 
                               
                                 { 
                                 
                                   
                                     cos 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           4 
                                           ⁢ 
                                           π 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           x 
                                         
                                         P 
                                       
                                       ) 
                                     
                                   
                                   + 
                                   1 
                                 
                                 } 
                               
                             
                           
                           + 
                           
                             
                               
                                 2 
                               
                               π 
                             
                             ⁢ 
                             Δϕ 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     Δϕ 
                                     2 
                                   
                                   ⁢ 
                                   
                                     cos 
                                     ⁡ 
                                     
                                       ( 
                                       Δθ 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     Δθ 
                                     ) 
                                   
                                 
                               
                               } 
                             
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   P 
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               Δϕ 
                               2 
                             
                             16 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             = 
                             . 
                           
                           . 
                         
                         ⁢ 
                           
                         ⁢ 
                         
                           
                             
                               4 
                               
                                 π 
                                 2 
                               
                             
                             ⁢ 
                             
                               { 
                               
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         π 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         x 
                                       
                                       P 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 1 
                               
                               } 
                             
                           
                           + 
                           
                             
                               
                                 2 
                               
                               π 
                             
                             ⁢ 
                             
                               Δϕsin 
                               ⁡ 
                               
                                 ( 
                                 Δθ 
                                 ) 
                               
                             
                             ⁢ 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   P 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The second expression in this expression (7) is an inversion of the sign of the second term (the intensity dependent on the systematic error Δϕ) in the third expression in Expression (5). 
     An exposure dose distribution I ave  after the overlay operation of the exposure with the spatial image of the phase distribution  56 A and the exposure with the spatial image of the phase distribution  56 B is an average of an approximate value of the intensity I 1 (x) in Expression (5) and an approximate value of the intensity I 2 (x) in Expression (7) as below, in which the term dependent on the systematic error in the intensity I 1 (x) and the term dependent on the systematic error in the intensity I 2 (x) cancel out each other. 
     
       
         
           
             
               
                 
                   
                     I 
                     ave 
                   
                   = 
                   
                     
                       
                         
                           
                             I 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         + 
                         
                           
                             I 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                       
                       2 
                     
                     = 
                     
                       
                         4 
                         
                           π 
                           2 
                         
                       
                       ⁢ 
                       
                         { 
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   4 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   x 
                                 
                                 P 
                               
                               ) 
                             
                           
                           + 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     It is also seen from this expression that when there is the systematic error ΔZ of the height of the mirror elements  30  (phase error Δϕ) in the periodic phase distribution, the double exposure provides the spatial image without influence of the phase error Δϕ. 
     The below will describe a situation where the exposure with the spatial image of the first phase distribution  50 A in  FIG. 6A  and the exposure with the spatial image of the second phase distribution  50 B in  FIG. 6B  which is the inversion of the phase distribution  50 A as described above are implemented by scanning exposure. In the present embodiment, the Y-directional intensity distribution INT of the illumination light IL in the exposure region  26 B on the surface of the wafer W varies in a trapezoidal shape with the width SY 1  of slant portions at the both ends and the width SY 2  of a flat portion, as shown in  FIG. 14A . In  FIG. 14A , the horizontal axis represents Y-coordinates on the wafer W driven by the wafer stage WST in  FIG. 1 . During scanning exposure, for example, the wafer stage WST is scanned at a constant speed in the +Y-direction and every time an arbitrary exposed point WP on the surface of the wafer W arrives at a Y-directional point Yi (i=1, 2, 3, . . . ) in the exposure region  26 B, one pulse of illumination light IL is emitted from the illumination optical system ILS onto the spatial light modulator  28 , thereby to expose a region including the exposed point WP, with the spatial image of the phase distribution set in the spatial light modulator  28 . In this case, when a Y-directional moving amount of the wafer W for each pulse emission is defined as ΔY, i.e., when a distance between position Yi and position Y(i+1) is defined as ΔY, the positions Yi are located in respective partial regions resulting from division of the exposure region  26 B by width ΔY in the Y-direction. In synchronism with the Y-directional movement of the exposed point WP, the spatial images of the phase distributions  50 A,  50 B also move at the same speed in the Y-direction. 
     In this case, when it is assumed in the present embodiment that the wafer W is exposed with the spatial image IA of the first phase distribution  50 A upon arrival of the exposed point WP at a position Yj (j is an integer), the wafer W is exposed with the spatial image IB of the second phase distribution  50 B upon arrival of the exposed point WP at a next position Y(j+1). Namely, while the exposed point WP moves in the Y-direction, the wafer is exposed alternately with the spatial images IA and IB. In the example of  FIG. 14A , the wafer is exposed with the spatial image IA upon every arrival of the exposed point WP at the odd-numbered position Y 1 , Y 3 , . . . and exposed with the spatial image IB upon every arrival at the even-numbered position Y 2 , Y 4 , . . . . Furthermore, in a duration in which the exposed point WP passes through either of the slant portions in the width SY 1  at the both ends of the intensity distribution INT, the same number of times of exposures are carried out with the spatial image IA of the phase distribution  50 A and with the spatial image IB of the phase distribution  50 B; in a duration in which the exposed point WP passes through the flat portion in the width SY 2  in the center of the intensity distribution INT, the same number of times of exposures are also carried out with the spatial images IA and IB. A condition for this operation is that an even number of moving amounts ΔY of the wafer W between pulse emissions fall within each of the widths SY 1  and SY 2  as below.
 
 SY 1/Δ Y =even number,  SY 2/Δ Y =even number  (9)
 
     When the conditions of Expression (9) do not hold, the number of exposures with the spatial image IA and the number of exposures with the spatial image IB during the movement of the exposed point WP through the slant portion of the intensity distribution in the width SY 1  (or through the flat portion in the width SY 2 ) are different and the influence of the systematic error ΔZ of the mirror elements  30  is not completely cancelled out, raising a possibility of remnants of the systematic error ΔZ. 
     For satisfying the conditions of Expression (9), as shown in  FIG. 14B , the Y-directional movement amount of the phase distribution  50 A or  50 B per pulse emission is set to ΔY/β (β is the projection magnification of the projection optical system PL) in the array of mirror elements  30  in the spatial light modulator  28 . In  FIG. 14B , the Y-directional intensity distribution INT 1  of the illumination area  26 A with the illumination light IL is a distribution in which the width of the slant portions of the intensity at the both ends is SY 1 /β and the width of the flat portion of intensity in the center is SY 2 /β. From Expression (9), the Y-directional movement amount ΔY/β of the phase distribution  50 A or  50 B per pulse emission is the width SY 1 /β of the slant portions of the intensity distribution INT 1  divided by the even number. 
     When the first one-pulse exposure is carried out with the phase distribution  50 A being set in the array of mirror elements  30 , the next one-pulse exposure is carried out with the phase distribution  50 B being set at the position resulting from Y-directional movement of the first phase distribution  50 A by ΔY/β; thereafter, the inverted phase distribution  50 A (or  50 B) is set at the position resulting from Y-directional movement of the phase distribution  50 B (or  50 A) by ΔY/β to carry out the next one-pulse exposure, followed by repetitions of the foregoing operations. Since in the present embodiment the projection optical system PL is assumed to form an erect image, when the scanning direction of the wafer W is the −Y-direction, the phase distributions  50 A,  50 B also move in the −Y-direction. 
     The below will describe a configuration example of the entire modulation control unit  48  of the spatial light modulator  28  in  FIG. 1 , with reference to  FIG. 15 . In  FIG. 15 , the modulation control unit  48  is provided with a controller  64 , a memory  65  storing data of phase distribution, a shift register circuit section  61 , and a multiplexer section  66  for converting, for example, 64-bit phase data read from the memory  65 , into plural sets of parallel outputs and feeding the outputs to the shift register circuit section  61 . Since the shift register circuit section  61  and the multiplexer section  66  can be disposed on the base member  32  of the spatial light modulator  28 , the shift register circuit section  61  and the multiplexer section  66  are regarded as a part of the spatial light modulator  28  in the present embodiment. The mirror elements  30  in the spatial light modulator  28  are arranged in M columns in the X-direction and N rows in the Y-direction (cf.  FIG. 17A ). The shift register circuit section  61  is a section in which M columns of shift registers  61 - j  (j=1, 2, . . . , M) for driving N rows of mirror elements  30  in the spatial light modulator  28  as a whole are arranged in parallel. As an example, M is 16000 (=64×250) and N 2000. Each shift register  61 - j  is of a serial-input and parallel-output type to process N-bit phase data. 
     Each shift register  61 - j  is composed of connected circuit units  63  each of which consists of one flip-flop  60 A or the like, one flip-flop to transfer data in the reverse direction (not shown), and one selection circuit  62 A or the like to select an output signal from the flip-flops  60  or the like, as shown in  FIG. 2B . The controller  64  writes information of phase distribution from the main control system  40  in  FIG. 1  into the memory  65 . Furthermore, the controller  64  supplies to the memory  65  and each shift register  61 - j , clock pulses CKP, which are, for example, ns times (ns is an integer and, for example, ns=20) the frequency of emission trigger pulses TP supplied from the main control system  40 , to shift data of phase distribution for one line of mirror elements  30  (M elements) sequentially read out of the memory  65 , in each shift register  61 - j . When the frequency of pulse emissions from the light source  2  is, for example, 2 MHz and the integer ns, e.g.,  20 , the frequency of clock pulses CKP is 40 MHz. Furthermore, the controller  64  supplies the selection signal SELS the level of which is inverted every emission trigger pulse TP, to the selection circuit  62 A or the like in each circuit unit  63 . This causes the phase distribution set in the array of mirror elements  30  to be inverted while shifting in the Y-direction, every pulse emission of the illumination light IL. 
     The below will describe an example of operation to perform scanning exposure of the wafer W while controlling the phase distribution set in the array of mirror elements  30  in the spatial light modulator  28 , in the exposure apparatus EX of the present embodiment, with reference to  FIG. 16 . It is assumed herein that the spatial image of the phase distribution  50 A in  FIG. 6A  and the spatial image of the phase distribution  50 B in  FIG. 6B  as the inversion of the phase distribution  50 A are alternately transferred by exposure in a part of each shot area on the wafer W. It is assumed for convenience&#39; sake of description that the wafer W is scanned in the −Y-direction and the shift register circuit section  61  in  FIG. 15  sequentially moves the phase data in the −Y-direction. 
     First, in step  102  in  FIG. 16 , the main control system  40  supplies the data of the phase distribution  50 A for the array of mirror elements  30  in the spatial light modulator (SLM)  28  corresponding to the spatial image to be transferred by exposure on the wafer W, to the controller  64  of the modulation control unit  48 . The controller  64  writes the data into the memory  65 . In next step  104 , the wafer W coated with a photoresist is loaded on the wafer stage WST and in next step  106 , the scanning in the −Y-direction of the wafer W is started by the wafer stage WST. In next step  108 , the controller  64  sets the selection signal SELS to the level of selecting the phase distribution  50 A (non-inverted phase distribution). 
     In next step  110 , the controller  64  outputs data of phases (0 or π) for one row of mirror elements  30  arranged in the X-direction, which is read out of the memory  65 , to each shift register  61 - j  (j=1, 2, . . . , M). In next step  112 , the controller  64  outputs one clock pulse CKP to advance the data to the subsequent-stage flip-flop in each shift register  61 - j  in the shift register circuit section  61 . Thereafter, it is determined in step  114  whether the phase data is shifted by ns rows (ns is, for example, 20) and, when the shift of ns rows is not achieved yet, the operation returns to step  110  to repeat the operation of steps  110  and  112 . 
     Thereafter, when the phase data is shifted by ns rows, the operation transfers to step  116  and the main control system  40  supplies the emission trigger pulse TP to the power unit  42  to make the light source  2  emit one pulse to illuminate the illumination area  26 A including the array of mirror elements  30  in the spatial light modulator  28 , as shown in  FIG. 17A . At this time, a partial phase distribution  50 A 1  of the phase distribution  50 A is set in a first region  57 A of ns rows from the +Y-direction in the array of mirror elements  30  and the wafer W is exposed with a spatial image of the phase distribution  50 A 1 . It is noted that in  FIG. 17A  and others, the ns rows are illustrated as seven rows and the number of mirror elements  30  in the array is illustrated as being much smaller than the actual number. It is determined in next step  118  whether one scanning exposure process is completed. When the scanning exposure is continued, the operation moves to step  120  in which the controller  64  sets the selection signal SELS to the level of selecting the phase distribution (the phase distribution  50 B herein) opposite to the preceding one. After that, the operation returns to step  110 . 
     In steps  110  to  114  after execution of this step  120 , the operation of outputting the phase data to the first-stage flip-flop in each shift register  61 - j  and shifting the phase data in the shift register is also repeated ns times. In step  116  after that, one pulse of illumination light IL is emitted to expose the wafer W with spatial images of partial phase distributions  50 B 2 ,  50 B 1  of the inverted phase distribution  50 B set in the first region  57 A and second region  57 B of ns rows from the +Y-direction on the array of mirror elements  30 , as shown in  FIG. 17B . In this case, the phase distribution  50 B 1  in the second region  57 B is a distribution resulting from inversion of the phases of the phase distribution  50 A 1  in the first region  57 A in  FIG. 17A . 
     By the next operation of steps  120 , and  110  to  116 , the wafer W is exposed with spatial images of partial phase distributions  50 A 3  to  50 A 1  of the phase distribution  50 A set in the first region  57 A to third region  57 C of ns rows from the +Y-direction on the array of mirror elements  30 , as shown in  FIG. 17C . On this occasion, the phase distribution  50 A being the phase distribution opposite to the preceding one is selected in step  120 . By the next operation of steps  120 , and  110  to  116 , the wafer W is exposed with spatial images of partial phase distributions  50 B 4  to  50 B 1  of the inverted phase distribution  50 B set in the first region  57 A to fourth region  57 D of ns rows from the +Y-direction on the array of mirror elements  30 , as shown in  FIG. 18A . However, a part of the fourth region  57 D is located outside the array of mirror elements  30  and the data as an inversion of the phase distribution in a region  58 A at an end in  FIG. 17C  is not used in  FIG. 18A . Similarly, by the next operation of steps  120 , and  110  to  116 , the wafer W is exposed with spatial images of partial phase distributions  50 A 5  to  50 A 2  of the phase distribution  50 A set in the first region  57 A to fourth region  57 D on the array of mirror elements  30 , as shown in  FIG. 18B . In this case, the data as an inversion of the phase distribution in a region  58 B at an end in  FIG. 18A  is not used, either. 
     In this manner, the wafer W is alternately exposed by scanning exposure with the spatial images of the phase distributions  50 A,  50 B. After completion of the scanning exposure in step  118 , the operation moves to step  122  to halt the wafer stage WST. Thereafter, for example, the wafer stage WST is stepwise moved in the X-direction and, with change of the scanning direction to the opposite direction, the operation of steps  106  to  122  is then repeated. Since on this occasion the present embodiment involves alternately performing the scanning exposure with the phase distributions  50 A,  50 B, even if there is the systematic error ΔZ of the height of the reflective surfaces of the mirror elements  30 , the exposure can be carried out with high accuracy by the maskless method while suppressing the influence of the error. 
     The effects and others of the present embodiment are as described below. 
     (1) The exposure apparatus EX of the present embodiment is provided with the spatial light modulator  28 . The driving method of the spatial light modulator  28  by the modulation control unit  48  is the method of driving the spatial light modulator  28  with the array of mirror elements  30  (optical elements) each of which can guide the illumination light IL to the projection optical system PL. This driving method includes the step (this step corresponds to steps  110  to  114  after execution of step  108 ) of setting, in the array of mirror elements  30 , the mirror elements  30 A in the first state for guiding reflected light of incident light without change in phase (in the first phase δ 1  of 0) to the projection optical system PL and the mirror elements  30 B in the second state for guiding reflected light of incident light with change in phase by the second phase δ 2  (δ 2  is approximately 180° where M is 0) different approximately 180° from the first phase δ 1  to the projection optical system PL, to the first arrangement with the phase distribution  50 A. Furthermore, the driving method includes the step (this step corresponds to steps  110  to  114  after an odd number of times of execution of step  120 ) of setting, in the array of mirror elements  30 , the mirror elements  30 A and the mirror elements  30 B to the second arrangement with the phase distribution  50 B which is the inversion of the phase distribution  50 A. 
     The mirror elements  30 A in the first state may guide the reflected light with the phase changed by the first phase δ 1  of an arbitrary value relative to the phase of incident light to the projection optical system PL. 
     The spatial light modulator  28  has: the array of mirror elements  30  each of which is to be illuminated with light; the flip-flops  60 A,  60 B (first circuits) which output the first signal to set the state of the mirror elements  30  to the first state (the state of the mirror elements  30 A) or the second signal to set the state of the mirror elements  30  to the second state (the state of the mirror elements  30 B); the multiplexer section  66  (control circuit) which controls the output signals from the shift registers  60 A,  60 B, in order to set, in the first region which is at least a part of the array of mirror elements  30 , the arrangement of the mirror elements  30 A in the first state and the mirror elements  30 B in the second state to the first arrangement; and the selection circuits  62 A,  62 B (second circuits) which invert the output signals from the flip-flops  60 A,  60 B, in order to set, in the second region which is at least a part of the array of mirror elements  30 , the arrangement of the mirror elements  30 A in the first state and the mirror elements  30 B in the second state to the second arrangement resulting from the inversion of the optical elements in the first state or in the second state in the first arrangement into the second state or into the first state, respectively. 
     The exposure apparatus EX is the exposure apparatus for exposing the wafer W (substrate) with the illumination light IL (exposure light) through the projection optical system PL, which has: the light source  2  and the illumination optical system ILS for emitting the illumination light; the spatial light modulator  28  arranged on the object plane side of the projection optical system PL and having the array of mirror elements  30  (optical elements) each of which can be controlled so as to guide the illumination light IL to the projection optical system PL; and the main control system  40  and the modulation control unit  48  (control device) which control the light source  2  and the spatial light modulator  28 . The main control system  40  and modulation control unit  48  set, in the first region which is at least a part of the array of mirror elements  30 , the arrangement of the mirror elements  30 A in the first state and the mirror elements  30 B in the second state to the first arrangement (the phase distribution  50 A), in accordance with the spatial image formed on the wafer W through the projection optical system PL, implement of exposure of the wafer W, set, in the second region which is at least a part of the array of mirror elements  30 , the arrangement of the mirror elements  30 A and  30 B to the second arrangement (the phase distribution  50 B) which is the inversion of the first arrangement, and implement overlay exposure of the wafer W. 
     The present embodiment includes setting the mirror elements  30 A,  30 B to the first arrangement in the first region of the array of mirror elements  30  and setting the mirror elements  30 A,  30 B to the second arrangement which is the inversion of the first arrangement in the second region of the array of mirror elements  30 , and the systematic error ΔZ of the height of the reflective surfaces occurring in the mirror elements  30  in the first arrangement has the sign opposite to that of the systematic error (−ΔZ) occurring in the mirror elements  30  in the second arrangement. For this reason, the influence of the systematic error ΔZ is alleviated when the wafer W is exposed by overlay exposure with the light from the mirror elements  30  in the first arrangement and with the light from the mirror elements  30  in the second arrangement. Furthermore, when there is light reflected by the gap regions  34   a  between the mirror elements  30 , the influence of the reflected light from the gap regions  34   a  on the spatial image is also alleviated. 
     (2) Since the spatial light modulator  28  has the mirror elements  30  (reflective elements) as optical elements, it has high efficiency of utilization of the illumination light IL. It is also possible, however, to use a transmission type spatial light modulator each of individual optical elements of which changes the phase of transmitted light by predetermined ϕ 1  or approximately (ϕ 1 +180°, in place of the spatial light modulator  28 . Such optical elements applicable herein can be electro-optic elements which vary the refractive index by voltage, or liquid crystal cells or the like. 
     (3) The exposure method by the exposure apparatus EX according to the present embodiment is the exposure method of exposing the wafer W (substrate) with the illumination light IL (exposure light) via the spatial light modulator  28  with the array of mirror elements  30  and via the projection optical system P 1 , which includes the steps  110  to  114  of setting the arrangement of states of the mirror elements  30  by the aforementioned driving method of the spatial light modulator  28 , and the step  116  of implementing overlay exposure of the wafer W with the illumination light IL from the illumination area  26 A including the first region and the second region of the array of mirror elements  30  via the projection optical system PL, in the state in which the mirror elements  30  are set in the first arrangement and in the state in which the mirror elements  30  are set in the second arrangement as the inversion of the first arrangement. 
     By the exposure method or the foregoing exposure apparatus EX, various patterns can be formed with high accuracy by the maskless method while alleviating the influence of the systematic error of the mirror elements  30  and/or the influence of the reflected light from the gap regions  34   a  between the mirror elements  30 . 
     Each mirror element  30  in the spatial light modulator  28  may be configured so that it can be set in a plurality of states including a third state and other states except for the first state and the second state. 
     (4) The illumination light IL from the illumination optical system ILS is obliquely incident approximately at the angle of incidence α to the mirror elements  30  and the reflected light from the mirror elements  30  is incident into the projection optical system PL so as to intersect with the optical axis AXW of the projection optical system PL. Therefore, the projection optical system PL is non-telecentric on the object plane side, and thus the whole of reflected light from the spatial light modulator  28  can be applied onto the wafer W through the projection optical system PL, achieving high efficiency of utilization of the illumination light IL. Furthermore, the polarization state of the illumination light IL set by the polarization control optical system  6  can be accurately reproduced on the surface of the wafer W. 
     (5) The mirror elements  30  are disposed in the rectangular region whose longitudinal direction is the X-direction, the exposure apparatus EX has the wafer stage WST (substrate stage) for moving the wafer W in the scanning direction corresponding to the Y-direction perpendicular to the X-direction on the image plane of the projection optical system P 1 , and the modulation control unit  48  moves the patterns (phase distribution) formed by the mirror elements  30 , in the Y-direction, according to the movement of the wafer W by the wafer stage WST. This allows efficient exposure over the entire surface of the wafer W. 
     The aforementioned embodiment can be modified as in modifications below. 
     First, instead of alternately setting the phase distributions  50 A,  50 B by the array of mirror elements  30  in one spatial light modulator  28  as in the present embodiment, it is also possible to adopt a method of arranging two spatial light modulators  28 A,  28 B adjacent to each other in the Y-direction on the object plane of the projection optical system PL, setting only the first phase distribution  50 A or the like in one spatial light modulator  28 A, and setting only the second phase distribution  50 B or the like in the other spatial light modulator  28 B, as shown in a modification example of  FIG. 14C . In this modification example, the intensity distribution INT 1  of the illumination light IL is set in the trapezoidal shape in the Y-direction in each of the spatial light modulators  28 A,  28 B. Moreover, the phase distributions  50 A,  50 B or the like move in the Y-direction every pulse emission in each of the spatial light modulators  28 A,  28 B. Furthermore, spatial light modulators may be arranged as many as an even number larger than 2 so that the number of spatial light modulators set in the first phase distribution  50 A becomes equal to the number of spatial light modulators set in the second phase distribution  50 B. For example, the number of spatial light modulators may be 2, 4, 6, or an even number larger than it. 
     Likewise, it is also possible to adopt a method of dividing one spatial light modulator into two regions, first half and second half, setting only the first phase distribution  50 A or the like in the first half region, and setting only the second phase distribution  50 B or the like in the second half region. In this modification example, the intensity distribution of the illumination light has a shape of two trapezoids coupled in the Y-direction corresponding to the first half and the second half of the spatial light modulator. Furthermore, one spatial light modulator may be divided into equal regions as many as an even number equal to or larger than two, and either of the first phase distribution  50 A and the second phase distribution  50 B is set in each region so that the first phase distributions  50 A and the second phase distributions  50 B can exist in the same number in the entire region of the spatial light modulator. In this case, the intensity distribution of the illumination light has a shape of trapezoids coupled in the Y-direction as many as the same number as the number of divided regions. 
     Furthermore, another possible modification is as follows: the array of mirror elements  30  in one spatial light modulator  28  is illuminated with the illumination light IL in an intensity distribution of trapezoidal shapes at two locations as in  FIG. 14C , and the first phase distribution  50 A or the like and the second phase distribution  50 B or the like are set in respective regions of the intensity distribution of the trapezoidal shapes at the two locations. 
     Next, the influence of the reflected light from the gap regions  34   a  will be discussed based on simulations for the case where the reflectance of the gap regions  34   a  in the array of mirror elements  30  in the spatial light modulator  28  in  FIG. 7A  is high. 
     First, let us assume that, as shown in  FIGS. 19A and 20A , the pitches px, py of the arrangement of the array of mirror elements  30  in the spatial light modulator  28  are 8 μm, the widths cx, cy of the gap regions  34   a  are 1 μm, and the reflectance Rc of the gap regions  34   a  is 100%. It is also assumed that when each mirror element  30  is set in the second state (phase π), the systematic error ΔZ in the distance between its reflective surface and the reference plane A 1  in  FIG. 2B  is 2 nm in  FIG. 19A  and 4 nm in  FIG. 20A . Then, simulations were conducted to obtain shape changes of resist patterns (changes with respect to targets  38 A,  38 B) formed by sequentially setting the phase distribution of the array of mirror elements  30  in the spatial light modulator  28  to the first phase distribution  50 A in  FIG. 7A  and the second phase distribution  50 B in  FIG. 7C  and doubly exposing the wafer W with their spatial images by the projection optical system PL, for each of cases where the gap phase δ 3  as the change amount of the phase of the reflected light from the gap regions  34   a  in  FIG. 19A  or  FIG. 20A  was set to 0°, 90°, 180°, and 270°.  FIGS. 19B to 19E  and  FIGS. 20B  to  20 E show the simulation results in the cases where the systematic error ΔZ is 2 nm and 4 nm, respectively. The slice level of each pattern in  FIGS. 19 and 20  was determined so that the maximum of the X-directional widths became approximately equal to the target when the reflectance Rc of the gap regions  34   a  was 100% and the systematic error ΔZ 0 nm. This slice level is independent of the gap phase δ 3  and thus is the same value. 
       FIG. 19B  shows patterns L 10 , R 10  with the best focus and patterns L 10 P, R 10 P, L 10 M, R 10 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 0°.  FIG. 19C  shows patterns L 11 , R 11  with the best focus and patterns L 11 P, R 11 P, L 11 M, R 11 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 90°.  FIG. 19D  shows patterns L 12 , R 12  with the best focus and patterns L 12 P, R 12 P, L 12 M, R 12 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 180°.  FIG. 19E  shows patterns L 13 , R 13  with the best focus and patterns L 13 P, R 13 P, L 13 M, R 13 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 270°. It is seen from  FIGS. 19B  to E that in the case of the systematic error ΔZ being 2 nm, the patterns close to the targets  38 A,  38 B are obtained with the best focus and with the defocuses when the gap phase δ 3  is 0° or 180°. 
       FIG. 20B  shows patterns L 14 , R 14  with the best focus and patterns L 14 P, R 14 P, L 14 M, R 14 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 0°.  FIG. 20C  shows patterns L 15 , R 15  with the best focus and patterns LISP, R 15 P, L 15 M, R 15 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 90°.  FIG. 20D  shows patterns L 16 , R 16  with the best focus and patterns L 16 P, R 16 P, L 16 M, R 16 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 180°.  FIG. 20E  shows patterns L 17 , R 17  with the best focus and patterns L 17 P, R 17 P, L 17 M, R 17 M with the defocuses of ±40 nm in the case of the gap phase δ 3  being 270°. It is seen from  FIGS. 20B  to E that in the case of the systematic error ΔZ being 4 nm, the patterns close to the targets  38 A,  38 B are obtained with the best focus and with the defocuses when the gap phase δ 3  is 0° or 180°. 
     Data sequences C 1 , C 2 , C 3 , and C 4  in  FIG. 21  are plots of change amounts ΔCD (%) of the line width of resist patterns from the line width (CD) of targets obtained by simulations with variations of the systematic error ΔZ (nm), in the cases where the phase of the reflected light from the gap regions  34   a  (gap phase δ 3 ) is 0°, 90°, 180°, and 270°, respectively, as in the cases of  FIGS. 19B  to E. In each of the data sequences C 1  to C 4 , the change amount ΔCD-L of the line width of the left pattern and the change amount ΔCD-R of the line width of the right pattern are superimposed on each other. It is seen from  FIG. 21  that in the case of the gap phase δ 3  being 0° or 180°, the change amount ΔCD of the line width is small, independent of the systematic error ΔZ. The reason why there is the difference between the change amounts ΔCD of the line width in the cases of the gap phase δ 3  being 0° and 180° is that the systematic error ΔZ is given to only the mirror elements  30  in the second state (phase π). 
     The data sequence in  FIG. 22  is plots of change amounts ΔCD (%) of the line width of resist patterns obtained by the same simulations as in  FIGS. 19B  to E with variations of the gap phase δ 3  at 30° intervals and with the systematic error ΔZ of 2 nm. It is also seen from  FIG. 22  that ΔCD is close to 0 at the gap phase δ 3  of 0° or 180°, so as to allow high-accuracy exposure of a pattern as an object. 
     Next, modification examples of the modulation control unit  48  in  FIG. 1  in the above embodiment will be described with reference to  FIGS. 23 to 25 .  FIG. 23  shows a part of the modulation control unit  48 A of the first modification example. In  FIG. 23 , the modulation control unit  48 A has: a shift register section  70 S composed of a large number of connected flip-flops  71  (three of which are shown in  FIG. 23 ) to which the clock pulses CKP and phase data Data are supplied; a memory section  70 M which holds data D 1 , D 2 , D 3  output from the shift resister section  70 S, in synchronism with a timing pulse Word(W); a 0-π inversion section  70 R which outputs signals M 1 , M 2 , M 3  obtained by inversion of the data SR 1 , SR 2 , SR 3  held in the memory section  70 M in synchronism with an inversion pulse Word(R), to terminals  75 A,  75 B,  75 C; and the controller  64  and memory  65  in  FIG. 15 . The signals at the terminals  75 A,  75 B are supplied, for example, to the electrodes  36 A for driving the mirror elements  30  in  FIG. 2B . The signal at the other terminal  75 C is also supplied to the electrode (not shown) for driving the other mirror element  30 . The clock pulses CKP, write pulse Word(W), and inversion pulse Word(R) are output from the controller  64  in  FIG. 15  and, the phase data Data from the memory  65  in  FIG. 15 . 
     The memory section  70 M is provided with three FETs  72  to which the respective data D 1  to D 3  output from the shift register section  70 S are supplied and to gates of which the write pulse, pulse Word(W), is supplied, and three sets of two ring-coupled inverters  73 A,  73 B, and each of respective outputs of the FETs  72  is supplied to an interconnection of inverters  73 A,  73 B. The 0-π inversion section  70 R is provided with FETs  74 A and inverters  73 C to which the respective data SR 1  to SR 3  written in the memory section  70 M in synchronism with the write pulse Word(W) are supplied, and is provided with FETs  74 B which connect outputs of the inverters  73 C to the terminals  75 A to  75 C. Outputs of the FETs  74 A are also connected to the terminals  75 A to  75 C and the inversion pulse Word(R) is supplied to gates of the FETs  74 A and to input-inverting gates of the FETs  74 B. 
       FIG. 24  shows an example of timing from the clock pulses CKP to the data SR 3  in  FIG. 23 . In  FIG. 24 , a predetermined time delay td is set for the write pulse Word(W) for holding the phase data and for the emission of illumination light IL (laser light) with respect to a clock pulse CKP. In the modulation control unit  48 A, the phase distribution of the array of mirror elements  30  in the spatial light modulator  28  can be readily inverted on a periodic basis by the aforementioned timing. 
     Next,  FIG. 25  shows a part of the modulation control unit  48 B of the second modification example. In  FIG. 25 , portions corresponding to those in  FIG. 23  are denoted by the same reference signs, and the detailed description thereof is omitted herein. In  FIG. 25 , the modulation control unit  48 B is provided with a shift register section  70 SA composed of a large number of connected flip-flops  71 A to which the clock pulses CKP and phase data Data are supplied; a 0-π inversion section  70 RA to which data output from the shift register section  70 SA and signal Word(W 2 ) for writing of data into subsequent-stage memory section  70 MA and for inversion of data are supplied; and the memory section  70 MA which holds the phase data supplied from the 0-π inversion section  70 RA. The phase data held in the memory section  70 MA is output (or read out) to the terminals  75 A to  75 C in synchronism with a readout signal Word(W 2 ). The signal Word(W 2 ) is a signal having two states, e.g., a low level to maintain the phase and a high level to invert the phase. 
     The 0-π inversion section  70 RA has FETs  74 A and  74 B to which the respective data and inverted data output from the flip-flops  71 A are supplied, the signal Word(W 2 ) is supplied to gates of the FETs  74 A and to input-inverting gates of the FETs  74 B, and data at connected output parts of the FETs  74 A and  74 B are supplied to the memory section  70 MA. The memory section  70 MA is provided with three sets of two ring-coupled inverters  73 A,  73 B to which the data from the 0-π inversion section  70 RA are supplied, and is provided with FETs  72 , and the FETs  72  output (read out) data at interconnections of the inverters  73 A,  73 B to the terminals  75 A to  75 C in synchronism with the readout signal Word(R 2 ). The other configuration is the same as in the first modification example. This modulation control unit  48 B can readily achieve the periodic inversion of the phase distributions in the array of mirror elements  30  in the spatial light modulator  28  as the modulation control unit  48 A can, though the 0-π inversion section  70 RA and the memory section  70 MA are interchanged. 
     Next, the foregoing embodiment involves the scanning exposure of the wafer W with continuous movement of the wafer W. Besides it, the exposure may be carried out as follows: as shown in  FIG. 3B , each of partial regions constituting each shot area (e.g., SA 22 ) on the wafer W is divided into a plurality of sub-regions SB 1  to SB 5  or the like in the Y-direction; when the sub-region SB 1  or the like comes in the exposure region  26 B of the projection optical system PL, the array of mirror elements  30  in the spatial light modulator  28  is set in the first phase distribution (the phase distribution  50 A or the like) and exposures are executed as many as a predetermined number of pulses; then the array of mirror elements  30  is set in the second phase distribution (the phase distribution  50 B or the like) and exposures are executed as many as the predetermined number of pulses, so as to expose the sub-region SB 1  or the like. In this case, the exposure region (first region) of the first phase distribution is the same as the exposure region (second region) of the second phase distribution. 
     After this, the wafer W is stepwise moved in the Y-direction and when the next sub-region SB 2  or the like reaches the exposure region  26 B, the exposure is carried out in the same manner in the sub-region SB 2  or the like. This method is substantially the step-and-repeat method, but the sub-regions SB 1  to SB 5  or the like are exposed with mutually different patterns. In this case, overlay exposure is implemented in joint portions between the sub-regions. 
     Next, the above embodiment uses the projection optical system PL non-telecentric on the object side. Besides it, it is also possible to use a projection optical system PLA bi-telecentric on the object side and on the image side, as in an exposure apparatus EXA in a modification example in  FIG. 26 . In  FIG. 26 , the exposure apparatus EXA is provided with an illumination optical system ILSA which emits s-polarized illumination light IL approximately in the +Y-direction, a polarization beam splitter  71  which reflects the illumination light IL into the +Z-direction, a quarter wave plate  72  which converts the illumination light IL from the polarization beam splitter  71  into circularly polarized light, the spatial light modulator  28  with the two-dimensional array of many mirror elements  30  for reflecting the circularly polarized illumination light IL into the −Z-direction, and the projection optical system PLA which receives the illumination light IL transmitted by the quarter wave plate  72  and the polarization beam splitter  71  after reflected by the mirror elements  30  and which projects a spatial image (pattern) onto the exposure region  26 B on the surface of the wafer W. The illumination optical system ILSA is an optical system obtained by excluding the mirrors  8 B,  8 C from the illumination optical system ILS in  FIG. 1 . The configuration and action of the spatial light modulator  28  are the same as those in the embodiment in  FIG. 1  and the modification examples thereof. 
     In this modification example, however, the illumination light IL is incident approximately at the angle of incidence of 0 to the mirror elements  30  in the spatial light modulator  28 . For this reason, in the case of small σ illumination, the reflected light from the mirror elements  30  is incident into the projection optical system PLA nearly in parallel with the optical axis AX of the projection optical system PLA. Since this exposure apparatus EXA of the second modification example can use the bi-telecentric projection optical system PLA, the configuration of the exposure apparatus can be simplified. 
     If the efficiency of utilization of the illumination light IL is allowed to decrease to half, an ordinary beam splitter may be used instead of the polarization beam splitter  71 , without use of the quarter wave plate  72 . In this case, polarized illumination is available. 
     It is also possible to use a rod type integrator as an internal reflection type optical integrator, in place of the microlens array  16  which is the wavefront division type integrator in  FIG. 1 . 
     The aforementioned embodiment and modification examples used the spatial light modulator to dynamically change the phase of light passing the optical elements, but it is also possible to use the spatial light modulator to provide a fixed phase difference to the light passing the optical elements. The spatial light modulator of this kind is, for example, disclosed in U.S. Pat. No. 7,512,926. The spatial light modulator disclosed therein is of the transmission type, but it may be modified into the reflection type. 
     In this case, two spatial light modulators are prepared, a first spatial light modulator (first mask) in which the phases of optical elements in the spatial light modulator are in the first phase distribution and a second spatial light modulator (second mask) in which the phases of optical elements in the spatial light modulator are in the second phase distribution as an inversion of the first phase distribution, and the wafer (substrate) is doubly exposed with the first mask and the second mask. 
     In other words, this exposure method is to expose at least a partial region on a substrate with the exposure light via the first spatial light modulator with the array of optical elements and via the projection optical system and to expose at least the partial region on the substrate with the exposure light via the second spatial light modulator with the array of optical elements and via the projection optical system. In this method, the arrangement of the optical elements in the first state for letting incident light pass as light with the same phase as that of the incident light or with a phase different by the first phase from that of the incident light and the optical elements in the second state for letting incident light pass as light with a phase different by the second phase different about 180° from the first phase is set to the first arrangement in the first region which is at least a part of the array of optical elements in the first spatial light modulator. In the second region which is at least a part of the array of optical elements in the second spatial light modulator, corresponding to the first region, the arrangement of the optical elements in the first state for letting incident light pass as light with the same phase as that of the incident light or with a phase different by the first phase from that of the incident light and the optical elements in the second state for letting incident light pass as light with a phase different by the second phase different about 180° from the first phase is set to the second arrangement. At this time, the arrangement of the optical elements in the first state in the first arrangement corresponds to the arrangement of the optical elements in the second state in the second arrangement, and the arrangement of the optical elements in the second state in the first arrangement corresponds to the arrangement of the optical elements in the first state in the second arrangement. 
     This exposure method can alleviate adverse influence caused by systematic phase error, if present, which is, for example, due to errors of etching amounts of mask substrate glass in manufacture of the first mask and the second mask. If there is light passing between the optical elements, adverse influence thereof can also be alleviated. 
     In manufacture of electronic devices (or microdevices), the electronic devices are manufactured, as shown in  FIG. 27 , through a step  221  of performing design of functionality and performance of the electronic devices, a step  222  of storing pattern data of masks based on this design step, into the main control system of the exposure apparatus EX in the embodiment, a step  223  of producing a substrate (wafer) as a base material of the devices and coat the substrate with a resist, a substrate processing step  224  including a step of exposing the substrate (photosensitive substrate) with the spatial images of the phase distributions generated in the spatial light modulator  28  by the aforementioned exposure apparatus EX (or the exposure method), a step of developing the exposed substrate, and heating (curing) and etching steps of the developed substrate, a device assembly step (including processing steps such as a dicing step, a bonding step, a packaging step, and so on)  225 , an inspection step  226 , and so on. 
     This device manufacturing method includes the step of exposing the wafer W with the use of the exposure apparatus (or the exposure method) of the above embodiment, and the step of processing the exposed wafer W (step  224 ). Therefore, the electronic devices can be manufactured with high accuracy. 
     The present invention is not limited to the application to semiconductor device manufacturing processes, but the present invention is also widely applicable, for example, to manufacturing processes of liquid crystal display devices, plasma displays, and so on and to manufacturing processes of various devices (electronic devices) such as imaging devices (CMOS type, CCD, etc.), micromachines, MEMS (Microelectromechanical Systems), thin film magnetic heads, and DNA chips. 
     The present invention is not limited to the above embodiments, but can be realized in various configurations within the scope not departing from the spirit and scope of the present invention. The disclosures in the foregoing Publications, International Publication, U.S. Patent, or U.S. Pat. Published Application cited in the present specification are incorporated as part of the description of the present specification. The entire disclosure of Japanese Patent Application No. 2010-277530 filed on Dec. 13, 2010, including the specification, the scope of claims, the drawings, and the abstract, is incorporated herein by reference in its entirety. 
     REFERENCE SIGNS LIST 
     EX exposure apparatus; ILS illumination optical system; PL projection optical system; W wafer;  28  spatial light modulator;  30  mirror elements;  40  main control system;  48  modulation control unit;  50 A,  53 A phase distribution;  50 B,  53 B inverted phase distribution;  60 A,  60 B flip-flops;  62 A,  62 B selection circuits.