Abstract:
An angle measuring interferometer comprises a source (10) which emits a light beam containing two linear orthogonally polarized components; means, such as a tilted shear plate (16) or a beamsplitter/beam folder assembly (116, 116A) for converting the input beam into two separated, parallel, orthogonally polarized beams; a half-wave retardation plate (29A, 29) located in one of the separated beams for converting the two separated parallel orthogonally polarized beams into two separated parallel beams with the same polarization; means including a polarizing beamsplitter (44), for causing each of the separated parallel beams with the same polarization to be reflected once by each of two plane mirrors (71, 70) to produce two parallel output beams with the same polarization; a half-wave retardation plate (29B, 29) located in one of the separated parallel output beams, for converting the two separated parallel output beams of the same polarization into two separated parallel output beams with orthogonal polarization, with means, such as the tilted shear plate (16) or the beamsplitter/beam folder assembly (116, 116B), converting the two separated parallel orthogonally polarized output beams into a single output beam in which the phase difference, &#34;δ&#34;, between the two polarization components of the single output beam is directly proportional to the angle, &#34;θ&#34;, between the two plane mirrors (70, 71); a polarizer (81) for mixing the orthogonal components of the output beam; a photoelectric detector (83) to produce the measurement signal; and an electronic module (90) to indicate the phase difference, &#34;Δδ&#34;, which is directly proportional to the changes in the angular orientation, &#34;Δθ&#34;, between the two plane mirrors (70, 71).

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of my copending U.S. patent application entitled &#34;Angle Measuring Interferometer,&#34; filed Mar. 28, 1986, and bearing U.S. Ser. No. 845,926, the contents of which are specifically incorporated by reference herein in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to apparatus for the measurement of changes in angular orientation between two plane mirrors. More particularly, the invention relates to optical apparatus which is useful for high accuracy angle metrology using interferometry. 
     2. The Prior Art 
     High accuracy displacement and angle measurements are required in the machine tool industry and in the semiconductor fabrication industry. Displacement is commonly measured with an interferometer. Angles are commonly measured with either an interferometer or an autocollimator. 
     While there are numerous interferometer configurations which can be used to measure changes in angular orientation between two plane mirrors, none provides a high speed electrical output which is insensitive to changes in the displacement between the two mirrors. In conventional interferometers, changes in angular orientation between two mirrors manifests itself, in general, as a change in fringe spacing and a rotation of the fringe pattern while changes in the displacement between the two mirrors manifests itself as a translation of the fringes. Thus, it takes rather complex, time consuming processing to separate these effects in order to extract the desired angular information. Therefore, for high accuracy angular measurement of precision, high speed X-Y stages used in microlithography, the prior art interferometers are not used. 
     An adaption of a displacement interferometer has been used to make angular measurements, see for example R. R. Baldwin, L. E. Truhe, and D. C. Woodruff, &#34;Laser Optical Components for Machine Tool and Other Calibration,&#34; Hewlett-Packard Journal, pp. 14-16, April 1983. However, this apparatus measures the changes in angular orientation of a pair of retroreflectors, not plane mirrors. Thus, it measures changes in angular orientation of a part which can be displaced in only one dimension, i.e., displacements parallel to the direction of the incident laser beams. Therefore, this apparatus is also not useful for the high accuracy angular measurements of precision X-Y stages. 
     Autocollimators provide many of the desired characteristics, see for example D. Malacara, Optical Shop Testing, p. 467, John Wiley &amp; Sons (1978). However, for high accuracy measurements, interferometers are preferred because their measurements are based directly on a stable, fixed, built-in measurement unit, i.e., the wavelength of light. 
     The present invention retains the preferred chacteristics of both the autocollimator and the interferometer while avoiding the serious limitations of prior art apparatus. In the present invention, the angular measurement is insensitive to not one but rather to three dimensional displacements of the plane mirrors, and the measurement is interferometric so that it is based on the wavelength of light. The improvements of the present invention thusly overcome the disadvantages of the prior art and allow the high accuracy, i.e., to a small fraction of an arc second, angular measurement required for precision, high speed X-Y stages. 
     SUMMARY OF THE INVENTION 
     In accordance with the instant invention, I provide an angle measuring interferometer system capable of measuring accurately changes in the angular orientation between two plane mirrors comprising: (1) a source of an input beam with two linear orthogonally polarized components which may or may not be of the same optical frequency; (2) means, most preferably a tilted shear plate with regions of antireflection and polarizing coatings, or a beamsplitter/beam folder assembly with regions of antireflection and polarizing coatings, for converting said input beam into two separated, parallel, orthogonally polarized beams; (3) means, most preferably a half-wave retardation plate, located in one of said separated beams, for converting said two separated, parallel, orthogonally polarized beams into two separated, parallel, beams with the same polarization and frequency difference; (4) means, most preferably a polarizing beamsplitter, quarter-wave retardation plate, and retroreflector, for causing each of said separated parallel beams with the same polarization to be reflected once by each of two plane mirrors to produce two parallel output beams with the same polarization; (5) means, most preferably a half-wave retardation plate, located in one of said separated, parallel output beams for converting said two separated, parallel output beams of the same polarization into two separated, parallel output beams with orthogonal polarization; (6) means, most preferably the aforementioned tilted plate with regions of antireflection and polarizing coatings, or a beamsplitter/beam folder assembly with regions of antireflection and polarizing coatings, for converting said two separated, parallel, orthogonally polarized output beams into a single output beam in which the variation in phase difference, &#34;Δδ&#34;, between the two polarization components of said single output beam is directly proportional to the variation in angle, &#34;Δθ&#34;, between said two plane mirrors; (7) means, most preferably, a polarizer, for mixing said orthogonal components of said single output beam; (8) means, most preferably a photoelectric detector, to produce an electrical measurement signal; and (9) means to extract said variation in phase difference, &#34;Δδ&#34;, from said electrical measurement signal, said variation in phase difference &#34;Δδ&#34;, being proportional to the variation in angle between said two plane mirrors. 
    
    
     THE DRAWING 
     In the drawings, 
     FIG. 1 depicts in schematic form one embodiment of the instant invention where all optical beams are in a single plane. 
     FIG. 2 depicts in schematic form a second embodiment of the instant invention where the optical beams are not in a single plane. 
     FIG. 3 depicts in schematic form an alternative embodiment of the arrangement shown in FIG. 1 where the tilted shear plate is replaced by a beamsplitter/beam folder assembly. 
     FIG. 4 depicts in schematic form an alternative embodiment of the arrangement shown in FIG. 2 where the tilted shear plate is replaced by a beamsplitter/beam folder assembly. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 depicts in schematic form one embodiment of the instant invention where all optical beams are in a single plane. While the apparatus has application for a wide range of radiation sources, the following description is taken by way of example with respect to an optical measuring system. Light source (10), which most preferably uses a laser, emits input beam (12) which is comprised of two linear orthogonally polarized components as indicated by the dot and arrow, which may or may not be of the same optical frequency. If the frequencies are the same, see for example, Downs et al. U.S. Pat. No. 4,360,271, issued Nov. 23, 1982. If the frequencies are different, see for example, Bagley et al. U.S. Pat. No. 3,458,259 issued July 26, 1969 and commonly owned, copending U.S. patent applications Ser. No. 710,859, entitled &#34;Apparatus to Transform a Single Frequency, Linearly Polarized Laser Beam Into a Beam with Two, Orthogonally Polarized Frequencies&#34;, filed Mar. 12, 1985; Ser. No. 710,927, entitled &#34;Heterodyne Interferometer System&#34;, filed Mar. 12, 1985; Ser. No. 710,927, entitled &#34; Apparatus to Transform a Single Frequency, Linearly Polarized Laser Beam into a High Efficiency Beam with Two, Orthogonally Polarized Frequencies&#34;, filed Mar. 12, 1985; Ser. No. 810,999, entitled &#34;Differential Plane Mirror Interferometer,&#34; filed Dec. 19, 1985; and the commonly owned copending contemporaneously filed application entitled &#34;Differential Plane Mirror Interferometer Having a Beamsplitter/Beam Folder Assembly,&#34; the contents of all of which are specifically incorporated by reference herein in their entirety, in which instance source (10) would provide an electrical reference signal (11), shown by dotted lines in FIG. 1, which would correspond to the frequency difference between the two stabilized frequencies. No such reference signal (11) is provided when the two linear orthogonally polarized components comprising input beam (12) are of the same optical frequency. 
     In the embodiment of FIG. 1, beam (12) is incident on shear plate (16) which is a tilted glass substrate with optically flat surfaces (17) and (18) which are mutually parallel. The function of shear plate (16) is to spatially separate the two polarization components using conventional polarization techniques. If desired, this function can be accomplished by a beamsplitter/beam folder assembly, such as illustrated in the embodiments of FIGS. 3 and 4, in place of tilted shear plate (16). Beam (12) passes through surface (17) to become beam (13) which has the same polarization as beam (12). Surface (17) has an antireflection coating (21A) over the region where beam (12) passes through it. Polarizing coating (23A) on surface (18) splits beam (13) so that one polarized component is transmitted as beam (30) whereas the other orthogonally polarized component is reflected as beam (14). Beam (14) is totally reflected from reflective coating (25A) on surface (17) to become beam (15). Beam (15) passes through surface (18) to become beam (31) which has the same polarization as beam (15). Surface (18) has an antireflection coating (27A) over the region where beam (15) passes through it. 
     Beam (31) passes through half-wave retardation (29A) which rotates the linear polarization of beam (31) by 90° so that resultant beam (33) has the same polarization as beam (30). Beams (30) and (33) enter polarizing beamsplitter (40) with polarizing coating (42) and are transmitted as beams (34) and (35), respectively. Beams (34) and (35) pass through quarter-wave retardation plate (44) and are converted into circularly polarized beams (50) and (51), respectively. Beams (50) and (51) are reflected from fixed reference mirror (71) to become beams (50A) and (51A). Beams (50A) and (51A) pass back through quarter-wave retardation plate (44) and are converted back into linearly polarized beams which are orthogonally polarized to the original incident beams (34) and (35). Beams (50A) and (51A) are reflected by polarizing coating (42) to become beams (52) and (53). Beams (52) and (53) are reflected by retroreflector (45) to become beams (54) and (55). Beams (54) and (55) are reflected by polarizing coating (42) to become beams (56) and (57). Beams (56) and (57) pass through quarter-wave retardation plate (44) and are converted into circularly polarized beams (58) and (59). 
     Beams (58) and (59) are reflected from movable mirror (70) to become beams (58A) and (59A). Beams (58A) and (59A) pass back through quarter-wave retardation plate (44) and are converted back into linearly polarized beams which are polarized the same as the original incident beams (34) and (35). Beams (58A) and (59A) are transmitted by polarized coating (42) and leave polarizing beamsplitter (40) as beams (60) and (63). Beams (60) and (63) are mutually parallel, independent of any tilt that may be present between mirrors (70) and (71). Beam (60) passes through half-wave retardation plate (29B) which rotates the linear polarization of beam (60) by 90° so that resultant beam (62) has a linear polarization which is orthogonal to beam (63). Beam (62) passes through surface (18) to become beam (64) which has the same polarization as beam (62). Surface (18) has an antireflection coating (27B) over the region where beam (62) passes through it. Beam (64) is totally reflected from reflective coating (25B) to become beam (65). Surface (18) has reflective coating (25B) over the region where beam (64) intersects it. Beams (65) and (63) are recombined to form beam (66) by polarizing coating (23B). Surface (17) has polarizing coating (23B) over the region where beams (65) and (63) intersect. Beam (66) passes through surface (17) to become beam (80). Surface (17) has an antireflection coating (21B) over the region where beam (65) passes through it. 
     Beam (80), like input beam (12), has two polarization components which are orthogonally polarized. Each polarization component has traversed exactly the same optical path length (through air and glass) except for the optical path length difference through shear plate (16) due to angular tilt between mirrors (70) and (71). This results in a phase difference, &#34;δ&#34;, between the two polarization components of beam (80) and is given by ##EQU1## where &#34;h&#34; is the thickness of shear plate (16), &#34;n&#34; is the refractive index of shear plate (16), &#34;λ&#34; is the wavelength of light source (10), &#34;α&#34; is the angle of incidence of beam (12) on shear plate (16) and &#34;θ&#34; is the angular tilt of mirror (70) in the plane of beams (58) and (59). Only tilt, or a compound of tilt, in this plane will cause &#34;δ&#34; to vary. Translation of mirror (70) will not influence &#34;δ&#34;. Small variations in the tilt, &#34;Δθ&#34;, are directly proportional to variations in phase difference, &#34;Δδ&#34; and are approximately given by ##EQU2## 
     This phase variation is measured by passing beam (80) through polarizer (81), oriented at 45° to each polarization component, which mixes the two orthogonally polarized components in beam (80) to give beam (82). The interference between the two polarization components is detected by photodetector (83) producing electrical signal (85). Electronic module (90) extracts the variation in phase difference from electrical signal (85). When the two polarization components of beam (12) are of the same optical frequency, module (90) does not require reference signal (11) since there is no corresponding frequency difference, and conventionally extracts the phase variation from signal (85) such as in the manner described in U.S. Pat. No. 4,360,271. However, when the two polarization components of beam (12) are of different frequencies, an additional sinusoidal electrical reference signal (11) equal in frequency to the difference between the two optical frequencies is required by electronic module (90), which reference signal (11), as previously mentioned, would be provided from source (10) in which instance photodetector (83) would detect the interference between the two frequency components as a sinusoidal intensity variation with a frequency approximately equal to the difference frequency between the two components of beam (12), such as described in the aforementioned copending U.S. patent application Ser. Nos. 710,928 and 810,999, and electronic module (90) would preferably comprise a phase meter accumulator, such as described therein. In either event, electronic module (90) provides output (92) which is directly proportional to the change in tilt between mirrors (70) and (71). This optical configuration is extremely insensitive to measurement error because changes in the other optical components, such as those induced mechanically or thermally, affect both polarization components equally and therefore have no influence on the measured phase variation (92). In addition, environmental effects, such as variations in the refractive index of air, can be minimized by placing mirror (71) close to mirror (70) to reduce the optical path length difference between the two polarization components. It should be noted that half-wave retardation plates (29A) and (29B) could be a single element with a hole in it to allow beam (63) to pass through it unaffected. 
     FIG. 2 depicts in schematic form a second embodiment of the instant invention where the optical beams are not in a single plane. This configuration permits a more compact optical system. The description of this figure is identical to FIG. 1 and is numbered correspondingly. The only differences are that now coatings (21A) and (21B), (23A) and (23B), (25A) and (25B), and (27A) and (27B) in FIG. 1 become coatings (21), (23), (25), and (27), respectively; and half-wave retardation plates (29A) and (29B) in FIG. 1 become single half-wave retardation plate (29). 
     Thus, in FIG. 2, light source (10), which as previously mentioned, most preferably uses a laser, emits input beam (12) which is comprised of two linear orthogonally polarized components as indicated by the two arrows, which again, may or may not be of the same optical frequency. Just as was mentioned with reference to FIG. 1, when the two linear orthogonally polarized components of beam (12) differ in frequency, source (10) provides an electrical reference signal (11), shown by dotted lines in FIG. 2, corresponding to this frequency difference, with no such reference signal (11) being provided when the two linear orthogonally polarized components comprising input beam (12) are of the same optical frequency. Beam (12) is incident on shear plate (16) which is a tilted glass substrate with optically flat surfaces (17) and (18) which are mutually parallel. The function of shear plate (16) is to spatially separate the two polarization components using conventional polarization techniques. Again, this function can also be accomplished by a beamsplitter/beam folder assembly if desired. Thus, in the embodiment of FIG. 2, beam (12) is divided by shear plate (16), with aid of antireflection coatings (21) and (27), polarizing coating (23) and reflective coating (25), to become vertically polarized beam (30) and horizontally polarized beam (31). Beam (31) passes through the single half-wave retardation plate (29) which rotates the linear polarizatioin of beam (31) by 90° so that resultant beam (33) has the same polarization as beam (30). Beams (30) and (33) enter polarizing beamsplitter (40) with polarizing coating (42) and are transmitted as beams (34) and (35), respectively. Beams (34) and (35) pass through quarter-wave retardation plate (44) and are converted into circularly polarized beams (50) and (51), respectively. Beams (50) and (51) are reflected from fixed reference mirror (71) to become beams (50A) and (51A). Beams (50A) and (51A) pass back through quarter-wave retardation plate (44) and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams (34) and (35). Beams (50A) and (51A) are reflected by polarizing coating (42), retroreflector (45), and polarizing coating (42) a second time to become beams (56) and (57). Beams (56) and (57) pass through quarterwave retardation plate (44) and are converted into circularly polarized beams (58) and (59). Beams (58) and (59) are reflected from movable mirror (70) to become beams (58A) and (59A). Beams (58A) and (59A) pass back through quarter-wave retardation plate (44) and are converted back into linearly polarized beams that are polarized the same as the original incident beams (34) and (35). Beams (58A) and (59A) are transmitted by polarized coating (42) and leave polarizing beamsplitter (40) as beams (60) and (63). Beams (60) and (63) are mutually parallel, independent of any tilt that may be present between mirrors (70) and (71). Beam 60 passes through the single half-wave retardation plate (29) which rotates the linear polarization of beam (60) by 90° so that resultant beam (62) has a linear polarization which is orthogonal to beam (63). Beams (62) and (63) are combined by shear plate (16), with the aid of antireflection coatings (21) and (27), polarizing coating (23) and reflective coating (25), to become beam (80). 
     Once again beam (80), in the embodiment of FIG. 2, like input beam (12), has two polarization components which are orthogonally polarized. Each polarization component, as was true with the FIG. 1 embodiment, has traversed exactly the same optical path length (through air and glass) except for the optical path length difference through shear plate (16) due to angular tilt between mirrors (70) and (71). This results in a phase difference, &#34;δ&#34;, between the two polarization components of beam (80) and is given by ##EQU3## where &#34;h&#34; is the thickness of shear plate (16), &#34;n&#34; is the refractive index of shear palte (16), &#34;λ&#34; is the wavelength of light source (10), &#34;α&#34; is the angle of incidence of beam (12) on shear plate (16) and &#34;θ&#34; is the angular tilt of mirror (70) in the plane of beams (58) and (59). Only tilt, or a component of tilt, in this plane will cause &#34;δ&#34; to vary. Translation of mirror (70) will not influence &#34;δ&#34;. Small variations in the tilt, &#34;Δθ&#34;, are directly proportional to variations in phase difference, &#34;Δθ&#34;, and are approximately given by ##EQU4## This phase variation is measured by passing beam (80) through polarizer (81), oriented at 45° to each polarization component, which mixes the two orthogonally polarized components in beam (80) to give beam (82). As was also true on the FIG. 1 embodiment, the interference between the two frequency components is detected by photodetector (83) producing electrical signal (85). Electronic module (90) extracts the variation in phase difference from electrical signal (85). Again, as was also true with respect to the Figure embodiment, when the two polarization components of beam (12) are of the same optical frequency, module (90) does not require reference signal (11) since there is no corresponding frequency difference, and conventionally extracts the phase variation from signal (85) such as in the manner described in U.S. Pat. No. 4,360,271. However, when the two polarization components of beam (12) are of different frequencies, an additional sinusoidal electrical reference signal (11) equal in frequency to the difference between the two optical frequencies is required by electronic module (90), which difference signal (11), as previously mentioned, would be provided from source (10) in which instance photodetector (83) would detect the interference between the two frequency components as a sinusoidal intensity variation with a frequency approximately equal to the difference between the two components of beam (12), such as described in the aforementioned copending U.S. patent application Ser. Nos. 710,928 and 810,999, and electronic module (90) would preferably comprise a phase meter accumulator, such as described therein. In either event, electronic module (90) provides output (92), which as previously mentioned with respect to the FIG. 1 embodiment, is directly proportional to the change in tilt between mirrors (70) and (71). Thus, both the FIGS. 1 and 2 embodiments employ optical configurations which are extremely insensitive to measurement error because changes in the other optical components, such as those induced mechanically or thermally, affect both polarization components equally and therefore have no influence on the measured phase variation (92). In addition, as was previously mentioned with reference to the FIG. 1 embodiment, environmental effects, such as variations in the refractive index of air, can be minimized by placing mirror (71) close to mirror (70) to reduce the optical path length difference between the two polarization components. 
     Although the configuration depicted in FIGS. 1 and 2 is the preferred embodiment, shear plate (16) may be replaced by one of a variety of optical elements which spatially separate the two polarization components of beam (12) to give two mutually parallel and orthogonally polarized beams (30) and (31) and which also recombine beams (62) and (63) to give a single beam (80) comprised of the two orthogonally polarized components. One such optical element is shown in FIGS. 3 and 4. 
     FIG. 3 depicts in schematic form one alternative to shear plate (16), which is shown in FIG. 1, where all the optical beams are in a single plane. This optical element is comprised of two beamsplitter/beam folder assemblies (116A) and (116B). In turn, beamsplitter/beam folder assemblies (116A) and (116B) are comprised of right angle prisms (125A) and (125B), and rhomboid prisms (122A) and (122B) respectively. Beam (12) passes through surface (117A) to become beam (113) which has the same polarization as beam (12). Surface (117A) has an antireflection coating over the region where beam (12) passes through it. Polarizing coating (123A) on surface (118A) splits beam (113) so that one polarized component is transmitted as beam (30) whereas the other orthogonally polarized component is reflected as beam (114). Beam (114) is reflected by surface (119A) with its state of polarization unaltered to become beam (115). Beam (115) passes through surface (120A) to become beam (31) which has the same polarization as beam (115) and which is parallel to beam (30). Surface (120A) has an antireflection coating over the regions where beams pass through it. 
     Return beams (62) and (63) are incident on beamsplitter/beam folder (116B). Beam (62) passes through surface (120B) to become beam (164) which has the same polarization as beam (62). Surface (120B) has an antireflection coating over the regions where beams pass through it. Beam (164) is totally reflected by surface (119B) with its state of polarization unaltered to become beam (165). Beams (165) and (63) are recombined to form beam (166) by polarizing coating (123B). Surface (118B) has polarizing coating (123B) over the region where beams (165) and (63) intersect. Beam (166) passes through surface (117B) to become beam (80). Surface (117B) has an antireflection coating over the region where beam (166) passes through it. 
     If desired, a single beamsplitter/beam folder assembly could be constructed to functionally perform the operations of the two beamsplitter/beam folder assemblies (116A) and (116B) without departing from the spirit and scope of the present invention, such as illustrated in the embodiment of FIG. 4. 
     FIG. 4 depicts in schematic form a second embodiment of the beamsplitter/beam folder where the optical beams are not in a single plane. This configuration permits a more compact optical system. The description of this figure is identical to FIG. 3 and is numbered correspondingly. The only differences are that now the two beamsplitter/beam folder assemblies (116A) and (116B) illustrated in the embodiments of FIG. 3 are replaced by a single beamsplitter/beam folder assembly (116) comprised of right angle prism (125) and rhomboid prism (122). Beam (12) is divided by beamsplitter/beam folder assembly (116) with aid of antireflection coatings on surfaces (117) and (120) and polarizing coating (123) on surface (118) to become vertically polarized beam (30) and horizontally polarized beam (31). Return beams (62) and (63) are recombined by beamsplitter/beam folder assembly (116) with aid of antireflection coatings on surfaces (117) and (120) and polarizing coating (123) on surface (118) to become beam (80). 
     Using the beamsplitter/beam folder assembly (116A, 116B, 116) in FIGS. 3 and 4 produces a resultant phase difference, &#34;δ&#34;, between the two polarization components of beam (80) now given by ##EQU5## where &#34;h&#34; is now the thickness of the rhomboid prism, &#34;n&#34; is the refractive index of the rhomboid prism, &#34;λ&#34; is the wavelength of the light source, and &#34;θ&#34; is the angular tilt of the pair of plane mirrors with respect to each other. Small variations in the tilt, &#34;Δθ&#34;, are now approximately given by ##EQU6## where &#34;Δδ&#34; is the variation in the phase difference &#34;δ&#34;. 
     The principal advantages of the instant invention are: (1) it uses plane mirrors rather than retroreflectors; (2) the measurement accommodates and is insensitive to mirror translation in three dimensions; (3) the measurements are based on the wavelength of light, and (4) high speed measurements can be made. 
     While a preferred embodiment of the invention has been disclosed, obviously modification can be made therein, without departing from the scope of the invention as defined in the following claims.