Apparatus for the measurement of the refractive index of a gas
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to my copending U.S. patent application, entitled &#34;Method and Apparatus for the Measurement of the Refractive Index of a Gas,&#34; bearing U.S. Ser. No. 821,773, filed Jan. 23, 1986, the contents of which are specifically incorporated by reference herein in its entirety and is an improvement thereon. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to apparatus for the measurement of the refractive index of a gas. More particularly, the invention relates to optical apparatus which is useful for high accuracy displacement metrology using interferometry in ambient air. 
     2. The Prior Art 
     An interferometer is the basic instrument for most of the high-accuracy displacement measurements in the machine tool and semiconductor fabrication industries. One type of interferometer representative of the current state-of-the-art is described in Bagley et al., U.S. Pat. No. 3,458,259 issued July 26, 1969. The absolute accuracy of interferometric displacement metrology is limited by two dominant factors: (1) the uncertainty in the vacuum wavelength of the light source, and (2) the uncertainty in the refractive index of the ambient air, see W. Tyler Estler, &#34;High-Accuracy Displacement Interferometry in Air&#34;, Applied Optics, Vol. 24, pp. 808-815 (Mar. 15, 1985) and Farrand et al., U.S. Pat. No. 4,215,938 issued Aug. 5, 1980. 
     As noted in the aforementioned references, interferometric displacement measurements in air are subject to environmental uncertainties, particularly to changes in air pressure, temperature, humidity, and molecular composition. Such factors alter the wavelength of the light used to measure the displacement. Under normal conditions the refractive index of air is approximately 1.0003 with a variation of ±1×10 -4 . In many applications the refractive index of air must be known with an arror of less than 10 -7  to 10 -8 . 
     One prior-art technique for correcting the environmental uncertainties is based on using individual sensors to measure the barometric pressure, temperature, and humidity, and, then, using these measurements to correct the measured displacement, see for example, Maeda, U.S. Pat. No. 4,355,894 issued Oct. 26, 1986. The commercially available Automatic Compensator, Model 5510 Opt 010, from Hewlett-Packard uses this technique. This technique has been only partly satisfactory due to the errors in the sensors and due to the errors arising from variations in the composition of the air, e.g., the percentage CO 2  content and presence of industrial gases, i.e., Freon and solvents are ignored in this technique. 
     A second prior-art technique is based on the aforementioned Farrand et el., U.S. Pat. No. 4,215,938 issued Aug. 5, 1980. This technique incorporates a rigid enclosure, the length of which must be accurately known, independent of environmental conditions and constant in time. This technique uses a plane mirror interferometer which itself has a high temperature coefficient and, thusly, is a source of systematic errors. 
     Another prior-art technique is disclosed in Downs, U.S. Pat. No. 4,571,082 issued Feb. 18, 1986. With this technique the well-known Jamin interferometer is combined with a modern fringe counting technique. However, it suffers from several serious limitations. First, significant parts of the measurement beam feed back directly into the laser thereby causing its frequency to become unstable. Second, it requires an auxiliary lens, retardation plate, and mirror which introduce errors. Third, it has low light efficiency. 
     Another prior-art technique, which is an absolute refractometer, is disclosed in my copending U.S. patent application, Ser. No. 821,773, entitled &#34;Method and Apparatus for the Measurement of the Refractive Index of a Gas,&#34; filed Jan. 23, 1986. 
     Consequently, while prior-art techniques for measuring the refractive index of a gas are useful for some applications, none known to the applicant provide the technical performance in a commercially viable form for applications requiring the high accuracy interferometric measurement of displacement in air. The disadvantages of the prior-art apparatus are overcome by the present invention. 
     SUMMARY OF THE INVENTION 
     In accordance with the instant invention, apparatus capable of measuring either changes in the refractive index, or, if desired, the absolute refractive index, of a gas is provided which comprises a differential plane mirror interferometer to produce a pair of measurement beams and a pair of reference beams; and a gas-tight refractive index cell means comprised, most preferably, of a window affixed to the end of a cylindrical tube closest to the interferometer and a mirror affixed to the other end of the tube, the cell being aligned to the interferometer so that the reference beams pass inside of the tube in a sealed volume and the measurement beams pass outside of the tube, such as in ambient air, for the measurement of changes in the refractive index of the gas surrounding the cell; or a gas-tight refractive index cell comprised, most preferably, a window affixed to the ends of a pair of cylindrical concentric tubes closest to the interferometer and a mirror affixed to the other ends of the tubes to provide two sealed volumes, with the refractive index cell being aligned to the interferometer so that the reference beams pass through sealed volume of the inner tube of the pair which is evacuated, and the measurement beams pass through the sealed volume between the tubes, which sealed volume is either evacuated or contains the gas whose absolute refractive index is to be measured; and in both embodiments, means for measuring the phase variation between the reference and measurement beams after they traverse the refractive index cell; and means, most preferably a microcomputer, for converting the measured phase variation to provide an output which is either the changes in or the absolute refractive index of a gas are provided. 
    
    
     THE DRAWINGS 
     FIG. 1 depicts in schematic form one embodiment of the apparatus of the instant invention where all the optical beams are in a single plane; and 
     FIG. 2 depicts in schematic form a second embodiment of the apparatus of the instant invention configured to measure the absolute refractive index of a gas. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 depicts in schematic form one embodiment of the apparatus of the instant invention where all the 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 an 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. Nos. 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; 710,928, entitled &#34;Heterodyne Interferometer System&#34; filed Mar. 12, 1985; and 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 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 the input beam (12) are of the same optical frequency. 
     Beam (12) is incident on a tilted parallel plate (16) which is preferably a tilted glass substrate with optically flat surfaces (17) and (18) which are mutually parallel. The function of the tilted parallel plate (16) is to spatially separate the two polarization components using conventional polarization techniques. 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. Polarization 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 phase retardation plate (29A) which rotates the linear polarization of beam (31) by 90° so that the resultant beam (33) has the same polarization as beam (30). Beams (30) and (33) enter polarizing beamsplitter (40), which has a polarization coating (42) and are transmitted as beams (34) and (35), respectively. Beams (34) and (35) then pass through quarter-wave phase retardation plate (44) and are converted into circularly polarized beams (50) and (51) respectively. 
     Beams (50) and (51) are incident on refractive index cell (78) which is preferably comprised of two optical windows (70) and (75) affixed to ends of a cylinder (73) to form a sealed volume (74) which is evacuated, or in some instances filled with a gas. Windows (70) and (75) and cylinder (73) are preferably made of the same low expansion transparent material, e.g. quartz. The surfaces (71) and (72) of window (70) are preferably coated with an antireflection coating, and surface (76) of window (75) is preferably coated with a high reflectivity coating, thus making window (75) effectively a mirror. 
     Beams (50) and (51) pass through window (70) unaffected to become beams (50A) and (51A), respectively. Beam (50A) is in the ambient air (77) whose refractive index changes are to be measured, while beam (51A) is within the sealed volume (74) whose refractive index is either identically equal to one if it is evacuated, or to a constant (but unknown) value if it is filled with a gas. Beams (50A) and (51A) are reflected from surface (76) as beams (50B) and (51B) and pass back through window (70) as beams (50C) and (51C), respectively. Beams (50C) and (51C) then pass back through quarter-wave phase retardation plate (44) and are converted back into linearly polarized beams which are orthogonally polarized to the original incident beams (34) and (35). Beams (50C) and (51C) are reflected by polarization 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 polarization coating (42) to become beams (56) and (57). Beams (56) and (57) pass through quarter-wave phase retardation plate (44) and are converted into circularly polarized beams (58) and (59). Beams (58) and (59) pass through window (70) to become beams (58A) and (59A) respectively. Beam (58A) like beam (50A), is in the ambient air (77), while beam (59A), like beam (51A), is within sealed volume (74). Beams (58A) and (59A) are reflected from surface (76) as beams (58B) and (59B) and pass back through window (70) as beams (58C) and (59C), respectively. Beams (58C) and (59C) are transmitted by polarization coating (42) and leave polarizing beamsplitter (40) as beams (60) and (63). Beams (60) and (63) are mutually parallel by virtue of the inherent optical properties of retroreflector (45), independent of any tilt that may be present in window (75). Beam (60) passes through half-wave phase retardation plate (29B) which preferably rotates the linear polarization of beam (60) by 90° so that the 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 (17) has reflective coating (25B) over the region where beam (64) intersects it. Beam (65) and (63) are recombined to form beam (66) by polarization coating (23B) on surface (18) 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 (66) passes through it. 
     Beam (80), like input beam (12), has two orthogonally polarized components. Each component has traversed exactly the same optical path length (through air and glass) except for the optical path difference in refractive index cell (78). The optical path difference, OPD, is given by 
     
         OPD=4L(n-n.sub.o), 
    
     where L is the predetermined separation between windows (70) and (75), n o  is the refractive index of sealed volume (74) (n o  =1 if evacuated), and n is the refractive index of ambient air (77). The optical path difference results in a phase difference, δ, between the two polarization components of beam (80) given by 
     
         δ=2πOPD/λ 
    
     
         δ=8πL(n-n.sub.o)/λ, 
    
     where λ is the wavelength of source (10). Changes in the refractive index, n, of ambient air (77) cause this phase difference to vary. This phase variation, Δδ, is given by 
     
         Δδ=8πLΔn/λ. 
    
     Therefore, changes in the refractive index, n, of ambient air (77) is expressed as, 
     
         Δn=(λ/8πL)Δδ. 
    
     The phase variation, Δδ, 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 phase variation 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 conventionaly 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 such an 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 explained in my copending U.S. patent application Ser. No. 810,999, the contents of which are specifically incorporated by reference herein in their entirety, and module (90) would preferably comprise a phase meter/accumulator such as described in the aforementioned copending U.S. patent application Ser. No. 710,928. In either event, electronic module (90) provides output (92) which is a direct measurement of the phase variation, and thus directly proportional to the change in refractive index of ambient air (77) as expressed in the previously described equations. 
     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). 
     While FIG. 1 depicts an embodiment of the instant invention where all of the optical beams are in a single plane, clearly modifications using multiple planes can be made without departing from the scope of the invention as defined in the following claims. 
     Referring now to FIG. 2, FIG. 2 depicts in schematic form a second embodiment of the instant invention in which the refractive index cell (78) is preferably configured to measure the absolute refractive index of a gas. Like reference numerals are used in FIG. 2 for like elements previously described with reference to FIG. 1. The modification to the embodiment of FIG. 1 exists in the area of the refractive index cell (78) which is now preferably comprised of two concentric tubes (73) and (86) which have the window (70) affixed to one end of each tube and the window or mirror (75) affixed to each of the other tube ends to provide two sealed volumes, namely (74) and (87). Once again the sealed volume (74) is evacuated so that n o  =1.0. The volume (87) is preferably connected to a vacuum pump (not shown) or to the supply of the gas to be measured using connecting pipe (89) and valve (88). The volume (87) is initially evacuated so that the initial value of the phase variation between the reference and measurement beams is zero, i.e. the optical path difference is zero. The gas to be measured is preferably allowed to slowly enter the volume (87). 
     Under these conditions the phase variation, Δδ, is given by 
     
         Δδ=8πL(n-1)λ 
    
     so that the absolute refractive index is given by 
     
         n=1+(λ/8πL)Δδ. 
    
     The remainder of the embodiment depicted in FIG. 2 is preferably the same as described in the description of FIG. 1 and will not be described again. 
     Some of the principal advantages of the instant invention are: (1) increased measurement accuracy, (2) the length, L, need not be known with extreme accuracy; (3) small variations in the length, L, during a measurement are tolerable; and (4) the air around the refractive index cell truly represents the ambient environment. 
     While a preferred embodiment of the invention has been disclosed, obvious modifications can be made therein, without departing from the scope of the invention as defined in the following claims.