Abstract:
An optical apparatus capable of measuring the absolute refractive index of a gas is provided which comprises: (1) an evacuated cell (50) comprised, most preferably, of a bellows (52) with transparent plano windows (41, 61) which have diameters larger than the outside diameter of said bellows (52) attached to each end of said bellows (52); (2) means, most preferably, high reflectivity mirror coating spots (46, 47, 66, 67), for obtaining reflections from the surfaces on the vacuum sides of said windows (41, 61); (3) means for varying the distances between said high reflectivity mirror coatings from less than a few micrometers to approximately 100 millimeters; (4) means, most preferably a first differential plane mirror interferometer (23) with its measurement leg in the gas to be measured outside of the vacuum cell (50); means, most preferably a second differential plane mirror interferometer (33) with its measurement leg in the vacuum cell (50); (6) means, for measuring the first phase variation (73, 75, 77) in said first differential plane mirror interferometer (23) as said distance varies from zero to approximately 100 milimeters; (7) means, for measuring the second phase variation (83, 85, 87) in said second differential plane mirror interferometer (33) as said distance varies from zero to approximately 100 millimeters; (8) means, most preferably a microcomputer (90) for taking the ratio of said first and second phase variations to provide an output (92) which is the absolute index of refraction of the gas.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method and 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 ±10 -4 . In many applications the refractive index of air must be known with an error 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. The commercially available Automatic Compensator, Model 5510 Opt 010, from Hewlett-Packard uses this technique. This technique has been only partly satifactory 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 al., 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. The change in optical path length of this enclosure is measured as remotely controlled valves allow the enclosure to be evacuated and refilled with ambient air. The wavelength of the air in the enclosure is proportional to the measured change in optical path length. This technique has also been only partly satisfactory due to the fact that the characteristics of the air in the enclosure do not adequately represent those of the air in the measurement path, thusly systematic errors are introduced. It has been found that even with a perforated enclosure, serious systematic differences exist between the characteristics of the air inside of and external to the enclosure. In addition, the need for valves and a vacuum pump makes this technique awkward to implement for many applications. 
     Another prior-art technique incorporates a fixed length optical reference path which contains the ambient air. The technique measures the difference in optical length of the fixed length due to the variations in the refractive index of the ambient air. This technique is only partly satisfactory due to the fact that since it is differential it depends critically on the precise knowledge of the initial conditions. 
     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, optical apparatus capable of measuring the absolute refractive index of a gas is provided which comprises: (1) an evacuated cell comprised, most preferably, of a bellows with transparent plano windows which have diameters larger than the outside diameter of said bellows attached to each end of said bellows; (2) means, most preferably, high reflectivity mirror coating spots, for obtaining reflections from the surfaces on the vacuum sides of said windows; (3) means for varying the distance between said high reflectivity mirror coatings from less than a few micrometers to approximately 100 millimeters: (4) means, most preferably a first differential plane mirror interferometer with its measurement leg in the gas to be measured outside of the vacuum cell; (5) means, most preferably a second differential plane mirror interferometer with its measurement leg in the vacuum cell; (6) means, for measuring the first phase variation in said first differential plane mirror interferometer as said distance varies from zero to approximately 100 millimeters; (7) means, for measuring the second phase variation in said second differential plane mirror interferometer as said distance varies from zero to approximately 100 millimeters; (8) means, most preferably a microcomputer for taking the ratio of said first and second phase variations to provide an output which is the absolute index of refraction of the gas. 
    
    
     THE DRAWINGS 
     FIG. 1 depicts in schematic form one embodiment of the instant invention. 
     FIG. 2 depicts one form of a differential plane mirror interferometer used in FIG. 1. 
     FIG. 3 depicts in schematic form one embodiment of the refractive index measurement cell used in FIG. 1. 
     FIG. 4 depicts in schematic form a second embodiment of the refractive index measurement cell used in FIG. 1. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 depicts in schematic form one embodiment of the instant invention. While the apparatus has application for a wide range of radiation sources, the following is taken by way of example with respect to an optical measuring system. Light source (10), which most preferably uses a laser, emits beam (12) comprised of two frequency components f 1  and f 2  which are orthogonally polarized as indicated by the dot and arrow, 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, 710,928, and 710,927. Beam (12) is divided equally by beamsplitter (15) into beams (13) and (20). Beam (13) is reflected by mirror (17) to become beam (30). Beams (20) and (30) are reflected by mirrors (21) and (31) to become beams (22) and (32), respectively. Beams (22) and (32) are incident on differential plane mirror interferometers (23) and (33), respectively. A differential plane mirror interferometer can take several forms, one of which is described in R. R. Baldwin and G. J. Siddall, &#34;A double pass attachment for the linear and plane interferometer,&#34; Proc. SPIE, Vol. 480, pp. 78-83 (May 1984). Another form is described with reference to FIG. 2. 
     A differential plane mirror interferometer measures the optical path changes between two external plane mirrors. In addition, it is insensitive to thermal and mechanical disturbances that may occur in the interferometer beamsplitting cube and associated optical components. Differential plane mirror interferometer (23) has four exit/return beams (25), (26), (27), and (28). Beams (25) and (28), which comprise one measurement leg, are of optical frequency, f 1 , and beams (26) and (27), which comprise the second measurement leg, are of optical frequency, f 2 . Likewise, differential plane mirror interferometer (33) has four exit/return beams (35), (36), (37), and (38). Beams (35) and (38), which comprise one measurement leg, are of optical frequency, f 1  and beams (36) and (37), which comprise the second measurement leg, are of optical frequency, f 2 . 
     Beams (25), (26), (27), and (28) are incident on refractive index measurement cell (50), described in detail in FIG. 3, which results in beam (71) leaving differential plane mirror interferometer (23). Beam (71) has both frequency components, f 1  and f 2 , which are orthogonally polarized. Beam (71) contains information about the optical path length through the gas whose index of refractive is to be determined. Likewise, beams (35), (36), (37), and (38) are incident on refractive index measurement cell (50), which results in beam (81) leaving differential plane mirror interferometer (33). Beam (81) has both frequency components which are orthogonally polarized. Beam (81) contains information about the optical path length through a vacuum which serves as an absolute reference for the refractive index measurement. Beams (71) and (81) pass through polarizers (73) and (83), respectively, oriented at 45° to each polarization component, which mix the two orthogonally polarized frequency components to give beams (74) and (84), respectively. The interference between the two components is detected by photodetectors (75) and (85) as sinusoidal intensity variations with a frequency equal to the difference frequency, f 2  -f 1 . Sinusoidal electrical output (76) of photodetector (75) is compared to sinusoidal electrical reference signal (11) by phase meter/accumulator (77), see, for example, commonly owned, copending U.S. patent application, Ser. No. 710,928, to measure their phase difference (79) which is directly proportional to the optical path length through the gas whose refractive index is to be determined. This measured phase difference (79) can be expressed as, 
     
         M.sub.gas =4nL, 
    
     where n is the refractive index of the gas and 4L is the total physical length change experienced by beams (25), (26), (27), and (28). Likewise, sinusoidal electrical output (86) of photodetector (85) is compared to the same sinusoidal electrical reference signal (11) by phase meter/accumulator (87) to measure their phase difference (89) which is directly proportional to the optical path length through a vacuum whose refractive index is exactly unity. This measured phase difference (89) can be expressed as, 
     
         M.sub.vac =4L 
    
     where 4L is the total physical length change experienced by beams (35), (36), (37), and (38). 
     The ratio between measured phase differences (79) and (89) is calculated by microcomputer (90) as, 
     
         M.sub.gas /M.sub.vac =4n L/4L=n 
    
     which gives output (92), the refractive index, n, of the gas. 
     FIG. 2 depicts in schematic form one embodiment of the differential plane mirror interferometer (23) shown in FIG. 1. It operates in the following way: Beam (22) is incident on shear plate (116) which is a tilted glass substrate with optically flat surfaces (117) and (118) which are mutually parallel. The function of shear plate (116) is to spatially separate the two frequency components using conventional polarization techniques. Beam (22) passes through surface (117) to become beam (113) which has the same polarization as beam (22). Surface (117) has an antireflection coating (121A) over the region where beam (22) passes through it. Polarizing coating (123A) on surface (118) splits beam (113) so that one polarized frequency component is transmitted as beam (130) whereas the other orthogonally polarized frequency component is reflected as beam (114). Beam (114) is totally reflected from reflective coating (125A) on surface (117) to become beam (115). Beam (115) passes through surface (118) to become beam (131) which has the same polarization as beam (115). Surface (118) has an antireflection coating (127A) over the region where beam (115) passes through it. 
     Beam (131) passes through half-wave retardation plate (129A) which rotates the linear polarization of beam (131) by 90° so that resultant beam (133) has the same polarization (but still a different frequency) as beam (130). Beams (130) and (133) enter polarizing beamsplitter (140) with polarizing coating (142) and are transmitted as beams (134) and (135) respectively. Beams (134) and (135) pass through quarter-wave retardation plate (144) and are converted into circularly polarized beams (25) and (26), respectively. Beams (25) and (26) are reflected back on themselves by mirrors within cell (50) and pass back through quarter-wave retardation plate (144) and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams (134) and (135). These beams are reflected by polarizing coating (142) to become beams (152) and (153). Beams (152) and (153) are reflected by retroreflector (145) to become beams (154) and (155). Beams (154) and (155) are reflected by polarizing coating (142) to become beams (156) and (157). Beams (156) and (157) pass through quarter-wave retardation plate (144) and are converted into circularly polarized beams (28) and (27), respectively. 
     Beams (28) and (27) are reflected back on themselves by the same mirrors within cell (50) and pass back through quarter-wave retardation plate (144) and are converted back into linearly polarized beams that are polarized the same as the original incident beams (134) and (135). These beams are transmitted by polarized coating (142) and leave polarizing beamsplitter (140) as beams (160) and (163). Beams (160) and (163) are mutually parallel by virtue of the inherent optical properties of retroreflector (145), independent of any tilt that may be present between the mirrors in cell (50). Beam (160) passes through half-wave retardation plate (129B) which rotates the linear polarization of beam (160) by 90° so that resultant beam (162) has a linear polarization which is orthogonal to beam (163). Beam (162) passes through surface (118) to become (164) which has the same polarization as beam (162). Surface (118) has an antireflection coating (127B) over the region where beam (162) passes through it. Beam (164) is totally reflected from reflective coating (125B) on surface (117) to become beam (165). Beams (165) and (163) are recombined to form beam (166) by polarizing coating (123B) over the region where beams (165) and (163) intersect. Beam (166) passes through surface (117) to become beam (71). Surface (117) has an antireflection coating (121B) over the region where beam (166) passes through it. 
     Beam (71), like input beam (22), has two frequency components which are orthogonally polarized. Each frequency component has traversed exactly the same optical path length (through air and glass) except for an optical path difference through the gas in cell (50). Thus, beam (71) contains information about the optical path length through the gas whose index of refraction is to be determined. Differential plane mirror interferometer (33) is a mirror image of (23) and operates in an analogue way. 
     FIG. 3 depicts in schematic form one embodiment of the refractive index measurement cell (50) shown in FIG. 1. Cell (50) is composed of two glass substrates (41) and (61) with optically flat and parallel surfaces (42) and (43), and (62) and (63), respectively, each sealed to one end of cylindrical bellows (52). Volume (55) is a vacuum with a pressure of less than 10 -4  mm Hg. Surface (43) has two opaque, highly reflecting coatings (46) and (47) near its center while surface (63) has two opaque highly reflecting coatings (65) and (68) near its periphery. In use, cell (50) measures the refractive index, n, of surrounding gas (56) as follows: First substrates (41) and (61) are brought close together so that L=0, i.e. L≦a few micrometers. It should be noted that the thickness of coatings (46), (47), (65), and (68) is of the order of one micrometer. 
     In this condition, beams (25) and (28) of optical frequency f 1  reflecting from coatings (65) and (68), respectively, travel the same optical path length as beams (26) and (27) of optical frequency f 2  reflecting from coatings (46) and (47), respectively. Likewise, beams (35) and (38) of optical frequency f 1  reflecting from coatings (65) and (68), respectively, travel the same optical path length as beams (36) and (37) of optical frequency f 2  reflecting from coatings (46) and (47). Phase meters/accumulators (77) and (87) shown in FIG. 1, are then initialized, i.e., zeroed. Substrates (41) and (61) are then pulled apart to a separation, L. It is not necessary to know the value of L but the accuracy of determining the refractive index, n, is greater for larger values of L. For example, to determine n to 1 part in 10 8 , L should be greater than 100 mm when the phase resolution of phase meters/accumulators (77) and (87) is 1°. Beams (25) and (28) reflecting from coatings (65) and (68), respectively, now travel a total additional optical path length through surrounding gas (56) of 4nL as compared to beams (26) and (27) reflecting from coatings (46) and (47), respectively. This is indicated as measurement (79) in FIG. 1. Beams (36) and (37) reflecting from coatings (46) and (47), respectively, now travel a total additional optical path length through vacuum (55) of only 4L as compared to beams (35) and (38) reflecting from coatings (65) and (68), respectively. This is indicated as measurement (89) in FIG. 1. The ratio, output (92), between measured (79) and (89), as calculated by microcomputer (90), is the refractive index, n. 
     This embodiment is preferred because the inherent symmetry of the beams in cell (50) makes the measurement of the refractive index less susceptible to thermal instabilities in substrates (41) and (61). Under certain circumstances where lower cost is desirable, the optical and electronic components (specifically items (15), (17), (31), (33), (83), (85), and (87)) that are needed to make measurement (89), M vac  (which in essence is a measurement of L), may be eliminated if the value of L is determined by some other means. 
     FIG. 4 depicts in schematic form a second embodiment of refractive index measurement cell (50) shown in FIG. 1 which is a modification of cell (50) detailed in FIG. 3. The modifications are the addition of two opaque, highly reflecting coatings (66) and (67) near the center of surface (63), and the slight offset of beams (26) and (27) so that they reflect from coatings (66) and (67), instead of coatings (46) and (47), respectively. The operation of cell (50) is identical to that just described in FIG. 3 except that beams (25) and (28) reflecting from coatings (65) and (68), respectively, now travel a total additional optical path length of 4(n-1)L as compared to beams (26) and (27) reflecting from (66) and (67), respectively. This changes measured phase difference (79) to M gas-vac  =4(n-1)L so that the ratio between measured phase differences (79) and (89), as calculated by microcomputer (90), is 
     
         M.sub.gas-vac /M.sub.vac =4(n-1)/4L=n-1 
    
     The resultant output (92) is then given by, 
     
         N=1+M.sub.gas-vac /M.sub.vac 
    
     This second embodiment of cell (50), because of the asymmetry of the beams, is more susceptible to thermal instabilities in substrates (41) and (61). However, under some circumstances where lower cost is desirable, the optical and electronic components that are needed to make measurement (89), M vac  (which in essence is a measurement of L), may be eliminated if the value of L is measured by some other means. In this case the precision to which L must be measured is four orders of magnitude less stringent than if the measurement (89), M vac , in the first embodiment of cell (50) in FIG. 3 is eliminated. 
     The principal advantages of the instant invention are: (1) increased measurement accuracy, (2) no errors are introduced due to variations in the composition of the gas, and (3) the gas to be measured need not be in an enclosed or ventilated sample chamber. 
     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.