WO1999018424A1 - Procede et appareil interferometriques - Google Patents

Procede et appareil interferometriques Download PDF

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Publication number
WO1999018424A1
WO1999018424A1 PCT/US1998/019855 US9819855W WO9918424A1 WO 1999018424 A1 WO1999018424 A1 WO 1999018424A1 US 9819855 W US9819855 W US 9819855W WO 9918424 A1 WO9918424 A1 WO 9918424A1
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Prior art keywords
beams
gas
frequency
light beams
heterodyne
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PCT/US1998/019855
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English (en)
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WO1999018424A9 (fr
Inventor
Henry Allen Hill
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Zygo Corporation
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Application filed by Zygo Corporation filed Critical Zygo Corporation
Priority to EP98948466A priority Critical patent/EP1019703A1/fr
Priority to JP2000515169A priority patent/JP3626907B2/ja
Publication of WO1999018424A1 publication Critical patent/WO1999018424A1/fr
Publication of WO1999018424A9 publication Critical patent/WO1999018424A9/fr

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
    • G01N21/45—Refractivity; Phase-affecting properties, e.g. optical path length using interferometric methods; using Schlieren methods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/02002—Interferometers characterised by controlling or generating intrinsic radiation properties using two or more frequencies
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/02007—Two or more frequencies or sources used for interferometric measurement
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02015—Interferometers characterised by the beam path configuration
    • G01B9/02027—Two or more interferometric channels or interferometers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration
    • G01B9/0207—Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/45—Multiple detectors for detecting interferometer signals
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/70—Using polarization in the interferometer

Definitions

  • the present invention generally relates to a method and apparatus for measuring and monitoring the intrinsic optical properties of a gas. More particularly, the invention relates to interferometric measurement of the reciprocal dispersive power of a gas and to optical apparatus which is useful for high accuracy displacement metrology in the presence of an uncontrolled turbulent gas.
  • Interferometric techniques have broad applicability to a variety of tasks requiring precision measurement.
  • interferometric displacement measurements in air are subject to environmental uncertainties, particularly to changes in air pressure, temperature, and humidity; air composition; and to the effects of turbulence in the air. Such factors alter the wavelength of the light used to measure the displacement.
  • the refractive index of air is approximately 1.0003 with a variation of the order of lxlO -5 to lxlO '4 .
  • the refractive index of air must be known with a relative precision of less than 0.1 ppm (parts per million) to 0.003 ppm, these two relative precisions corresponding to a displacement measurement accuracy of 100 nm and 3 nm, respectively, for a one meter interferometric displacement measurement.
  • One prior-art technique of the type described in the preceding paragraph 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 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 C0 2 content and presence of industrial gases, i.e. Freon and solvents are ignored in the technique.
  • refractivity technique Another type of technique for correcting for the effects of air is based on a measurement of the refractivity of the air.
  • a procedure of this type will hereinafter be referred to as a refractivity technique.
  • the refractivity of a gas is directly proportional to the density of the gas which is dependent in first order on environmental conditions such as temperature and pressure.
  • the environmental conditions at the latter site relative to the environmental conditions at the former site must be known with a relative precision of less than 300 ppm to 10 ppm, the required relative precision for the refractive index at the latter site being less than 0.1 ppm to 0.003 ppm in accordance with relative precisions previously cited.
  • This serious limitation in regard to use in high precision distance measuring interferometry will in general be present with all techniques classified as refractivity techniques.
  • a prior-art refractivity technique for correcting for environmental uncertainties is based on the C. L. Farrand, V. F. Foster, and W. H. Grace U.S. Pat., op . ci t . .
  • 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 refractivity of the air in the enclosure is proportional to the measured change in optical path length.
  • the correction for index fluctuations due to air turbulence is typically on the order of 0.1 ppm in magnitude, and the residual errors due to index fluctuations resulting in part from air turbulence in the corrected measured path length must be with a relative precision less than or of the order of 0.003 ppm in high accuracy displacement interferometry, a relative precision corresponding to a displacement measurement accuracy of 3 nm for a one meter interferometric displacement measurement.
  • This high level of precision involves frequency-stabilized laser sources and high-resolution phase detection.
  • the system of Hall et. al . includes use of a refractometer exposed to an ambient atmosphere and having light directed thereto to form an optical interference fringe pattern having a dependence upon the refractivity of the ambient atmosphere.
  • the fringe pattern is measured as a function of angle either by sequentially scanning a collimated input beam in angle while detecting the transmitted light, or by imaging (onto a multi-element detector) the angular exit space of the interferometer illuminated with a diverging input beam.
  • the measuring path of the apparatus of Hall et. al . is substantially a combination of two right circular cones whereas the measuring path of a distance measuring interferometer is substantially comprised of a set of right circular cylinders.
  • the apparatus of Hall et. al. is not suited to measuring fluctuations in the optical path length of distance measuring interferometers due to atmospheric turbulence.
  • the basic principle may be understood as follows. Interferometers and laser radar measure the optical path length between a reference and an object, most often in open air.
  • the optical path length is the integrated product of the refractive index and the physical path traversed by the measurement beam.
  • the refractive index varies with wavelength, but the physical path is independent of wavelength, it is generally possible to separate the physical path length from the contributions of the refractive index, provided that the instrument employs at least two wavelengths.
  • the variation of index with wavelength is known in the art as dispersion, accordingly this technique will be referred to hereinafter as the dispersion technique.
  • the dispersion technique measures the difference in optical path at two different wavelengths and then uses properties of the refractive index to compute the effects of the refractive index on a path length from the measured difference in optical path at two different wavelengths.
  • the dispersion technique encounters two serious limitations. The more basic limitation arises from the fact that the dispersion technique is by definition a technique which uses properties of the first derivative with respect to wavelength of the refractive index. The second limitation arises from the fact that the properties of the refractive index must be available to the required accuracy.
  • the first derivative character of the dispersion technique increases the relative precision at which interferometric phase measurements must be made relative to distance measuring interferometers by more than one to two orders of magnitude.
  • the first derivative character of the dispersion technique also increases the relative precision to which properties of the refractive index must be known relative to refractivity techniques by more than one to two orders of magnitude.
  • the information available on the refractive index is not known with sufficient relative precision for certain applications of the refractivity technique and consequently is not known with sufficient relative precision for even fewer applications of the dispersion technique.
  • the dispersion technique for refractive index measurement has a long history, and predates the introduction of the laser. An article entitled "Long-Path Interferometry Through An Uncontrolled Atmosphere" by K. E.
  • the technique of Zipin et al . is not a dispersion technique.
  • the dispersion technique being described as a technique which uses properties of the first derivative of the refractive index with respect to wavelength, the technique of Zipin et al . may be described as a technique which uses properties of the second derivative of the refractive index with respect to wavelength and accordingly, will hereinafter be referred to a second derivative refractive index technique .
  • the second derivative refractive index technique encounters two serious limitations.
  • the more basic limitation arises from the fact that the second derivative refractive index technique is by definition a technique which uses properties of the second derivative with respect to wavelength of the refractive index.
  • the second limitation arises from the fact that the properties of the refractive index must be available to the required relative precision.
  • the second derivative character of the second derivative refractive index technique increases the relative precision at which interferometric phase measurements must be made relative to dispersion techniques by more than one to two orders of magnitude.
  • the second derivative character of the second derivative refractive index technique also increases the relative precision to which properties of the refractive index must be known relative to dispersion techniques by more than one to two orders of magnitude.
  • the information available on the refractive index is not known with sufficient relative precision for certain applications of the refractivity technique, to fewer applications of the dispersion technique, and consequently to yet an even smaller set of applications of the second derivative refractive index technique.
  • An Ar + laser source provides both wavelengths simultaneously by means of a frequency-doubling crystal known in the art as BBO.
  • BBO frequency-doubling crystal
  • the use of a BBO doubling crystal results in two wavelengths that are fundamentally phase-locked, thus greatly improving the stability and accuracy of the dispersion measurement.
  • the phase detection and signal processing means are not suitable for dynamic measurements, in which the motion of the object results in rapid variations in phase that are difficult to detect accurately.
  • the cited patents of Lis are all based on the dispersion technique and therefore have the basic limitations of the dispersion technique previously cited.
  • the relative precision of any dispersion technique depends directly on the accuracy to which both the dispersion and the reciprocal dispersive power of the gas in the measurement path is known, the reciprocal dispersive power being defined as the ratio of the refractivity of a gas measured at a first wavelength to the dispersion of the refractivity of the gas between a second and third wavelengths.
  • the first wavelength is preferably the same wavelength as used in an associated distance measuring interferometer.
  • the second or third wavelengths used in the measurement of the dispersion may be the same as the first wavelength used in the measurement of the refractivity.
  • the reciprocal dispersive power is used to compute the refractivity of a gas in the measuring path of for example a distance measuring interferometer from measured values of the dispersion of the gas in the measuring path of the distance measuring interferometer.
  • the reciprocal dispersive power depends on the three wavelengths for which a specific reciprocal dispersive power is defined as well as on the composition of the gas.
  • the principle advantage of the dispersion technique is that the reciprocal dispersive power is independent of environmental conditions such as temperature and pressure for environmental conditions normally encountered in high- precision distance-measuring interferometers.
  • the composition of the gas may be unknown, the gas composition may vary in time in an unknown way, and the dispersion of the refractivity and/or the refractivity of the gas constituents is not available or not known to the accuracy required for a given application. Either lack of the knowledge of the gas composition or of the reciprocal dispersive power to the necessary relative precision can pose serious limitations on the utility of the dispersion technique.
  • the relative precision to which the reciprocal dispersive power can be computed using either of these two cited sources for the refractivity of water vapor is of the order of 0.1%, the first, second, and third wavelengths used in the computing the reciprocal dispersive power being in the visible part of the spectrum, the first and second wavelengths being equal, and the second and third wavelengths being in the ratio of 2:1, respectively.
  • the situation respect to C0 2 is only better by approximately a factor of 3. It is evident from the examples given in the preceding paragraph that current knowledge of the refractivity of water vapor and C0 2 are not accurate enough to make absolute length measurements using dispersion interferometry in ambient air to the relative precision of approximately 0.003 ppm.
  • the prior art does not provide a practical, high-speed, high-precision method and corresponding means for measuring and compensating the refractive index including fluctuations in the refractive index of a gas.
  • the limitations in the prior art arise principally from the following, unresolved technical difficulties: (1) the refractivity technique does not measure for example the refractivity of a gas in a measurement path of a distance measuring interferometer directly and as a consequence, requires detailed high precision knowledge of the environmental conditions at two separated sites; (2) the dispersion technique does not measure the refractivity of a gas in a measurement path of a distance measuring interferometer directly and as a consequence requires knowledge of the constituents of the gas in the measurement path and knowledge of the reciprocal dispersive powers of the gas constituents; (3) the gas composition may not be known with sufficient accuracy for the dispersion technique in either a turbulent or a non turbulent gas; (4) the composition of a gas may be changing significantly on relative short time scales; (5) the data age of composition determinations may be too
  • the present invention generally relates to apparatus and methods by which information about intrinsic optical properties of gases can be measured and monitored for use in electro-optical metrology and other applications. More specifically, the invention operates to provide measurements of relative dispersion and reciprocal dispersive power, the relative dispersion and the reciprocal dispersive power being substantially independent of environmental conditions such as gas temperature and pressure.
  • the gas may be turbulent, the gas composition may not be known, the gas composition may be variable in time, and knowledge of refractivities and dispersions of the refractivities for constituents of the gas is not required.
  • the information generated by the inventive apparatus is particularly suitable for use in interferometric distance measuring instruments (DMI) to compensate for errors related to refractive index in the measurement leg and especially to refractive index changes in the measurement leg brought about by environmental effects and turbulence induced by rapid stage slew rates.
  • DMI interferometric distance measuring instruments
  • Several embodiments of the invention have been made and these fall broadly into two categories which address the need for more or less precision in final measurements. While the various embodiments share common features, they differ in some details to achieve individual goals.
  • the inventive apparatus comprises interferometer means having a reference leg and a measurement leg.
  • each of the constituent legs has a predetermined physical path length with the reference leg configured and arranged to be occupied by a predetermined medium, preferably a vacuum, and the measurement leg configured and arranged to be occupied by the gas whose intrinsic optical properties are to be measured and monitored.
  • the interferometer means comprises a concentric cell having a closed inner chamber that serves as the reference leg and an outer chamber, surrounding the inner chamber, that serves as the measurement leg.
  • the inner chamber is substantially evacuated to provide the vacuum, and the outer chamber is opened to the ambient surroundings which, in a typical interferometric DMI application, is air.
  • the concentric cell is preferably in form a right circular cylinder with end sections capped with wavelength selective mirrors fixed normal to the cell's longitudinal axis.
  • a source generates a set of light beams, the set of light beams being comprised of at least two light beams, each beam of the set of light beams having a different wavelength, the wavelengths of the beams of the set of light beams having an approximate harmonic relationship to each other.
  • the approximate harmonic relationship is known and expressed as a sequence of ratios, each ratio being comprised of a ratio of low order non zero integers, e . g. 1/2, to a relative precision of an order of magnitude less than the dispersive power of the gas, the dispersive power of the gas being the inverse of the reciprocal dispersive power, times the relative precision required for the measurement of the reciprocal dispersive power.
  • a set of frequency-shifted light beams is generated from the set of light beams by introducing a frequency difference between two orthogonally polarized components of each beam of the set of light beams such that no two beams of the set of frequency-shifted light beams have the same frequency difference.
  • the ratios of the wavelengths are expressible as a sequence of low order non zero integers to a relative precision, the relative precision of the approximate harmonic relationship, of an order of magnitude less than the dispersive power of the gas times the relative precision required for the measurement of the reciprocal dispersive power of the gas.
  • means are provided for monitoring the relative precision of the approximate harmonic relationship and either providing feedback to control the relative precision of the approximate harmonic relationship, information to correct subsequent calculations influenced by undesirable departures of the relative precision of the approximate harmonic relationship from the desired relative precision, or some combination of both.
  • At least a portion of each of the frequency shifted light beams are introduced into the interferometer means by suitable optical means so that each light beam portion travels through the predetermined medium and the gas along predetermined paths of substantially the same physical path length.
  • the light beam portions emerge from the interferometer means as exit beams containing information about the optical path length through the predetermined medium (preferably a vacuum) in the reference leg and about the optical path length through the gas in the measurement leg.
  • the optical means for introducing the light beam portions into the interferometer means is configured and arranged to introduce one of the light beam portions corresponding to one wavelength through one of the wavelength selective end mirrors of the concentric cell and another of the light beam portions corresponding to another of the wavelengths through the other wavelength selective mirror of the end sections of the concentric cell.
  • three sets of light beam portions are generated, one at one wavelength being introduced into one end of the concentric cell and two at another wavelength into the other end of the concentric cell.
  • the optical means are configured to cause certain of the light beam portions to undergo multiple passes as they travel through the concentric cell .
  • Combining means are provided for receiving the exit beams to produce mixed optical signals which contain information corresponding to the phase differences between the exit beams of each light beam portion from the reference and measurement legs.
  • the mixed optical signals are then sensed by a photodetector which operates to generate electrical interference signals that contain information corresponding to the refractivities of the gas at the different beam wavelengths.
  • the electrical interference signals are then analyzed by electronic means that operate to determine the select intrinsic optical properties of the gas.
  • the electronic means can be in the form of a microprocessor or a general purpose computer suitably programmed in well-known ways to perform the needed calculations.
  • the electronic means is configured to determine the relative refractivities at different beam wavelengths where the relative refractivities are of the form:
  • the reciprocal dispersive power, T of the gas can be determined.
  • the electrical interference signals comprise heterodyne signals containing phase information corresponding to the refractivities of the gas and the apparatus further comprises means for adding the heterodyne signals to generate at least one superheterodyne signal containing phase information corresponding to the dispersion of the refractivities of the gas. Means are also included for resolving phase ambiguities of the heterodyne and superheterodyne signals.
  • additional or different electronics are provided which, in one embodiment, requires the production of modified heterodyne signals prior to final data processing.
  • FIGS, la-lf taken together illustrate, in diagrammatic form, the presently preferred first embodiment of the present invention with FIG. la showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 69, plane mirror interferometer group 70, measurement cell 90, detectors 85, 86, and 286 and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 85, 86, and 286, electronic processor 108, and computer 109;
  • FIG. lb illustrates plane mirror interferometer 69
  • FIG. lc illustrates plane mirror interferometer group 70
  • FIG. Id illustrates measurement cell 90 furnishing the external mirrors for plane mirror interferometer 69
  • FIG. le illustrates measurement cell 90 furnishing the external mirrors for plane mirror interferometer group 70;
  • FIG. If is a drawing showing a block diagram of the processing electronics 108.
  • FIG. 2a-2b taken together illustrate, in diagrammatic form, the presently preferred variant of the first embodiment of the present invention with FIG. 2a showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 69, plane mirror interferometer 170, measurement cell 90, detectors 85 and 186 and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 85 and 186, electronic processor 1108, and computer 109;
  • FIG. 2b illustrates plane mirror interferometer 170
  • FIGS. 3a-3d taken together illustrate, in diagrammatic form, the presently preferred second embodiment of the present invention with FIG. 3a showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 269, plane mirror interferometer 270, measurement cell 90, and detectors 85 and 86; and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 85 and 86, electronic processor 208, and computer 109;
  • FIG. 3b illustrates plane mirror interferometer 269
  • FIG. 3c illustrates plane mirror interferometer 270
  • FIG. 3d is a drawing showing a block diagram of the processing electronics 208;
  • FIGS. 4a-4d taken together illustrate, in diagrammatic form, the presently preferred third embodiment of the present invention with FIG. 4a showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 369, plane mirror interferometer 270, measurement cell 90, and detectors 485 and 86 and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 485 and 86, electronic processor 408, and computer 109;
  • FIG. 4b illustrates plane mirror interferometer 369 for the case of light beam 11 entering plane mirror interferometer 369
  • FIG. 4c illustrates plane mirror interferometer 369 for the case of light beam 445 exiting plane mirror interferometer 369
  • FIG. 4d is a drawing showing a block diagram of the processing electronics 408;
  • FIGS. 5a-5d taken together illustrate, in diagrammatic form, the presently preferred fourth embodiment of the present invention with FIG. 5a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the first preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/% , a number of elements of the apparatus for determination of the ratio K/ ⁇ performing analogous operations as apparatus for determination of reciprocal dispersive power of the first preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio
  • FIG. 5b illustrates measurement cell 90b furnishing the external mirrors for plane mirror interferometer 69b
  • FIG. 5c illustrates measurement cell 90b furnishing the external mirrors for plane mirror interferometer group 70b
  • FIG. 5d is a drawing showing a block diagram of the processing electronics 108b;
  • FIGS. 6a-6b taken together illustrate, in diagrammatic form, the variant of the presently preferred fourth embodiment of the present invention with FIG. 6a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the variant of the first preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/ ⁇ , a number of elements of the apparatus for determination of the ratio K/ ⁇ performing analogous operations as apparatus for determination of reciprocal dispersive power of the variant of the first preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio K/ ⁇ ;
  • FIG. 6b is a drawing showing a block diagram of the processing electronics 1108b;
  • FIGS. 7a-7b taken together illustrate, in diagrammatic form, the presently preferred fifth embodiment of the present invention with FIG. 7a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the second preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/ ⁇ , a number of elements of the apparatus for determination of the ratio K/ ⁇ performing analogous operations as apparatus for determination of reciprocal dispersive power of the second preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio ⁇ / ⁇ ;
  • FIG. 7b is a drawing showing a block diagram of the processing electronics 208b
  • FIGS. 8a- 8b taken together illustrate, in diagrammatic form, the presently preferred sixth embodiment of the present invention with FIG. 8a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the third preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/ ⁇ , a number of elements of the apparatus for determination of the ratio K/ ⁇ performing analogous operations as apparatus for determination of reciprocal dispersive power of the third preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio K/ ⁇ ;
  • FIG. 8b is a drawing showing a block diagram of the processing electronics 408b.
  • Fig. 9 is a high-level flowchart depicting various steps carried out in practicing a method in accordance with the invention.
  • the present invention relates to apparatus and methods by which intrinsic optical properties of a gas, especially its reciprocal dispersive power, may be quickly measured and used in subsequent downstream or contemporaneous applications as, for example, in an interferometric distance measuring instrument to enhance accuracy by compensating for index of refraction changes that take place proximate to or during the measuring period because of changing environmental conditions or air turbulence induced in the measurement leg by rapid stage slew rates.
  • the first broad group of embodiments to be described comprise three and a variant of the first embodiment. This group is intended for applications where the stability of the adopted light sources is sufficient and the wavelengths of the light beams generated by the adopted light sources are harmonically related to a relative precision sufficient to meet the required precision imposed on the output data by the final end use application.
  • the second group of embodiments also comprise three and one variant, and these are particularly suitable for use where it is necessary to monitor the stability of the light sources and measure the wavelengths of the light beams generated by the adopted light sources to meet performance requirements on accuracy.
  • apparatus is disclosed for dealing with phase ambiguities that may arise in analyzing homodyne, heterodyne, and/or superheterodyne signals, and methods are disclosed for implementing the steps of the invention.
  • FIGS, la-lf depict in diagrammatic form one preferred embodiment of the apparatus of the present invention for measuring intrinsic optical properties of a gas, particularly its reciprocal dispersive power. 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.
  • a light beam 7 emitted from source 1 passes through a modulator 3 becoming light beam 9.
  • Modulator 3 is excited by a driver 5.
  • Source 1 is preferably a laser or like source of coherent radiation, preferably polarized, and having a wavelength ⁇ 1 .
  • Modulator 3 may for example be an acousto- optical device or a combination of acousto-optical devices with additional optics for selectively modulating polarization components of beam 7.
  • Modulator 3 preferably shifts the oscillation frequency of one linearly polarized component of beam 7 an amount f with respect to an orthogonally linearly polarized component, the directions of polarizations of the components denoted herein as x and y .
  • the x polarization component of beam 9 has an oscillation frequency shifted an amount f with respect to the y polarization component of beam 9 without departing from the spirit or scope of the present invention.
  • Modulator 4 is excited by a driver 6, similar to modulator
  • Source 2 similar to source 1, is preferably a laser or like source of polarized, coherent radiation, but preferably at a different wavelength, ⁇ 2 , having a known approximate harmonic relationship with respect to ⁇ x , i . e .
  • the x polarized component of beam 10 has an oscillation frequency shifted an amount f 2 with respect to the y polarized component of beam 10.
  • the directions of the frequency shifts of the x components of beams 9 and 10 are the same.
  • beams 9 and 10 may be provided alternatively by a single laser source emitting more than one wavelength, or by a single laser source combined with optical frequency doubling means, or any equivalent source configuration capable of generating light beams of two or more wavelengths. It will also be appreciated by those skilled in the art that one or both of the frequency shifts f x and f 2 may be the result of Zeeman splitting or like phenomena characteristic of the laser sources themselves.
  • beam 9 is subsequently reflected by mirror 53 becoming beam 11.
  • a portion of beam 10 is reflected by a beam splitter 54A, preferably a non polarizing type, as beam 12, and a second portion of beam 10 is transmitted by beam splitter 54A and subsequently reflected by mirror 54B becoming beam 212.
  • Beam 11 is incident on differential plane mirror interferometer 69 and beams 12 and 212 are incident on differential plane mirror interferometer group 70 comprised of two differential plane mirror interferometers.
  • Differential plane mirror interferometer 69 and differential plane mirror interferometer group 70 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift ⁇ 1 between the x and y components of beam 11, a phase shift ⁇ 2 between the x and y components of beam 12, and a phase shift ⁇ 3 between the x and y components of beam 212.
  • Measurement cell 90 is conveniently formed as a set of nested, concentric chambers in the form of a right circular cylinder, the inner chamber of which is evacuated to a vacuum and the outer occupied by the gas whose intrinsic optical properties are to be monitored.
  • 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 69 as shown in FIG. lb has eight exit/return beams 17, 25, 33, 41, 117, 125, 133, and 141. Beams 17, 25, 33, and 41 originating from one frequency component of beam 11, the first frequency component, comprise beams for one measurement leg and beams 117, 125, 133, and 141 originating from a second frequency component of beam 11 comprise beams for a second measurement leg. Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIG. lb by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIG. lb by dotted lines .
  • One differential plane mirror interferometer of differential plane mirror interferometer group 70 has four exit/return beams 18, 26, 118, and 126. Beams 18 and 26 originating from one frequency component, a first frequency component of beam 12 comprise beams for one measurement leg and beams 118 and 126 originating from a second frequency component of beam 12 comprise beams for a second measurement leg. Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. lc by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. lc by dotted lines. A second differential plane mirror interferometer of differential plane mirror interferometer group 70 has four exit/return beams 218, 226, 318, and 326.
  • Beams 218 and 226 originating from one frequency component, a first frequency component, of beam 212 comprise beams for one measurement leg and beams 318 and 326 originating from a second frequency component of beam 212 comprise beams for a second measurement leg.
  • Beams for which the first frequency component of beam 212 is the sole progenitor are indicated in FIG. lc by lines comprised of alternating dots and dashes and beams for which the second frequency component of beam 212 is the sole progenitor are indicated in FIG. lc by lines comprised of alternating dot pairs and dashes .
  • Beams 17, 25, 33, 41, 117, 125, 133, and 141 are incident on measurement cell 90, illustrated in FIG. Id, which results in beams 43 and 143.
  • Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIG. Id by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIG. Id by dotted lines.
  • Beams 43 and 143 contain information at wavelength ⁇ 1 about the optical path length through the gas whose reciprocal dispersive power is to be determined and about the optical path length through a vacuum, respectively.
  • beams 18, 26, 118, and 126 are incident on measurement cell 90, illustrated in FIG. le, which results in beams 28 and 128.
  • Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. le by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. le by dotted lines.
  • beams 218, 226, 318, and 326 are incident on measurement cell 90, as shown in FIG. le, which results in beams 228 and 328.
  • Beams for which the first frequency component of beam 212 is the sole progenitor are indicated in FIG. le by lines comprised of alternating dots and dashes and beams for which the second frequency component of beam 212 is the sole progenitor are indicated in FIG. le by lines comprised of alternating dot pairs and dashes.
  • Beams 28 and 228 contain information at wavelength ⁇ 2 about optical path lengths through the gas whose reciprocal dispersive power is to be determined and beams 128 and 328 contain information at wavelength ⁇ 2 about optical path lengths through a vacuum.
  • Beam 43 is reflected by mirror 63B, a portion of which is reflected by beamsplitter 63A, preferably a non polarizing type, to become one component of beam 45.
  • a portion of beam 143 is transmitted by beam splitter 63A to become a second component of beam 45.
  • Beam 45 is a mixed beam, the first and second components of beam 45 having the same linear polarizations. Beam 45 exits the differential plane mirror interferometer 69.
  • Beam 28 is reflected by mirror 58B, a portion of which is reflected by beamsplitter 58A, preferably a non polarizing beamsplitter, to become a first component of beam 30.
  • a portion of beam 128 is transmitted by beamsplitter 58A to become a second component of beam 30.
  • Beam 30 is a mixed beam, the first and second components of beam 30 having the same linear polarizations.
  • Beam 228 is reflected by mirror 58D, a portion of which is reflected by beam splitter 58C, preferably a non polarizing beamsplitter, to become a first component of beam 230.
  • a portion of beam 328 is transmitted by beamsplitter 58C to become a second component of beam 230.
  • Beam 230 is a mixed beam, the first and second components of beam 230 having the same linear polarizations.
  • Beams 30 and 230 exit differential plane mirror interferometer group 70.
  • phase shifts ⁇ , ⁇ 2 , and ⁇ 3 are related to the round-trip physical length Z_ of path of measurement path 97 or reference path 98 shown in FIGS. Id and le according to the formulae
  • n are the indices of refraction of gas in path i of measurement path 97 corresponding to wavenumber k , and the index of refraction in the reference path 98 has been set to 1.
  • the phase offsets ⁇ comprise all contributions to the phase shifts ⁇ e that are not related to the measurement path 97 or reference path 98.
  • the generalization to the case when p 1 ⁇ 2p 2 is a straight forward procedure.
  • the coefficients p and p 2 are preferably identical to the like-denoted coefficients p and p used to define the approximate harmonic relationship in Eq. (1) .
  • beams 45, 30, and 230 impinge upon photodetectors 85, 86, and 286, respectively, resulting in three interference signals, heterodyne signals s 1 , s 2 , and s 2 , respectively, preferably by photoelectric detection.
  • the signal s ⁇ corresponds to wavelength ⁇ 1
  • signals s 2 and s 3 correspond to the wavelength ⁇ 2 .
  • the signals s e have the form
  • Heterodyne signals s 1 , s 2 , and s 3 are transmitted as electronic signals 103, 104, and 304, respectively, to electronic processor 108 for analysis.
  • electronic processor 108 preferably comprises electronic processor 1081 for electronically adding the heterodyne signals s 2 and s 3 together to create a superheterodyne signal S , the first superheterodyne signal, having the mathematical form
  • the first superheterodyne signal S 1 may be rewritten as
  • the second term on the right hand side of Eq. (7) is a term that enters as a second order term in [A 2 - and
  • phase ⁇ 1 is in general quite small, differential plane mirror interferometer group 70 being comprised of two differential plane mirror interferometers with associated measurement and reference paths substantially the same. Combining Eqs. (2) and (9), the phase ⁇ ⁇ can be written as
  • ⁇ x is not sensitive to either displacements or tilts of either reflecting surfaces 95 or 96, a feature of differential plane mirror interferometers; not sensitive to changes in the mean temperature or pressure or to gradients in temperature or pressure of the gas in measuring path 97, a consequence of the paths in 90 associated with s 2 and of the paths in 90 associated with s 3 having center lines that are collinear in differential plane mirror interferometers; and not sensitive to composition of the gas in measuring path 97
  • the primary contributions to phase ⁇ ⁇ will be second order derivatives with respect to spatial coordinates of temperature and pressure of the gas and through air turbulence in measuring path 97. The magnitudes of the latter two contributions will generally be quite small, i.e. «1 rad., for applications such as high precision distance measuring interferometry .
  • electronic processor 108 further comprises electronic processor 1083 for electronically adding together the heterodyne signal s and the carrier signal C x from 1081 to create a second level superheterodyne signal S 2 , the second superheterodyne signal, having the mathematical form
  • the second superheterodyne signal S 2 may be rewritten as
  • the second superheterodyne signal S 2 is therefore comprised of a carrier signal C 2 of frequency v modulated by an envelope signal M 2 of frequency F and what can be a series of negligible secondary terms by proper adjustment of amplitude coefficients A ⁇ , A 2 , and A 3 , by keeping ⁇ x close to zero as described above, and by use of the proper phase in the extraction of the M 2 C 2 term.
  • electronic 108 preferably comprises processor 1085 to separate envelope signal M 2 from carrier signal C 2 , using rectification and filtering, signal squaring, or any of the like techniques for extracting an amplitude modulation and demodulating a carrier.
  • Electronic processor 108 further comprises a processor 1086 to determine the modulation phase ⁇ 2 using time-based phase detection or the like.
  • Electronic processor 108 additionally comprises processors 1082 to determine the phase shift ⁇ 1 .
  • the reciprocal dispersive power T of the gas defined as
  • L G and L v are the average physical lengths of measurement path 97 and reference path 98, respectively.
  • the approximate harmonic ratio can be expressed in terms of K and ⁇ from Eqs. (22) and (23) with the result
  • the ratio of the modulation phase ⁇ 2 and carrier phase ⁇ 2 has a value
  • Eq. (21) reduces to the more simple form [( ⁇ Pi- i)-(A ; - v)x] : 29 ) (- 2 + ⁇ 2 )
  • Eq. (29) is the equation used in the first preferred embodiment to compute the reciprocal dispersive power T .
  • the condition on the wavelengths ⁇ ⁇ and ⁇ 2 which leads to Eq. (29) from Eq. (21) expressed as an equation is
  • Eq. (30) is the basis for the conclusion that sources 1 and 2 need not be phase locked for the first preferred embodiment.
  • Eq. (30) is actually a weak condition when viewed in terms of a phase- locked requirement for sources 1 and 2.
  • the condition expressed by Eq. (30) written in terms of source frequencies v ⁇ ⁇ and v 2 instead of wavelengths ⁇ 1 and ⁇ 2 , respectively, is
  • electronic processing means 108 transmits to the computer 109 ⁇ 1 and ⁇ 2 as electronic signal 105 in either digital or analog format for the computation of T according to Eq. (29) .
  • the computation of T using Eq. (29) requires resolution of the phase redundancy in ⁇ 1 and ⁇ 2 .
  • the equivalent wavelengths comprising ⁇ 1 and ⁇ 2 are significantly larger than either of the wavelengths ⁇ ⁇ and ⁇ 2 and as a consequence, produces a significant simplification in a procedure implemented for resolution of phase redundancy in ⁇ 1 and ⁇ 2 .
  • the equivalent wavelengths ⁇ ⁇ and ⁇ ⁇ for ⁇ 1 and ⁇ 2 are
  • any one of several procedures may be easily employed to resolve the phase redundancy in ⁇ 1 and ⁇ 2 , given their equivalent wavelengths as expressed by Eqs. (35) and (36).
  • One procedure which may be employed to resolve the phase redundancy in ⁇ 1 and ⁇ 2 is based on the use of a series of measurement cells where the physical lengths for the measuring and reference paths of the series of measurement cells form a geometric progression.
  • the smallest or first physical length in the series will be approximately ⁇ /pA divided by the relative precision that the initial value of ⁇ ⁇ is known.
  • the physical length of the second measurement cell in the series will be approximately the length of the first measurement cell divided by the relative precision that ⁇ x is measured using the first measurement cell.
  • a typical physical length for the first measurement cell in the series is of the order of 0.5 mm
  • a typical physical length for the second measurement cell in the series is of the order of 50 mm
  • a typical physical length for a third measurement cell in the series if required is of the order of 5000 mm.
  • a second procedure is based upon the use of a source (not shown in FIGS, la-lf) of a series of known wavelengths and measuring ⁇ 1 and ⁇ 2 for these wavelengths .
  • the number of known wavelengths required for the resolution of the phase redundancy is generally comprised of a small set as a direct consequence of the relatively large equivalent wavelengths as expressed by Eqs. (35) and (36) .
  • a second reciprocal dispersive power, T 2 may also be defined for the gas where
  • first preferred embodiment with regard to T 2 is substantially the same as the description of first preferred embodiment with regard to r.
  • the intrinsic property of a gas represented by T may be obtained and subsequently used down stream in another form such as the ratio (n 1 - l)/(n 2 - 1) .
  • the ratio (n 1 - l)/(n 2 - 1) .
  • the ratio (n 1 - l)/( « 2 - 1) can also be expressed in terms of T or r and T 2 by the equations
  • FIG. lb depicts in schematic form one embodiment of the differential plane mirror interferometer 69 shown in FIG. la. It operates in the following way: Beam 11 is incident on beamsplitter 55A, preferably a polarizing beamsplitter, with a portion of beam 11 being transmitted as beam 13. A second portion of beam 11 is reflected by beam splitter 55A, subsequently reflected by mirror 55B, and then transmitted by half -wave phase retardation plate 79 as beam 113, the half-wave phase retardation plate 79 rotating the plane of polarization of the reflected portion of beam 11 by 90°. Beams 13 and 113 have the same polarizations but still have different frequencies.
  • Beam 13 and beams for which beam 13 is the sole progenitor are indicated in FIGS, lb and Id by dashed lines and beam 113 and beams for which beam 113 is the sole progenitor are indicated in FIGS, lb and Id by dotted lines.
  • the function of beamsplitter 55A and mirror 55B is to spatially separate the two frequency components of beam 11 using conventional polarization techniques.
  • Beams 13 and 113 enter polarizing beam splitter 71, which has a polarizing coating 73, and are transmitted as beams 15 and 115, respectively.
  • Beams 15 and 115 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 17 and 117, respectively.
  • Beams 17 and 117 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 15 and 115.
  • These beams are reflected by polarizing coating 73 to become beams 19 and 119, respectively.
  • Beams 19 and 119 are reflected by retroreflector 75 to become beams 21 and 121, respectively.
  • Beams 21 and 121 are reflected by polarizing coating 73 to become beams 23 and 123, respectively.
  • Beams 23 and 123 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 25 and 125, respectively.
  • Beams 25 and 125 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams the same as the original incident beams 15 and 115.
  • These beams are transmitted by polarizing coating 73 to become beams 27 and 127, respectively.
  • Beam 27 is reflected by mirrors 57A and 57B and beam 127 is reflected by mirrors 59C and 59D to become beams 29 and 129, respectively.
  • Beams 29 and 129 enter polarizing beam splitter 71 and are transmitted by polarizing beam splitter 71 with polarizing coating 73 as beams 31 and 131, respectively.
  • Beams 31 and 131 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 33 and 133, respectively.
  • Beams 33 and 133 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 31 and 131. These beams are reflected by polarizing coating 73 to become beams 35 and 135, respectively.
  • Beams 35 and 135 are reflected by retroreflector 75 to become beams 37 and 137, respectively.
  • Beams 37 and 137 are reflected by polarizing coating 73 to become beams 39 and 139, respectively.
  • Beams 39 and 139 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 41 and 141, respectively.
  • Beams 41 and 141 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams the same as the original incident beams 15 and 115.
  • These beams are transmitted by polarizing coating 73 to become beams 43 and 143, respectively.
  • Beams 43 and 143 contain information at wavelength ⁇ x about the optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about the optical path lengths through a vacuum, respectively.
  • FIG. lc depicts in schematic form one embodiment of differential plane mirror interferometer group 70 shown in FIG. la. It operates in the following way: Beam 12 is incident on beamsplitter 56A, preferably a polarizing beamsplitter, with a portion of beam 12 being transmitted as beam 14.
  • a second portion of beam 12 is reflected by beam splitter 56A, subsequently reflected by mirror 56B, and then transmitted by half-wave phase retardation plate 80 as beam 114, the half-wave phase retardation plate 80 rotating the plane of polarization of the reflected portion of beam 12 by 90°.
  • Beams 14 and 114 have the same polarizations but still have different frequencies. Beam 14 and beams for which beam 14 is the sole progenitor are indicated in FIGS, lc and le by dashed lines and beam 114 and beams for which beam 114 is the sole progenitor are indicated in FIGS, lc and le by dotted lines.
  • the function, in part, of beamsplitter 56A and mirror 56B is to spatially separate the two frequency components of beam 12 using conventional polarization techniques.
  • Beams 14 and 114 enter polarizing beam splitter 72, which has a polarizing coating 74, and are transmitted as beams 16 and 116, respectively.
  • Beams 16 and 116 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 18 and 118, respectively.
  • Beams 18 and 118 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 16 and 116. These beams are reflected by polarizing coating 74 to become beams 20 and 120, respectively.
  • Beams 20 and 120 are reflected by retroreflector 76 to become beams 22 and 122, respectively.
  • Beams 22 and 122 are reflected by polarizing coating 74 to become beams 24 and 124, respectively.
  • Beams 24 and 124 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 26 and 126, respectively.
  • Beams 26 and 126 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams the same as the original incident beams 16 and 116. These beams are transmitted by polarizing coating 74 to become beams 28 and 128, respectively.
  • Beams 28 and 128 contain information at wavelength ⁇ 2 about the optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about the optical path lengths through a vacuum, respectively.
  • Beam 28 is reflected by mirror 58B, and then a portion reflected by beam splitter 58A, preferably a non polarizing type, as a first component of beam 30.
  • Beam 128 is incident on beamsplitter 58A with a portion of beam 128 being transmitted as a second component of beam 30, the first and second components of beam 30 having the same linear polarizations but still having different frequencies .
  • Beam 212 is incident on beamsplitter 56A with a portion of beam 212 being transmitted as beam 214.
  • a second portion of beam 212 is reflected by beam splitter 56A, subsequently reflected by mirror 56B, and then transmitted by half-wave phase retardation plate 80 as beam 314, the half-wave phase retardation plate 80 rotating the plane of polarization of the reflected portion of beam 212 by 90°.
  • Beams 214 and 314 have the same polarizations but still have different frequencies.
  • Beam 214 and beams for which beam 214 is the sole progenitor are indicated in FIGS, lc and le by lines comprised of alternating dots and dashes and beam 314 and beams for which beam 314 is the sole progenitor are indicated in FIGS, lc and le by lines comprised of alternating dot pairs and dashes.
  • the function, in part, of beamsplitter 56A and mirror 56B is to spatially separate the two frequency components of beam 212 using conventional polarization techniques.
  • Beams 214 and 314 enter polarizing beam splitter 72, which has a polarizing coating 74, and are transmitted as beams 216 and 316, respectively.
  • Beams 216 and 316 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 218 and 318, respectively.
  • Beams 218 and 318 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 216 and 316. These beams are reflected by polarizing coating 74 to become beams 220 and 320, respectively.
  • Beams 220 and 320 are reflected by retroreflector 76 to become beams 222 and 322, respectively.
  • Beams 222 and 322 are reflected by polarizing coating 74 to become beams 224 and 324, respectively.
  • Beams 224 and 324 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 226 and 326, respectively.
  • Beams 226 and 326 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams the same as the original incident beams 216 and 316. These beams are transmitted by polarizing coating 74 to become beams 228 and 328, respectively.
  • Beams 228 and 328 contain information at wavelength ⁇ 2 about the optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about the optical path lengths through a vacuum, respectively.
  • Beam 228 is reflected by mirror 58D, and then a portion reflected by beam splitter 58C, preferably a non polarizing type, as a first component of beam 230.
  • Beam 328 is incident on beamsplitter 58C with a portion of beam 328 being transmitted as a second component of beam 230, the first and second components of beam 230 having the same linear polarizations but still having different frequencies .
  • FIGS. 2a-2b depict in schematic form a variant of the first preferred embodiment of the present invention for measuring the reciprocal dispersive power or other intrinsic optical properties of a gas.
  • the description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the variant of the first preferred embodiment is the same as the description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment .
  • beam 9 is reflected by mirror 53 becoming beam 11.
  • Beam 11 is incident on differential plane mirror interferometer 69.
  • a portion of beam 10 is reflected by a beam splitter 54A, preferably a non polarizing type, as beam 12, and a portion of beam 10 is transmitted by beam splitter 54A and subsequently reflected by mirror 54B becoming beam 212.
  • Beams 12 and 212 are incident on differential plane mirror interferometer group 170 comprised of two differential plane mirror interferometers. Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. 2b by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. 2b by dotted lines.
  • Differential plane mirror interferometer 69 and differential plane mirror interferometer group 170 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift ⁇ x between the x and y components of beam 11 and a phase shift ( ⁇ 2 + ⁇ 3 )/2 between the x and y components of beam
  • Differential plane mirror interferometer 69 is the same as differential plane mirror interferometer 69 of the first preferred embodiment.
  • the paths of the optical beams in differential plane mirror interferometer group 170 are the same as the paths of the optical beams in differential plane mirror interferometer group 70 of the first preferred embodiment up through and including the generation of beams 28, 228, 128, and 328 as illustrated in FIG. 2b.
  • beams 28, 228, 128, and 328 are combined optically to generate beam 32.
  • Beam 32 is a mixed beam detected by detector 186, beam 32 being comprised of two components having the same polarizations but different frequencies.
  • the heterodyne signal generated in detector 186, preferably by photoelectric detection, from the mixed beam 32 is transmitted to electronic processor 1108 as electronic signal 1104.
  • Beam 32 is generated from beams 28, 228, 128, and 328 by the following steps.
  • Beam 28 is reflected by mirror 60B, a portion subsequently reflected by mirror 60A, preferably a 50/50 non polarizing beam splitter, to form one part of beam 30A.
  • a portion of beam 228 is transmitted by beam splitter 60A to form a second part of beam 30A, the first and second parts of beam having the same polarization and the same frequencies.
  • beam splitter 60A is a 50/50 beam splitter
  • optical paths lengths for beams 28 and 228 are the same, substantially all of the beams 28 and 228 will be present in beam 30A because of constructive interference.
  • Beam 128 is reflected by mirror 60D, a portion subsequently reflected by mirror 60C, preferably a 50/50 non polarizing beam splitter, to form one part of beam 130A.
  • a portion of beam 328 is transmitted by beam splitter 60C to form a second part of beam 130A, the first and second parts of beam 130A having the same polarizations and the same frequencies.
  • the amplitudes of beams 128 and 328 are the same, to the extent that beam splitter 60C is a 50/50 beam splitter, and to the extent that the optical paths lengths for beams 128 and 328 are the same, substantially all of the beams 128 and 328 will be present in beam 130A because of constructive interference.
  • Beams 30A and 130A also have the same polarizations but different frequencies. Beam 30A and 130A contain information at wavelength ⁇ 2 about optical path lengths through the gas and about optical path lengths through a vacuum, respectively.
  • beam 30A is reflected by mirror 62B and then a portion of beam 30A reflected by beamsplitter 62A, preferably a non polarizing beamsplitter, to become a first component of beam 32.
  • a portion of beam 130A is transmitted by beamsplitter 62A to become a second component of beam 32.
  • Beam 32 is a mixed beam, the first and second components of beam 32 having the same polarizations but different frequencies.
  • FIGS. 3a-3d depict in diagrammatic form the second preferred embodiment of the present invention for measuring the reciprocal dispersive power or other intrinsic optical properties of a gas.
  • the description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the second embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment of the present invention.
  • beam 9 is reflected by mirror 53 becoming beam 11 and beam 10 is reflected by mirror 54 becoming beam 12.
  • Beam 11 is incident on differential plane mirror interferometer 269 and beam 12 is incident on differential plane mirror interferometer 270.
  • Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIG. 3b by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIG. 3b by dotted lines.
  • Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. 3c by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. 3c by dotted lines.
  • Differential plane mirror interferometers 269 and 270 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift ⁇ 1 between the x and y components of beam 11 and a phase shift ⁇ 2 between the x and y components of beam 12.
  • Differential plane mirror interferometer 269 has four exit/return beams 17, 25, 117, and 125 as shown in FIG. 3b.
  • Beams 17 and 25 originating from one frequency component of beam 11 comprise one measurement leg and beams 117 and 125 originating from a second frequency component of beam 11 comprise a second measurement leg.
  • Differential plane mirror interferometer 270 has four exit/return beams 18, 26, 118, and 126 as shown in FIG. 3c.
  • Beams 18 and 26 originating from one frequency component of beam 12 comprise one measurement leg and beams 118 and 126 originating from a second frequency component of beam 12 comprise a second measurement leg.
  • Beams 17, 25, 117, and 125 are incident on measurement cell 90, the same as described in detail in FIG. Id which results in beams 27 and 127.
  • Beams 27 and 127 contain information at wavelength ⁇ 1 about the optical path length through the gas whose reciprocal dispersive power r is to be determined and about the optical path lengths through a vacuum, respectively.
  • Beams 18, 26, 118, and 126 are incident on measurement cell 90, the same as described in detail in FIG. le which results in beams
  • Beam 28 and 128 contain information at wavelength ⁇ 2 about optical path lengths through the gas and about optical path lengths through a vacuum, respectively.
  • phase shifts ⁇ 1 and ⁇ 2 are related to the round-trip physical length Z. of path i of measurement path 97 or reference path 98 shown in FIGS. Id and le according to the formulae
  • Beam 27 is reflected by mirror 63B and then a portion reflected by beamsplitter 63A, preferably a non polarizing beamsplitter, to become a first component of phase shifted beam 29A.
  • a portion of beam 127 is transmitted by beamsplitter 63A to become a second component of phase- shifted beam 29A.
  • Phase shifted beam 29A is a mixed beam, the first and second components of beam 29A having the same polarizations but different frequencies.
  • Beam 28 is reflected by mirror 58B and then a portion reflected by beamsplitter 58A, preferably a non polarizing beamsplitter, to become a first component of phase-shifted beam 30.
  • a portion of beam 128 is transmitted by beamsplitter 58A to become a second component of phase- shifted beam 30.
  • Phase shifted beam 30 is a mixed beam, the first and second components of beam 30 having the same polarizations but different frequencies.
  • phase-shifted beams 29A and 30 impinge upon photodetectors 185 and 86, respectively, resulting in two interference signals, heterodyne signals s ⁇ and s 2 , respectively, preferably by photoelectric detection.
  • the signal 5 , 1 corresponds to wavelength ⁇ x and signal s 2 corresponds to the wavelength ⁇ 2 .
  • the signals s ( have the form expressed by Eq. (4) with time-dependent arguments . ( (t) given by Eq. (5) .
  • Heterodyne signals s 1 and s 2 are transmitted to electronic processor 208 for analysis as electronic signals 203 and 104, respectively, in either digital or analog format.
  • electronic processing means 208 preferably comprises means 281 for electronically multiplying time-dependent arguments ⁇ x (t) and 2 (t) of heterodyne signals s ⁇ and s 2 , respectively, by coefficients p ⁇ and p 2 , respectively, so as to create two modified heterodyne signals 7 X and ? 2 having the form
  • the multiplication may be achieved by any one of the conventional frequency multiplying techniques commonly known in the art, such as signal squaring followed by electronic filtering. It will be understood by those skilled in the art that such electronic multiplying techniques may introduce offsets and modifications in signal strength that may be neglected in the present, simplified description of the analysis technique of the present invention. It is noteworthy that the coefficients p l and p 2 are preferably identical to the like-denoted coefficients p ⁇ and p 2 used to define the approximate harmonic relationship in Eq. (1) .
  • electronic processing means 108A preferably comprises means 108b for electronically adding two modified heterodyne signals and " s 2 together to create a superheterodyne signal S 2 having the mathematical form
  • M 2 cos(2 ⁇ Ft + ⁇ ⁇ , (46;
  • Superheterodyne signal S 2 is therefore a carrier signal C 2 of frequency v modulated by an envelope signal M 2 of frequency F .
  • modified heterodyne signals 7 and s 2 are of different amplitude, the resulting mathematical expression is more complicated, but nonetheless may be described in terms of a carrier signal modulated by an envelope signal.
  • modified heterodyne signals 7 1 and 7 2 have the same amplitude.
  • the remaining description of the second embodiment of the present invention is the same as the description given for corresponding steps of the first embodiment of the present invention.
  • Alternative signal S 2M may be generated by selecting the appropriate term in the binomial expansion of (s ⁇ +.s 2 ) through the use of phase sensitive detection. Alternative signal S 2M would then be comprised of the sum, rather than the product, of two signals having frequencies F and v. Such a processing technique would prove advantageous for example if it were found useful to replace detectors 185 and 86 in FIG. 3a with a single detector.
  • FIGS. 4a-4d depict in diagrammatic form the third preferred embodiment of the present invention for measuring the reciprocal dispersive power or other intrinsic optical properties of a gas.
  • the description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the third embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment of the present invention.
  • beam 9 is reflected by mirror 53 becoming beam 11 and beam 10 is reflected by mirror 54 becoming beam 12.
  • Beam 11 is incident on differential plane mirror interferometer 369 and beam 12 is incident on differential plane mirror interferometer 270.
  • Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIGS. 4b and 4c by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIGS. 4b and 4c by dotted lines.
  • Differential plane mirror interferometers 269 and 270 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift ⁇ 1 between the x and y components of beam 11 and a phase shift ⁇ 2 between the x and y components of beam 12.
  • Differential plane mirror interferometer 369 has eight exit/return beams, four exit/return beams 417, 425, 517, and 525 as shown in FIG. 4b and four exit/return beams 433, 441, 533, and 541 as shown in FIG. 4c.
  • Beams 417, 425, 433, and 441 originating from one frequency component of beam 11 comprise one measurement leg and beams 517, 525, 533, and 541 originating from a second frequency component of beam 11 comprise a second measurement leg.
  • Beams 417, 425, 433, 441, 517, 525, 533, and 541 are incident on measurement cell 90, as described in detail in FIGS. 4b and 4c, which results in beams 443 and 543.
  • Beam 443 and 543 contain information at wavelength ⁇ about optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about optical path lengths through a vacuum, respectively.
  • Differential plane mirror interferometer 270 has four exit/return beams 18, 26, 118, and 126 the same as for the second preferred embodiment as shown in FIG. 3c.
  • Beams 18 and 26 originating from one frequency component of beam 12 comprise one measurement leg and beams 118 and 126 originating from a second frequency component of beam 12 comprise a second measurement leg.
  • Beams 18, 26, 118, and 126 are incident on measurement cell 90, which results in beams 28 and 128.
  • Beam 28 and 128 contain information at wavelength ⁇ 2 about optical path lengths through the gas and about optical path lengths through a vacuum, respectively.
  • the magnitude of phase shifts ⁇ 1 and ⁇ 2 are related to the round-trip physical length Z, of path i of measurement path 97 or reference path 98 shown in FIGS. Id and le according to the formulae
  • Half-wave phase retardation plate 179C and Faraday rotator 179A each rotate the polarization of beam 443 by 45° so that the first component of phase shifted beam 445 is orthogonally polarized to the polarization of beam 443.
  • Beam splitter 61A is preferably a polarizing beam splitter and beam splitter 61B is preferably a non polarizing beam splitter.
  • Beam 543 is transmitted by half-wave phase retardation plate 179D and Faraday rotator 179B, reflected by beam splitter 61C, reflected by mirror 61D, reflected by beam splitter 61B, and then reflected by mirror 63 to become a second component of phase shifted beam 445.
  • Half-wave phase retardation plate 179D and Faraday rotator 179B each rotate the polarization of beam 543 by 45° so that the second component of phase shifted beam 445 is orthogonally polarized to the polarization of beam 543.
  • Beam splitter 61C is preferably a polarizing beam splitter.
  • Phase shifted beam 445 is a mixed beam, the first and second components of phase shifted beam 445 having the same polarizations but different frequencies.
  • Beam 28 is reflected by mirror 58B and then a portion reflected by beamsplitter 58A, preferably a non polarizing beamsplitter, to become a first component of phase-shifted beam 30.
  • a portion of beam 128 is transmitted by beamsplitter 58A to become a second component of phase- shifted beam 30.
  • Phase shifted beam 30 is a mixed beam, the first and second components of phase shifted beam 30 having the same polarizations but different frequencies.
  • phase-shifted beams 445 and 30 impinge upon photodetectors 485 and 86, respectively, resulting in two interference signals, heterodyne signals ⁇ and s 2 , respectively, preferably by photoelectric detection.
  • the signal s ⁇ corresponds to wavelength ⁇ and signal s 2 corresponds to the wavelength ⁇ 2 .
  • the signals s have the form expressed by Eq. (4) with time-dependent arguments a e (t) given by Eq. (5) .
  • Heterodyne signals s 1 and s 2 are transmitted to electronic processor 408 for analysis as electronic signals 403 and 104, respectively, in either digital or analog format.
  • electronic processing means 408 preferably comprises means 1084 for electronically adding the two heterodyne signals s 1 and s 2 together to create a superheterodyne signal S 2 having the mathematical form
  • ⁇ 2 ( ⁇ 1 + ⁇ 2 ) , (58)
  • Superheterodyne signal S 2 is therefore a carrier signal C 2 of frequency v modulated by an envelope signal M 2 of frequency F.
  • Those skilled in the art will appreciate that when heterodyne signals s 1 and s 2 are of different amplitude, the resulting mathematical expression is more complicated, but nonetheless may be described in terms of a carrier signal modulated by an envelope signal. For simplicity in the present disclosure, it is assumed that heterodyne signals s 1 and s 2 have the same amplitude.
  • the operation of differential plane mirror interferometer 369 is the same as the operation described for differential plane mirror interferometer 69 except for the means used to separate the two frequency components of input beam 11 and the means used to create the mixed output beam 445. Referring to FIG.
  • a portion of beam 11 is reflected by beam splitter 55A, preferably a polarizing beam splitter, reflected by mirror 55B, transmitted by half-wave phase-retardation plate 79, transmitted by beam splitter 61C, preferably a polarizing beam splitter, transmitted by Faraday rotator 179B, and transmitted by half-wave phase-retardation plate 179D to become beam 513.
  • the Faraday rotator 179B and the half- wave phase-retardation plate 179D rotate the plane of polarization of transmitted beams by ⁇ 45° and +45°, respectively, producing no net rotation of the plane of polarization of transmitted beams.
  • a portion of beam 11 is transmitted by beam splitter 55A, transmitted by beam splitter 61A, preferably a polarizing beamsplitter, transmitted by Faraday rotator 179A, and transmitted by half-wave phase-retardation plate 179C to become beam 413.
  • the Faraday rotator 179A and the half-wave phase- retardation plate 179C rotate the plane of polarization of transmitted beams by ⁇ 45° and +45°, respectively, producing no net rotation of the plane of polarization of transmitted beams.
  • Half-wave phase-retardation plate 79 rotates the plane of polarization of transmitted beam by 90° so that beams 413 and 513 have the same polarizations but have different frequencies.
  • the purpose of the Faraday rotators 179A and 179B and the half-wave phase- retardation plates 179C and 179D is to have substantially no effect on the properties of beams 413 and 513 but to rotate the polarizations of beams 443 and 543 by 90° as previously described so as to achieve an efficient spatial separation of beams 443 and 543 from the path of beam 11.
  • the remaining description of the third embodiment is the same as the description given for corresponding steps of the first embodiment of the present invention.
  • the second three preferred embodiments of the present invention and variant thereof, the preferred fourth preferred embodiment, the variant of the fourth preferred embodiment, the fifth preferred embodiment, and the sixth preferred embodiment of the present invention illustrated in FIGS. 5a-5d, 6a-6b, 7a-7b, and 8a-8b, respectively, are all embodiments to measure a reciprocal dispersive power when the condition set fourth in Eq. (30) for the first three preferred embodiments and variant thereof, the preferred first preferred embodiment, the variant of the first preferred embodiment, the second preferred embodiment, and the third preferred embodiment of the present invention, is not satisfied, i.e.
  • the approximate harmonic ratio preferably the ratio (K/ ⁇ ) , must be either known or measured in accordance with Eq.
  • each of the first three preferred embodiments and variant thereof can be converted from an apparatus and method for measuring a reciprocal dispersive power T to an apparatus and method for measuring the ratio (K/ ⁇ ) by changing the measurement cell of a given embodiment so that the measuring path through the gas has substantially zero physical length, a property demonstrated in the following descriptions.
  • each of the second three preferred embodiments and variant thereof are comprised of an unmodified and a modified apparatus and method from one of the first three preferred embodiments and variant thereof, the modified apparatus and method being comprised of the unmodified apparatus and method with a modified measurement cell.
  • FIGS. 5a-5d depict in diagrammatic form the fourth preferred embodiment of the present invention.
  • the description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the fourth preferred embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment of the present invention except that the condition on wavelengths ⁇ ⁇ and ⁇ 2 expressed by Eq. (30) is replaced by the condition set fourth in Eq. (61) .
  • the fourth preferred embodiment is comprised in part of the same apparatus and method as for the first preferred embodiment and of additional means for determination of the ratio ⁇ K/ ⁇ ) ⁇
  • the additional means for determination of the ratio (K/ ⁇ ) is the same as the apparatus and method of the first preferred embodiment except for the measurement cell. Consequently, a number of elements of the apparatus shown in FIGS. 5a-5d for determination of the ratio (K/ ⁇ ) perform analogous operations as apparatus for determination of reciprocal dispersive power T of the third preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio
  • the measurement cell 90b of the fourth preferred embodiment is shown in FIGS. 5b and 5c.
  • the description of measurement cell 90b is the same as that for measurement cell 90 except with respect to the coatings on surfaces 95b and 96b.
  • surface 95b is coated so as to reflect with high efficiency beams 17b, 25b, 33b, and 41b and to transmit with high efficiency beams 117b, 125b, 133b, and 141b.
  • surface 96b is coated so as to reflect with high efficiency beams 18b, 26b, 218b, and 226b and to transmit with high efficiency beams 118b, 126b, 318b, and 326b.
  • the differences in the measurement cells 90b and 90 lead to modifications of Eqs. (2) such that the magnitude of phase shifts ⁇ lb , ⁇ 2b , and ⁇ 3b are related to the round-trip physical length Z, of path i of reference path
  • a first superheterodyne signal S lb and a second superheterodyne signal S 2b are generated by electronic processors 1081b, 1083b, and 1084b, electronic processors 1081b, 1083b, and 1084b performing analogous operations on heterodyne signals s lb , s 2h , and s 3b of the fourth preferred embodiment the same as electronic processors 1081, 1083, and 1084 perform on heterodyne signals s 1 , s 2 , and s 3 of the first preferred embodiment.
  • the second superheterodyne signal S 2b is comprised of a carrier signal C 2b of frequency v modulated by an envelope signal M 2b of frequency F where
  • ⁇ 2b ( ⁇ ib+ ⁇ i b)/ ⁇ lb (66)
  • the quantities K and ⁇ are related to the carrier phase ⁇ 2b and the modulation phase ⁇ 2b according to the formulae
  • ⁇ 2b ⁇ 2 P ⁇ + p 2 ⁇ 2b +p 3 ⁇ 3b )/4 (72)
  • Eqs. (69) and (70) show that within a multiplicative factor (l/Z) and phase offset terms, ⁇ and K are equal to the carrier phase ⁇ 2b and the modulation phase ⁇ 2b , respectively, which is the basis for referring in the description of the first preferred embodiment to K and ⁇ as the vacuum superheterodyne wavenumber and the vacuum carrier wavenumber, respectively.
  • the ratio (K/ ⁇ ) can be expressed by the formula
  • the ratio (K/ ⁇ ) is obtained by substantially dividing ⁇ 2b by ⁇ 2b without the requirement of an accurate measurement of Z to the same precision as required for (K/ ⁇ ) .
  • the phase redundancy of ⁇ 2b as well as ⁇ 2b can be determined as part of the same procedure used to remove the phase redundancy of ⁇ 1 and ⁇ 2 in the unmodified apparatus and method of the first preferred embodiment incorporated as part of the fourth preferred embodiment.
  • the procedure to determine the phase redundancy ⁇ 2b and ⁇ 2b will generally not introduce additional complexity beyond that present in the procedure used to remove the phase redundancy of ⁇ x and ⁇ 2 when ⁇ 1 , ⁇ 2 , and Z are known with relative precisions of ⁇ (f ⁇ -l).
  • the reciprocal dispersive power T is subsequently obtained using Eq. (21) .
  • the remainder of the description of the fourth preferred embodiment is the same as that given for corresponding aspects of the first preferred embodiment .
  • FIGS. 6a- 6b depict in diagrammatic form a variant of the fourth preferred embodiment of the present invention for measuring the reciprocal dispersive power of a gas.
  • the description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the variant of the fourth embodiment is the same as that for description of the sources of light beams 9 and 10 for the fourth preferred embodiment of the present invention.
  • the ratio (K/ ⁇ j has to be measured in the variant of the fourth preferred embodiment, the same as in the fourth preferred embodiment, in order to achieve the required accuracy in the determination of a refractive-dispersion constant.
  • the variant of the fourth embodiment is comprised in part of the same apparatus and method as for the variant of the first preferred embodiment and of additional means for determination of the ratio (K/ ⁇ ) .
  • the additional means for determination of the ratio (K/ ⁇ ) is the same as the apparatus and method of the variant of the first preferred embodiment except for the measurement cell. Consequently, a number of elements of the apparatus shown in FIGS. 6a-6b for determination of the ratio (K/ ⁇ ) perform analogous operations as apparatus for determination of reciprocal dispersive power T of the variant of the first preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio (K/ ⁇ j .
  • the measurement cell 90b of the variant of the fourth preferred embodiment is the same as the measurement cell 90b of the fourth preferred embodiment. Consequently, the remaining description of the variant of the fourth preferred embodiment is the same as the description given for corresponding aspects of the fourth preferred embodiment.
  • FIGS. 7a-7b depict in diagrammatic form the fifth preferred embodiment of the present invention for measuring the reciprocal dispersive power r .
  • the description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the fifth embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the fourth preferred embodiment of the present invention.
  • the ratio (K/ ⁇ ) has to be measured in the preferred fifth embodiment in order to achieve the required accuracy in the determination of a reciprocal dispersive power T .
  • the fifth embodiment is comprised in part of the same apparatus and method as for the second preferred embodiment and of additional means for determination of the ratio (K/ ⁇ ) .
  • the additional means for determination of the ratio (K/ ⁇ ) is the same as the apparatus and method of the second preferred embodiment except for the measurement cell.
  • the measurement cell 90b is the same as the measurement cell 90b of the fourth preferred embodiment. Consequently, a number of elements of the apparatus shown in FIGS. 7a-7b for determination of the ratio (K/ ⁇ ) perform analogous operations as apparatus for determination of reciprocal dispersive power T of the second preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio (K/ ⁇ .
  • a superheterodyne signal S 2b is generated by electronic processors 281b and 1084b, electronic processors 281b and 1084b performing analogous operations on heterodyne signals s lb and s 2b of the fifth preferred embodiment the same as electronic processors 281 and 1084 perform on heterodyne signals s and s 2 of the second preferred embodiment.
  • the superheterodyne signal S 2b is comprised of a carrier signal C 2b of frequency v modulated by an envelope signal M 2b of frequency F where
  • the quantities K and ⁇ are related to the carrier phase ⁇ 2b and the modulation phase ⁇ 2b according to the formulae
  • FIGS. 8a-8b depict in diagrammatic form the sixth preferred embodiment of the present invention for measuring the reciprocal dispersive power r .
  • the description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the sixth embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the fourth preferred embodiment of the present invention.
  • the ratio (K/ ⁇ j has to be measured in the preferred sixth embodiment in order to achieve the required accuracy in the determination of the reciprocal dispersive power T .
  • the sixth embodiment is comprised in part of the same apparatus and method as for the third preferred embodiment and of additional means for determination of the ratio (K/ ⁇ ) .
  • the additional means for determination of the ratio (K/ ⁇ ) is the same as the apparatus and method of the third preferred embodiment except for the measurement cell .
  • the measurement cell 90b is the same as the measurement cell 90b of the fourth preferred embodiment. Consequently, a number of elements of the apparatus shown in FIGS. 8a-8b for determination of the ratio (K/ ⁇ ) perform analogous operations as apparatus for determination of reciprocal dispersive power F of the second preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio (K/ ⁇ ) .
  • a superheterodyne signal S 2b is generated by electronic processor 1084b, electronic processor 1084b performing analogous operations on heterodyne signals s lb and ,s 2b of the sixth preferred embodiment the same as electronic processors 1084 perform on heterodyne signals s and s 2 of the third preferred embodiment.
  • the superheterodyne signal S 2b is comprised of a carrier signal C 2b of frequency v modulated by an envelope signal M 2b of frequency F where
  • the quantities K and ⁇ are related to the carrier phase ⁇ 2b and the modulation phase ⁇ 2b according to the formulae
  • the ratio (K/ ⁇ ) is obtained from Eqs . ( 93 ) and ( 94 ) as
  • FIGS, la-le, 2a-2b, 3a-3c, 4a- 4c, 5a-5c, 6a, 7a, and 8a depict six preferred embodiments and two variants thereof of the present invention wherein all of the optical beams for an embodiment are in a single plane.
  • modifications using multiple planes can be made to one or more of the six preferred embodiments and two variants thereof without departing from the scope or spirit of the invention.
  • the six preferred embodiments and two variants thereof of the present invention have measurement cells 90 or 90b wherein the measurement paths for ⁇ x and ⁇ 2 have the same physical lengths and the reference paths for ⁇ ⁇ and ⁇ 2 have the same physical lengths. It will be appreciated by those skilled in the art that the measurement paths for ⁇ 1 and ⁇ 2 can have different physical lengths and the reference paths for ⁇ j ⁇ and ⁇ 2 can have different physical lengths without departing from the scope and spirit of the present invention as defined in the claims.
  • the measurement paths for ⁇ 1 and ⁇ 2 can be physically displaced one from the other and the reference paths for ⁇ 1 and ⁇ 2 can be physically displaced one from the other without departing from the scope and spirit of the present invention as defined in the claims.
  • the six preferred embodiments and two variants thereof of the present invention are all configured for use of heterodyne detection. It will be appreciated by those skilled in the art that homodyne detection can be employed in each of the six preferred embodiments and two variants thereof without departing from the scope and spirit of the present invention as defined in the claims. Homodyne receivers would be employed such as disclosed in commonly owned U.S. Pat. No.
  • the second set of preferred embodiments of the present invention and variant thereof measure the ratio ⁇ K/ ⁇ ) and use the measured value of (K/ ⁇ ) in the computation of the reciprocal dispersive power T .
  • the measured value of (K/ ⁇ ) can be used as an error signal in a feedback system such the condition expressed by Eq. (30) is satisfied without departing from the scope and spirit of the present invention as defined in the claims.
  • the measured value of (K/ ⁇ ) in the feedback system is sent to either source 1 or source 2 and used to control the respective wavelength of either source 1 or source 2, for example by controlling the injection current and/or temperature of a diode laser or the cavity frequency of an external cavity diode laser.
  • differential plane mirror interferometers and the measurement cell may be configured such that the light beams corresponding to two or more differing wavelengths may enter and exit from the same end of the measurement cell in contrast to opposite ends as disclosed in the preferred embodiments and variants thereof without departing from the scope or spirit of the invention as defined in the claims.
  • FIG. 9 is a generalized flowchart depicting via blocks 600-626 various steps for practicing an inventive method for measuring intrinsic optical properties of a gas, particularly its reciprocal dispersive power. While it will be evident that the inventive method depicted in FIG. 9 may be carried out using the inventive apparatus disclosed hereinabove, it will also be apparent to those skilled in the art that it may also be implemented with apparatus other than that disclosed. For example, it will be apparent that one need not use a concentric measurement cell arrangement such as that used in the preferred embodiments, but rather may use more conventional interferometric arrangements so long as the required reference and measurement legs are present. In addition, it will be evident that one may use either a homodyne approach or one in which heterodyning techniques are advantageously employed.
  • many of the steps in FIG. 9 may be carried out via appropriate software run on a general purpose computer or a suitably programmed microprocessor either of which may be used to control other elements of the system as needed.
  • a general purpose computer or a suitably programmed microprocessor either of which may be used to control other elements of the system as needed.
  • one starts in block 600 by providing two or more light beams having different wavelengths which preferably have an approximate harmonic relationship as previously described.
  • the light beams are separated into components which in block 604 are preferably altered by either polarization or spatial encoding, or frequency shifting or both.
  • the light beams may simply be left unaltered and passed through to block 606.
  • the relationship of the wavelengths of the light beams may be monitored and if their wavelengths are not within the limits previously discussed, one can adopt corrective measures to compensate from departures of the relationship of the wavelengths from the desired relationship of the wavelengths. Either the departures can be used to provide feedback to control the wavelengths of the light beam sources or corrections can be established and used in subsequent calculations which are influenced by departures or some combination of both approaches can be implemented.
  • the previously generated light beam components are introduced into the interferometer legs so that each component has its phase shifted based on the optical path length it experiences in traveling through the physical length of its assigned leg.
  • the physical length for a commonly related pair of components is the same.
  • the beams After the beams emerge from block 608, they are combined in block 610 to generate a mixed optical signal. These mixed optical signals are then sent to block 612 where by means of photodetection corresponding electrical signals, preferably heterodyne, are generated, and these electrical signals contain information about the relative phases between the light beam components. Preferably the electrical signals are heterodyne signals brought about by previously frequency shifting treatment.
  • the electrical signals may be analyzed to extract relative phase information which can then be passed on to blocks 616-620 or, preferably, superheterodyne signals are generated for this purpose. Alternatively, depending on the wavelength relationships between the original beams and the optical paths over which they subsequently traveled, modified heterodyne signals are generated prior to making superheterodyne signals .
  • any phase ambiguities in homodyne, heterodyne, and/or superheterodyne signals are resolved, preferably by means and calculations previously elaborated in connection with describing the preferred apparatus.
  • the intrinsic optical properties including the relative dispersive power are calculated, corrections are applied as previously decided, and output signals are generated for subsequent downstream applications or data format requirements.

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Abstract

L'invention concerne un appareil et un procédé interférométriques permettant de mesurer et de contrôler les propriétés optiques intrinsèques d'un gaz, notamment le pouvoir dispersant réciproque du gaz, de manière à permettre l'utilisation des informations relatives aux propriétés du gaz dans des applications aval, telles que dans des instruments interférométriques de mesure de distance, afin d'augmenter la précision par correction de l'indice de réfraction du gaz et notamment des effets de turbulence dus à l'environnement et à l'air dans le chemin de mesure. L'appareil comprend une cellule de mesure concentrique présentant une chambre intérieure contenant un vide entouré d'un espace extérieur occupé par le gaz. Des miroirs présentant une sélectivité de longueur d'onde sont agencés à chaque extrémité de la cellule de mesure et fonctionnent conjointement avec des interféromètres à miroir plan pour changer la phase de composantes polarisées hortogonalement de faisceaux de lumière de longueurs d'ondes différentes introduits dans la cellule de mesure à partir des extrémités opposées de la cellule. De préférence, les composantes polarisées sont décalées en fréquence pour faciliter la production de signaux hétérodynes et superhétérodynes contenant des informations relatives aux propriétés optiques intrinsèques du gaz. Les signaux hétérodynes et superhétérodynes sont analysés électroniquement par un ordinateur polyvalent programmé à cette fin ou à partir d'un microprocesseur programmé spécialement.
PCT/US1998/019855 1997-10-02 1998-09-23 Procede et appareil interferometriques WO1999018424A1 (fr)

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Publication number Priority date Publication date Assignee Title
WO1999042786A1 (fr) 1998-02-23 1999-08-26 Zygo Corporation Appareil et procedes pour la mesure des proprietes optiques intrinseques d'un gaz
JP2002543372A (ja) * 1999-04-28 2002-12-17 ザイゴ コーポレイション 屈折率変動を補償する干渉装置および方法
CN116379961A (zh) * 2023-06-05 2023-07-04 广东普洛宇飞生物科技有限公司 一种相位测量系统及方法

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WO2008051232A2 (fr) * 2006-10-25 2008-05-02 Zygo Corporation Compensation des effets de perturbations atmosphériques en métrologie optique

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EP0094836A1 (fr) * 1982-05-18 1983-11-23 National Research Development Corporation Appareil et méthode pour mesurer un indice de réfraction
WO1991003729A1 (fr) * 1989-09-08 1991-03-21 Michael John Downs Appareil mesurant l'indice de refraction des milieux gazeux
DE19727404A1 (de) * 1996-08-20 1998-02-26 Zygo Corp Überlagerungsverfahren und Vorrichtung zur Messung des Brechungsindex von Luft unter Benutzung der Mehrfach-Interferometrie
DE19727402A1 (de) * 1996-08-20 1998-02-26 Zygo Corp Überlagerungsverfahren und Vorrichtung zur Messung des Brechungsindex von Luft unter Benutzung der Mehrfach-Interferometrie

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Publication number Priority date Publication date Assignee Title
EP0094836A1 (fr) * 1982-05-18 1983-11-23 National Research Development Corporation Appareil et méthode pour mesurer un indice de réfraction
WO1991003729A1 (fr) * 1989-09-08 1991-03-21 Michael John Downs Appareil mesurant l'indice de refraction des milieux gazeux
DE19727404A1 (de) * 1996-08-20 1998-02-26 Zygo Corp Überlagerungsverfahren und Vorrichtung zur Messung des Brechungsindex von Luft unter Benutzung der Mehrfach-Interferometrie
DE19727402A1 (de) * 1996-08-20 1998-02-26 Zygo Corp Überlagerungsverfahren und Vorrichtung zur Messung des Brechungsindex von Luft unter Benutzung der Mehrfach-Interferometrie

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999042786A1 (fr) 1998-02-23 1999-08-26 Zygo Corporation Appareil et procedes pour la mesure des proprietes optiques intrinseques d'un gaz
JP2002543372A (ja) * 1999-04-28 2002-12-17 ザイゴ コーポレイション 屈折率変動を補償する干渉装置および方法
CN116379961A (zh) * 2023-06-05 2023-07-04 广东普洛宇飞生物科技有限公司 一种相位测量系统及方法
CN116379961B (zh) * 2023-06-05 2023-08-11 广东普洛宇飞生物科技有限公司 一种相位测量系统及方法

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