This invention relates in general to the field of interferometry and, in particular, to a novel spectrally controllable light source for performing true heterodyne spectrally controlled interferometry.
Spectrally controlled interferometry (“SCI”) is a recently developed interferometric technique that allows implementation of white light interferometry (“WLI”) measurement schemes in common-path interferometers. See U.S. Pat. No. 8,422,026, U.S. Pat. No. 8,810,884 and U.S. Pat. No. 8,675,205, all hereby incorporated by reference. WLI is characterized by the absence of coherent noise because of the light's short coherence length, typically on the order of a few micrometers. High-coherence units such as laser interferometers, on the other hand, are prone to reduced measurement accuracy due noise produced by dust and other contamination, diffraction on rough surfaces, etc.
Despite these difficulties, laser interferometry is extremely popular and useful because it allows the use of common-path interferometer designs—a particular class of devices in which most of the errors introduced by the optical system cancel out. This allows the manufacture of less expensive and more accurate instruments. High-coherence interferometry is also described as producing a non-localized interference pattern because the interference of beams occurs over a large volume of space, which is an advantage in setting up the measurement apparatus. The most commonly used design is the Fizeau interferometer.
WLI is immune to the problems of laser interferometers but requires careful balancing of the optical path difference between the test and reference arm of the interferometer (OPD) so that interference can take place in the measurement space (i.e., within the coherence length of the light). Such arrangements can be complex and prevent the use of common-path interferometers, therefore forfeiting the above-described advantages. WLI produces localized interference because it is visible only in a limited space around zero OPD.
SCI successfully combines both approaches and provides the advantages of both common-path interferometry and WLI. SCI produces localized interference in an unbalanced OPD interferometer and thus allows, for example, the use of a Fizeau interferometer in WLI mode, thus eliminating the problem of coherent noise. Therefore, one of the major advantages of SCI is that existing instrumentation can be adapted to its modality of operation by replacing only the laser light source with one capable of proper spectral modulation. Different interferometric techniques can be carried out by manipulating only the spectral properties of such light source. See, for example, the time-multiplexed SCI approach described in co-owned U.S. Pat. No. 9,581,428.
Heterodyne interferometry is one of the most precise methods of phase measurement. Its precision can be orders of magnitude better than with conventional phase-shifting interferometry, but it requires laser illumination. Therefore, it is susceptible to the same problems of conventional phase-shifting interferometers; that is, coherent noise and multiple interference. Co-owned U.S. Pat. No. 9,618,320 teaches an approach whereby heterodyne measurement methods are utilized and their related precision is achieved by modulating the light produced by a spectrally controlled source to introduce a time-varying phase shift in the spectral distribution. The present invention teaches a light source that enables the practicing of true heterodyne interferometry by modulating frequency-shifted beams according to SCI principles.
The invention lies in the general idea of combining equal spectrally modulated beams where one of the beams has been frequency shifted to form a heterodyne wavefront, thereby providing the spectral modulation required for SCI and the heterodyne frequency required for heterodyne interferometry.
Alternatively, the same result can be achieved by spectrally modulating the combination of two equal but frequency shifted beams, it being understood that the order of spectral modulation and frequency shifting is inconsequential to the resulting heterodyne wavefront.
The concept of the invention is embodied by optically coupling a white-light source with a delay line that splits the light and introduces a time delay in one of the resulting beams, thereby yielding a recombined output beam with a sinusoidally modulated spectrum. By introducing a frequency shift in one of the beams in the delay line, the output beam is also continuously phase shifted in the spectral domain in a time-varying fashion, as required for heterodyne SCI. The delay line is preferably implemented with a Twyman-Green interferometer configuration. The frequency shift is carried out with an acousto-optic modulator inserted in one of the interferometer's arms.
Various other advantages will become clear from the description of the invention in the specification that follows and from the novel features particularly pointed out in the appended claims. Therefore, this invention includes the features hereinafter illustrated in the drawings, fully described in the detailed description of the preferred embodiments and particularly pointed out in the claims, but such drawings and description disclose only some of the various ways in which the invention may be practiced.
As used in this disclosure, “white light” is intended to refer to any broadband light of the type used in the art of white-light interferometry, typically having a bandwidth in the order of many nanometers. “Monochromatic” light, on the other hand, is intended to refer to any high-coherence narrowband light capable of producing high-contrast interference fringes within the entire measurement space of the particular apparatus utilizing such light as a source. Light “irradiance” and “intensity” are used interchangeably, as normally done in the art, though it is recognized that the former technically refers to light received at a detector and the latter to light emitted by a source. A source is defined as “temporally coherent” or “coherent” if, at any given time, interference fringes can be detected within the measurement space of the interferometric apparatus used to implement SCI. The term “extended” refers to any spatially incoherent light source, as contrasted to a spatially coherent source, such as a point source generated by a focused laser beam. “Channeled spectrum” refers to the sinusoidally modulated spectrum produced by a broadband light passed through a delay line. With reference to light in general, the terms “frequency” and “wavelength” are used alternatively, as commonly done in the art, because of their well known inverse relationship. “Optical path difference” or “OPD” and “time delay” are used alternatively because of their space/time relationship in interferometry. As normally done in the art with reference to interferometric apparatus, “optical path difference” and “OPD” are also used to refer to the difference between the lengths of the optical paths of the test and reference arms of the apparatus. Similarly, “sine” and “cosine,” as well as related terms, are used alternatively unless specifically indicated otherwise.
The terms “modulate” and “modulation” are used in connection with a light source in the broadest sense to include any alteration of the frequency distribution, amplitude distribution or phase distribution of energy produced by the light source, and to also include the synthesis by any means of a light signal having a desired frequency, amplitude or phase distribution. When used in connection with interference fringes, the term “modulation” refers to the fringe envelope. In the case of spectrally-controlled or multiple-wavelength sources, “localized fringes” is intended to mean unambiguously identifiable fringe patterns formed at predetermined distances from the reference surface. Localized fringes are described as positioned at the surfaces from which they are produced to illustrate how they relate to those surfaces and surface shapes that produce them; however, it is to be understood that physically such localized fringes are only virtual fringes and that actual fringes are in fact formed in measurement space only at the surface of a detector. Also, the phrase “producing localized fringes at a predetermined position in space” and related expressions are used for convenience, but it is understood that the precise intended meaning is “producing an interferometric environment whereby unambiguously identifiable fringe patterns are produced when a test surface is placed at a predetermined position in space” relative to a reference surface. The terms “fringes” and “fringe patterns” are used interchangeably within the meaning normally accorded to them in the art. Finally, the generic term “interferometry” and related terms should be construed broadly as used in the art and not limited to shape measurements using an imaging interferometer. As such, interferometry is intended to include, without limitation, the measurement of changes in the position of an object, or of thickness of optical elements, using any known interferometric technique, and therefore it should not limited to shape measurements using an imaging interferometer. Finally, the term “spectrally controllable light source” is intended to mean any light source capable of spectral modulation, whether the source is a single-component spectrally controllable source, such as currently available lasers capable of spectral modulation, or a multi-component source, such as a source that includes a broadband source and a modulator as separate components.
Heterodyne interferometry is typically associated with an interferometric measurement setup where the two interfering beams have slightly different optical frequencies. Accordingly, “heterodyne wavefront” or “heterodyne beam” is used herein to indicate a wavefront composed of beams having different optical frequencies. The resulting interference fringes are not stationary in time, but oscillate at a rate equal to the difference in the optical frequencies of the two beams (referred to in the art as heterodyne frequency). The heterodyne interferometric signal carries information about the optical path difference (OPD) between the beams and can be used for its measurement. The main advantage of such arrangement is that the heterodyne frequency can be isolated with very high fidelity and its phase can be analyzed with a high degree of accuracy. This enables interferometric measurements with a precision that is orders of magnitude greater than that obtained with conventional phase shifting interferometry (PSI). See F. Zernike, “A Precision Method for Measuring Small Phase Differences,” J. Opt. Soc. Am. 40:326-328 (1950).
As described in U.S. Pat. No. 8,422,026, one of the properties of SCI is the ability to manipulate the location of the interference fringes by changing the period of sinusoidal modulation of the source's spectrum. Further, as illustrated in
In a conventional two-beam heterodyne interferometer, the two beams have slightly different optical frequencies, v1 and v2. The resulting irradiance on the detector is described generally by the equations below, where for clarity the heterodyne term with frequency v1+v2 has been omitted because outside the detection range of detectors suitable to practice the invention,
I(t)=∫0+∞|E1(v)E*2(v)e−2πiτve−2πiΔvt|dv=E12+E22+2|E1E*2|cos(−2π(τ
and
v=c/λ. (2)
where the indices 1 and 2 denote the two interfering heterodyne beams, I is intensity, t is time, v=(v1+v2)/2 is the mean optical frequency, Δv=(v1−v2)/2 is the difference in optical frequencies of the two beams, E is the complex amplitude of the light, c is the speed of light, λ is its wavelength, τ is the time delay between the reference and object beams corresponding to the OPD, ψ is the relative phase difference between the beams, and * denotes the complex conjugate.
The irradiance must be registered by a detector that is fast enough to capture the variations of the signal with time; accordingly, the heterodyne frequency must be chosen to match detector capabilities. The phase of the heterodyne signal is related to the OPD present in the interferometer and, by analyzing it, it is possible to gain information about its value. Equation (1) is the basis of operation of conventional heterodyne interferometry. After simplifications based on the reasonable assumption that E is the same for both the 1 and 2 beams, the combination of the terms related to E in Equation (1) yields the form,
I(t)=0.5I(1+A cos(−2π(τ
where I is the mean beam intensity, and A is the normalized amplitude of the interferometric fringes.
Considering the apparatus normally used for heterodyne interferometry modified only with a source capable of operation using SCI principles (such as a light with a spectrum that is modulated sinusoidally, for example), U.S. Pat. No. 8,422,026 teaches (in Equation 11, expressed in a different form in terms of Fourier Transforms that the instantaneous intensity is described by the equation
where φ is the normalized phase of the sinusoidal modulation of the source spectrum and Δl is the OPD in the interferometer. Equations (3) and (4) are similar, the only difference being in the last term, which in Equation (3) describes the time-dependent sinusoidal modulation of the signal due to the difference in the optical frequencies of the interfering beams while in Equation (4) it describes the modulation due to the phase of the spectral modulation.
In a conventional phase-shifting interferometer the value of φ in Equation (4) is constant in time (or changing in a controllable way to implement, for instance, phase-stepping algorithms). However, in a setup where the phase φ is constantly varying with time, the effect is functionally identical to that of heterodyne interferometry—that is, the output signal is modulated by a time-dependent cosine function the phase of which depends on the OPD. In particular, assuming that φ is a linear function of time, that is
φ=ft, (5)
where f is the frequency of phase (φ) change, then Equation (4) becomes
I(t)=0.5I(1+A cos(−2π(τ
which is identical in form to the basic heterodyne Equation (3).
Based on the foregoing, it is possible to implement a heterodyne detection scheme, with all its advantages, using SCI by introducing a time-varying (preferably, but not necessarily, linear) phase shift in the modulation of the source's spectrum. It is again worth noting that such manipulation of the spectrum does not cause any other changes in the fringe distribution in space (other than phase); in particular, the location of the envelope of fringes stays the same. This is an important feature of SCI because any change in the intensity of the output signal not attributed to the heterodyne signal would lower the measurement accuracy. In contrast, in conventional interferometry the change of fringe phase is typically done by altering the OPD between the interfering beams, e.g., by moving the position of the reference surface. This in turn shifts the location of the fringe envelope.
The implementation of spectrally-controlled heterodyne interferometry is therefore reduced to the means of introducing a continuously time-varying phase shift in the spectral domain. Two such embodiments of heterodyne SCI are described in U.S. Pat. No. 8,422,026. The present invention discloses a novel spectrally controllable source that is particularly suitable for producing the continuously time-varying phase shift in the spectral domain required for heterodyne SCI.
Referring to
When used with a broadband source, the Twyman-Green interferometer can be used to generate a sinusoidal modulation of the spectrum, which is commonly referred to in the art as a channeled spectrum. This property can be utilized advantageously in practicing spectrally controlled interferometry because the time of flight difference between the arms A1 and A2 of the interferometer produces the sinusoidal modulation of the spectrum and the period of modulation corresponds to the distance between fringe peaks, which in turn corresponds to the difference in the optical paths of the interferometer's arms. Based on this realization, expressing Equation (3) above in terms of optical frequencies and distances rather than time, one obtains the following,
where c is the speed of light and l is the optical path difference between the interferometer arms. Equation 7 shows that the basic Twyman-Green setup can be used to generate modulation that is useful for practicing SCI. A conventional scanning mechanism 16 is coupled to one of the mirrors to change the period of the sinusoidal modulation. Thus, the delay line in the interferometer amounts to a spectral modulator. However, it lacks the ability to shift the phase of spectral modulation as required to cause corresponding continuous phase shifts in the interferometric fringes, a critical requirement for heterodyne SCI. Any mechanical movement of either mirror M1 or M2 will also cause the period of spectral modulation to change, therefore introducing undesirable changes in an SCI device.
In particular with the objective of implementing SCI for heterodyne detection, a continuous phase shift in the spectral modulation is necessary. Therefore, according to the invention, an optical frequency shift is introduced in one of the arms of the Twymann-Green modulator; that is, the two arms of the delay line are caused to have slightly different frequencies, such that the recombined beams exhibit a heterodyne frequency without losing their relative correlation. This can be achieved, as shown for example in
After passing through the AOM, the beam propagated in arm A1 is combined at beam splitter 12 and will interfere with the beam propagated in arm A2 that has not been frequency shifted but is delayed in time due to different optical paths of interferometer's arms. The combined beam, as previously shown, will have sinusoidal modulation of the spectrum and, due to the optical frequency difference between the beams, the spectral modulation phase will vary linearly in time with a period corresponding to the frequency of the shift introduced by the acousto-optic modulator. Based on Equation (3) above, this combined effect on the resulting irradiance as a function of time and optical frequency can be expressed as follows,
which demonstrates how the output beam O of
The embodiment of
Thus, the general concept of the invention has been illustrated by the combination of a white-light source with a delay line and the introduction of a frequency shift in one of the arms in the delay line. However, the scope of the invention is not limited to such embodiment because the same result can be achieved more generally by combining any spectrally controllable source, as herein defined, with any means for splitting the output of the source into two beams, such as with a conventional beam splitter, and with any means for inducing a frequency shift in one of the split beams. To that end, such spectrally controllable light source could be one of the spectrally controllable sources described in U.S. Pat. No. 8,810,884, herein incorporated by reference, or a source that comprises a conventional broadband source and a spectral modulator, as described in copending Ser. No. 15/806,717. Any such source combined with a beam splitter and a means for inducing a frequency shift in one of the split beams would be capable of producing a combined heterodyne wavefront suitable for practicing the invention. Therefore, as claimed, the scope of the invention should be so construed.
While the invention has been shown and described herein in what is believed to be the most practical and preferred embodiment, it is recognized that departures can be made therefrom within the scope of the invention. For example, the continuous linear phase shift in the spectral modulation produced by the delay line of the invention is preferred because of its simple implementation; however, it is understood that the invention could also be practiced with non-linear and/or discrete phase changes in the modulation of the spectrum so long as the corresponding phase shifts in the resulting interferometric fringes are suitable for interferometric analysis. Similarly, the delay line could be implemented with an interferometer of Michelson configuration as well as the Twyman-Green design described here. Therefore, the invention is not to be limited to the disclosed details but is to be accorded the full scope of the claims, including any and all equivalents thereof.
This application is based on and claims the priority of U.S. Provisional Application No. 62/427,980, filed Nov. 30, 2016, hereby incorporated by reference in its entirety.
Number | Date | Country | |
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62427980 | Nov 2016 | US |