1. Field of the Invention
The present invention relates to the determination of an optical property of a device under test (DUT) by analyzing a response signal of said DUT, or a signal derived therefrom.
2. Brief Description of Related Developments
According to a known technique commonly referred to as “swept homodyne interferometry”, a DUT is implemented in one of the interferometer arms of an interferometric measurement set-up introducing an additional wavelength dependent optical path length. A laser source is swept over a range of wavelengths. Due to a discrepancy of the arm lengths a modulated signal—the interferogram—is observed at a detector. The set-up is comparable to a Mach-Zehnder set-up when viewed in transmission, and to a Twyman-Green interferometer when viewed in reflection. More details concerning this approach can be found in “Phase and Group Delay Relation in Swept Homodyne Interferometry” by Thomas Jensen, and in EP-A-1202038 by the assignee, the teaching thereof shall be incorporated herein by reference.
It is an object of the invention to improve the determination of an optical property by analyzing a DUT response signal, or a signal derived therefrom. The object is solved by the independent claims. Preferred embodiments are shown by the dependent claims.
The invention relates to an apparatus adapted for determining an optical property of a device under test (DUT). The apparatus comprises a delay unit that forms a composite signal, whereby said composite signal comprises superimposed signals that are delayed with respect to each other. The DUT response signal representing a signal response of the DUT in response to the composite signal, or in response to a signal derived from said composite signal, is detected. The apparatus further comprises a first determination unit that determines an optical property of the DUT from said DUT response signal, or from a signal derived therefrom.
The composite signal comprises at least two superimposed signals. When the DUT response to said composite signal, or to a signal derived from said composite signal, is detected and analyzed, it is possible to find out how the composite signal is modified by said DUT. Instead of analyzing the DUT response to a simple signal, e.g. to a signal comprising only one signal component, the DUT response to a composite signal is used for determining an optical property of the DUT. The composite signal comprises different signal components that are affected by said DUT in different ways. The use of a composite signal allows to collect much more information per measurement, because each of the various components of said composite signal might be affected by said DUT in a different way. For example, said composite signal might comprise different frequency components that interfere with each other. By detecting the DUT response to a composite signal of this kind, it is possible to obtain information about the DUT response at different frequencies with one single measurement.
Another advantage of providing a composite signal to the DUT is that the measurement set-up is considerably simplified. The delay unit is connected to the DUT input, and the DUT output is connected to the first determination unit. Because the composite signal already comprises several signal components, it is not necessary any longer to provide an extra reference signal to the determination unit.
The invention can be used both for single-port and for multi-port devices. A multi-port device might for example comprise several input ports, whereby the input signals provided at said input ports are combined to at least one output signal comprising several channels. A multi-port device might as well comprise several output ports, whereby the various channels of an input signal are distributed to said output ports. For multi-port devices comprising several input ports, the composite signal can be provided to each of said input ports by establishing fiber connections between the delay unit and each of said input ports. The output ports are connected to one or more determination units. For a measurement set-up of this kind, it is especially advantageous that no reference signals are required, because all the necessary signal components are contained within the composite signal.
Another advantage of preferred embodiments is that the mechanical stability of the simplified set-up is improved, and that distortions due to vibrations are reduced.
According to a preferred embodiment, the superimposed signals that are used for forming the composite signal are derived from one incident signal. When said signal components are derived from one common source, they have a well-defined phase relation relative to each other.
According to another preferred embodiment of the invention, the incident optical signal is generated by a tunable light source, and preferably by a narrow-band tunable laser source. The frequency of the light generated by the tunable light source can be varied as a function of time, for example, the frequency of said light might be swept over a certain range of frequencies. In this case, the relative delay between the superimposed signals causes a frequency difference between the superimposed signals. Therefore, the composite signal comprises different frequency components that interfere with each other, and the composite signal comprises an interference signal. This interference signal, or a signal derived therefrom, can be provided to the DUT. By detecting and analyzing the DUT response signal, or a signal derived therefrom, it is possible to find out how the interference pattern of the composite signal is affected by said DUT. By comparing the interference pattern of the composite signal with the interference pattern of the response signal, it is possible to gather information about the optical properties of the DUT. For example, information concerning the DUT's dispersion and the frequency dependence of the DUT's refractive index can be obtained.
According to another preferred embodiment of the invention, the incident optical signal is split up into at least two different light paths, said light paths having different optical path lengths. When said superimposed signals are delayed by different optical paths, there is a relative delay of said superimposed signals with respect to each other.
According to a preferred embodiment of the invention, the DUT response signal is either an optical signal transmitted through said DUT, or an optical signal reflected by said DUT. Preferably, the apparatus comprises a first and a second determination unit for simultaneously detecting both the signal transmitted through said DUT and the signal reflected by said DUT. This allows comparing the transmitted and the reflected intensity, and the correspondence of the transmitted and the reflected intensity can be understood. This is especially helpful for understanding the optical properties of more complex optical devices, such as for example the properties of a Fabry-Perot-Etalon.
According to a preferred embodiment of the invention, the respective optical property is obtained by analyzing the phase of the interference pattern obtained in response to said composite signal. This can for example be done by setting up a mathematical model of the phase, whereby a set of fit parameters is adjusted during a fitting procedure. By doing this, the various contributions to the phase can be distinguished.
From the time dependent intensity of the DUT response signal, for example, the insertion loss of the DUT might be determined. This can be done by relating the intensity of the response signal to the composite signal's intensity. Besides that, the frequency dependence of the group delay might be determined by analyzing the phase of the DUT response signal. For example, the way the interference pattern of the DUT response signal is modified by the DUT permits to derive the variation of the group delay τgroup as a function of frequency. The invention is not limited to these examples, though. Any phase properties of the DUT or loss or gain properties of the DUT might be determined.
According to another preferred embodiment of the invention, the incident signal is swept with a predefined sweep speed vf over a range of wavelengths. In this case, the frequency separation Δf can be related to the relative delay ΔT by means of the equation Δf=ΔT·vf. In case of a constant sweep speed vf, the frequency separation Δf is constant as well.
According to another preferred embodiment of the invention, the frequency separation Δf between the signal components of the composite signal is varied by varying the sweep speed vf. Thus, it is possible to adapt the frequency separation Δf to the respective determination unit that is used in the set-up. Furthermore, the frequency resolution of the measurement can be adjusted in accordance with the user's needs. For example, in case of a broad band device, a rather high sweep speed might be chosen, while in case of a narrow band device, the frequency is e.g. swept slowly. The sweep speed can be varied on part of the tunable laser source, and therefore, the delay lines of the various light paths don't have to be modified. According to an alternative embodiment, the frequency separation Δf is changed by modifying at least one variable delay in at least one of said light paths.
In another preferred embodiment, at least one of the light paths comprises a polarization controller for optimizing the contrast of the detected interference pattern. A high-quality interference pattern is obtained when the polarization states of the various frequency components are substantially equal to each other.
According to another preferred embodiment of the invention, the time dependent intensity of the DUT response signal, or of a signal derived therefrom, is recorded for different frequency separations Δf1, Δf2, etc. From the variety of interference patterns, the various contributions that affect the DUT response signal can be understood and distinguished from each other.
According to another preferred embodiment of the invention, the apparatus comprises a reference determination unit adapted for performing a reference measurement of the composite signal, or of a signal derived from said composite signal. There might occur variations of the intensity of said composite signal, or, in case a frequency sweep is performed, of the sweep speed vf, that cause measurement errors. By performing a reference measurement of the composite signal, it is possible to consider these variations when determining the desired optical property. Besides that, the frequency separation Δf between different frequency components of the composite signal (or of a signal derived therefrom) can be determined by analyzing the phase of said composite signal. During further analysis, the knowledge of Δf might be helpful.
According to another preferred embodiment of the invention, the apparatus further comprises an optical modulator that is inserted at any position of the light path between the tunable light source and the determination unit. Said modulator, modulates the respective optical signal with an external frequency. As a result, each frequency component of the respective optical signal is shifted by said external frequency. An appropriate choice of the external frequency allows shifting said frequency components to any desired range of frequencies, which might simplify the detection of said frequency components.
According to a further preferred embodiment of the invention, the incident signal is split up into at least three different optical signals, whereby the light path of the first signal and the light path of the third signal each comprise a polarization controller. The first optical signal is set to a first polarization state, and the third optical signal is set to a second polarization state. Besides that, said first and said third signal are delayed with respect to the second signal. When the three signals are combined to form a composite signal, the second signal interferes with the delayed first signal, thereby generating a first interference pattern, and the second signal also interferes with the third signal, thereby producing a second interference pattern. For this reason, the composite signal comprises two interference patterns that oscillate within two different planes of polarization. This embodiment of the invention allows finding out how the DUT modifies an interference pattern in dependence on the pattern's respective state of polarization.
According to another preferred embodiment of the invention, the first determination unit comprises a polarization diversity receiver. A polarization diversity receiver detects how the polarization of a received interference pattern is oriented. For this purpose, the polarization diversity receiver might for example comprise a polarization dependent beam splitter and a set of power meters for detecting the signal intensity for different directions of polarization. By performing a polarization resolved measurement of the DUT response signal, or of a signal derived therefrom, it is possible to analyze how the polarization of the composite signal affects the way that signal is modified by the DUT. For example, the DUT might rotate the state of polarization of the composite signal. A polarization diversity receiver allows understanding polarization dependent effects within the DUT.
The invention can be partly or entirely embodied or supported by one or more suitable software programs, which can be stored on or otherwise provided by any kind of data carrier, and which might be executed in or by any suitable data processing unit. Software programs or routines are preferably applied for controlling the tunable light source, e.g. for performing frequency sweeps. Furthermore, software programs or routines might be applied for analyzing the phase of a detected interference pattern.
Other objects and many of the attendant advantages of the present invention will be readily appreciated and become better understood by reference to the following detailed description when considering in connection with the accompanied drawings. Features that are substantially or functionally equal or similar will be referred to with the same reference sign(s).
the second delayed signal is delayed by
and therefore, the relative time delay ΔT=T2−T1 between said two signals can be written as
The first and the second delayed signal are superimposed, and a composite signal 7 is obtained. The composite signal 7 is incident upon the DUT 8, and at the DUT output, a transmitted signal 9 is obtained. The intensity of the transmitted signal 9 is recorded, as a function of time, by the power meter 10.
During a frequency sweep, the frequency of the emitted beam of light 2 is continuously increased according to the formula
f(t)=f0+vf·t (2)
whereby vf is the sweep speed of the tunable laser source, and whereby f0 is the starting frequency. Alternatively, the frequency f(t) of the emitted light might as well be continuously decreased with time. In terms of wavelength, the sweep speed might be
or even greater than
In case a tunable laser source is used that emits light in the infrared, the starting frequency f0 might for example be in the order of 193 THz.
In the following, it is assumed that the tunable laser source 1 shown in
In
This frequency difference Δf gives rise to interference when the delayed signals of the first and the second light paths are superimposed, and the composite signal 7 of
The composite signal 7 with its well-defined interference pattern is now incident upon the device under test 8, and said DUT 8 will modify said interference pattern in a way that is characteristic for said DUT.
The phase of the interference pattern detected at the output of the DUT can be derived analytically.
At the output of the DUT 14, two light waves u1 and u2 are obtained that can be expressed as follows:
u1=a1·exp[2πi·f(t0−τ1)·(t0+τ1)]
u2=a2·exp[2πi·f(t0−ΔT−τ2)·(t0+ΔT+τ2)] (4)
From these expressions for the light waves u1 and u2, the time dependence of the power detected by the power meter can be derived:
P(t0)=|u1+u2|2=a12+a22++2·a1·a2·cos[2π·f(t0−τ1)·(t0+τ1)−2π·f(t0−ΔT−τ2)·(t0+ΔT+τ2)] (5)
The terms a12 and a22 are constant, and therefore, the interference pattern detected by the power meter is caused by the cosine term. In the following, the phase φ(t0) of said cosine term will be analyzed more closely. The phase φ(t0) can be written as follows:
When assuming that the frequency sweep is performed in a way that the frequency increases as a function of time, the frequency f(t−τ1) will be larger than f(t−ΔT−τ2). In case the DUT exhibits normal dispersion, the refractive index nDUT of the DUT will increase with increasing frequency. When the refractive index nDUT is large, the time of traversal τ will become large as well. This leads to the conclusion that in case the DUT exhibits normal dispersion Δτ=τ1−τ2 will be greater than zero. The quantity Δτ can be seen as a measure for the dispersion of the DUT. Of course, Δτ might as well assume negative values.
Usually, the path difference ΔL between the first and the second light path is chosen such that the frequency difference Δf assumes a value within the desired range. For example, when ΔL=200 m, ΔT will be in the order of microseconds, and Δf will be in the order of 5 MHz. Different orders of magnitude might be used as well. Anyway, the relation Δτ<<ΔT generally holds, and for this reason, the frequency difference at the DUT output is approximately equal to Δf:
f(t0−τ1)−f(t0−ΔT−τ2)≈Δf (7)
When inserting Δτ and Δf in the above formula (6), the following expression for the phase φ(t0) is obtained:
In this expression for the phase of the interference pattern, five terms can be identified. The fourth term (Δf·ΔT) is a constant and does not depend on time. The fifth term (Δf·τ2) is very small, because both Δf and τ2 are small. Besides that, τ2 does not strongly depend on time.
The first term (Δf·t) linearly increases with time, whereby Δf can be considered as a constant in the order of 5 MHz. The sweep speed vf might for example be 5 THz/sec, and the additional time delay ΔT might be in the order of microseconds. Due to the frequency sweeping, the frequency f(t−τ1) in the second and third term of the above formula (8) also shows a linear dependence on time.
The quantity Δτ is the change of the time of traversal τ over the frequency interval Δf. This variation of the traversal time τ with frequency is caused by the variation of the DUT's refractive index with frequency. Thus, Δτ allows tracing the dispersion of the DUT.
The meaning of the second term of the above formula (8) becomes clearer by rewriting this term as follows:
The group delay τgroup of the DUT can be written as:
Therefore, the second term of the phase φ(t) in formula (8) can be identified as the difference between the group delay τgroup and the phase delay τphase.
Especially for more complex devices, for example for devices like a Fabry-Perot-Etalon, it makes sense to record both the transmitted and the reflected signal. In
The remaining intensity of the composite signal 17 is incident upon the DUT 20. In a power meter 22, the intensity of the transmitted signal 21 is determined as a function of time. The signal reflected by the DUT 20 is partly transmitted and partly reflected by the beam splitter 18, and the intensity of the reflected signal 23 is determined by a power meter 24. In the embodiment shown in
In order to distinguish the different contributions to the phase φ(t) in formula (8), it is helpful to record the interference patterns for at least two different frequency separations Δf1, Δf2, etc. The frequency separation Δf can be expressed as Δf=ΔT·vf. According to a first method for varying the frequency separation Δf, the sweep speed vf of the tunable laser source is varied, while the delay ΔT between the two light paths is kept constant:
Δf1=ΔT·vf1
Δf2=ΔT·vf2 (11)
According to a second method for varying the frequency separation Δf, the additional delay ΔT between the first and the second light path is changed. This can for example be done by modifying the length of the second light path, for example by adding an additional delay line. The larger the extra delay ΔT is chosen, the larger the frequency separation Δf will be:
Δf1=ΔT1·vf
Δf2=ΔT2·vf (12)
Furthermore, it is possible to combine the first and the second method for varying Δf. The respective values of Δf can always be determined by a reference measurement of the composite signal's interference pattern.
The light paths for detecting the interference patterns might additionally comprise at least one optical modulator. In
Furthermore, a polarization controller might be added to at least one of the light paths.
The state of polarization of the transmitted signal 21 or of the reflected signal 23 can be analyzed with a polarization diversity receiver. Any one of the power meters 19, 22, 24 can be replaced by such a polarization diversity receiver. Besides recording the respective signal's intensity as a function of time, a polarization diversity receiver also permits to determine the received signal's polarization state.
In
For understanding the composite signal 47, it is helpful to think of the second signal 38 as being composed of two different components, whereby the first component of the signal 38 is polarized in a −45° direction, and whereby the second component is polarized in a +45° direction. The frequency of the signal 35 is continuously swept with a sweep frequency vf, and therefore, the delay line 41 in the first light path causes a frequency separation Δf between the signal 38 and the delayed signal 42. Because of this frequency separation, the delayed signal 42 interferes with the first component of the signal 38 in a plane of polarization oriented at −45°. The composite signal 47 therefore comprises a first interference pattern that oscillates in a plane of polarization oriented at −45°. Similarly, the delay line 45 in the third light path causes a frequency separation Δf between the signal 38 and the delayed signal 46 and therefore, the second component of the signal 38 interferes with the delayed signal 46 in a polarization plane oriented at +45°. The composite signal 47 therefore comprises two interference patterns, whereby the first interference pattern oscillates in a plane of polarization oriented at −45°, and whereby the second interference pattern oscillates in a plane of polarization oriented at +45°.
The composite signal 47 is forwarded, via the beam splitter 48, to the DUT 49. The beam splitter 48 provides the composite signal 47 to the reference determination unit 50. There, the interference patterns are analyzed, and the frequency separation Δf is determined. At the output of the DUT 49, a transmitted signal 51 is obtained, and this transmitted signal 51 is detected and analyzed by a determination unit. In the embodiment shown in
Number | Date | Country | Kind |
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02025426 | Nov 2002 | EP | regional |
Number | Name | Date | Kind |
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6486961 | Szfraniec et al. | Nov 2002 | B1 |
6606158 | Rosenfeldt et al. | Aug 2003 | B1 |
Number | Date | Country |
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1 202 038 | Feb 2002 | EP |
Number | Date | Country | |
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20040130724 A1 | Jul 2004 | US |