Optics: measuring and testing – By light interference – Using fiber or waveguide interferometer
Reexamination Certificate
2000-10-19
2004-02-03
Kim, Robert H. (Department: 2871)
Optics: measuring and testing
By light interference
Using fiber or waveguide interferometer
Reexamination Certificate
active
06687008
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an interferometer that contains waveguides and a 3×3 directional coupler.
2. Background Information
Interferometers are often employed in metrology, remote sensing, and process control applications in which the property or process parameter of interest is encoded as a phase shift between a sample and reference optical beam.
For example, in the disk drive industry, determining the microscopic topology of a disk surface at various stages during production is becoming an increasingly important factor in estimating the likelihood of producing a favorable quality disk. Cost pressures are increasingly forcing manufacturers to weed out unviable disks at earlier stages of production. Given the very high density of data stored on such disks, topographic profiles with heights ranging from less than 1 nm to tens of microns must be monitored at a lateral resolution on the order of 1 micron. Given the throughput of disks required for cost effective use of capital, a disk should be inspected in a period on the order of 10 seconds to 1 minute. This means that the inspection apparatus would need an effective data collection rate on the order of 100 to 600 MHz to inspect one side of a 95 mm diameter disk. The technical challenge is then to produce a very sensitive, high speed interferometric system that has a wide dynamic range. The system should also be accurate, compact, reliable, and cost effective.
Fundamentally, interferometers are devices which convert the phase difference between two input waves into intensity variations on one or more output waves which carry information about the phase difference between the input waves. The interferometer outputs are superpositions of portions of the two input waves. The amount of each input delivered to each output, and the phase shift imparted during delivery determines the characteristics of the interferometer.
For example, in the canonical interferometer employing a beamsplitter as shown in
FIG. 1
, two input beams with electric field magnitudes Ea and Eb are each split into two components of equal magnitude by the beamsplitter. However because of the reflections at the interface within the beamsplitter, the phase of the component which is reflected in the beamsplitter is shifted 90 degrees with respect to the phase of the component which is transmitted. The two key properties of this interferometer that determine its operational characteristics are i) that the inputs are split into equal magnitude components, and ii) that the phase shift imparted to one of those components is 90 degrees.
The consequences of this interferometer's properties may be seen by inspecting the results of the math describing these properties:
input beam
1
: E
a
e
i((w)t)
input beam
2
: E
b
e
i(wt+Ø)
ouput beam
1
: ½ (E
a
e
i(wt)
+E
b
e
i(wt+Ø−
&pgr;
/2)
)
ouput beam
2
: ½ (E
a
e
i(wt−
&pgr;
/2)
+E
b
e
i(wt+Ø)
)
Here, w is the optical frequency of the light beams, Ø is the phase relation between input beam
1
and
2
, and &pgr;/2 represents the 90 degree phase shift incurred by the reflection within the beamsplitter.
The intensities of the two output beams are proportional to the magnitude squared of their component electric fields, so the measurable intensities of the two beams are:
output beam
1
:=½ ( E
a
2
+E
b
2
+2 E
a
E
b
sin(Ø))
output beam
2
:=½ ( E
a
2
+E
b
2
−2 E
a
E
b
sin(Ø))
These equations are the canonical equations describing interference between two waves, and are illustrated in
FIG. 2
where E
a
=E
b
. The intensity of each measured output beam is sinusoidally modulated from minimum to maximum as a function of the relative phase difference Ø between the two input beams. Also, the second output beam is modulated in exact opposition with respect to beam
1
.
Together, the combined intensity of the two beams conserves the combined intensity of the input beams, but aside from this, the phase information in the second output beam is entirely complementary to the phase information carried in the first beam. In this sense, the second beam provides only redundant information about the phase Ø. The fact that the second output is modulated in exact opposition to the first is a direct consequence of the property of the beamsplitter that imparted a 90 degree phase shift on the reflected beam components. It is not a fundamental aspect of interferometry or of a generalized interferometric apparatus.
As simple as this canonical interferometer is, it has a number of undesirable characteristics, the foremost being that the output intensity, which carries the phase information between the input beams, is bounded and periodic while the input phase difference is not. Consequently, as the intensities of both output beams reach their respective minima or maxima, the sensitivity of the interferometer to changes in the input phase-difference drops to zero. Said another way, the sensitivity of the interferometer is proportional to the slope of the intensity vs. phase-difference relation. Since the slope goes to zero at the maxima and minima, the sensitivity drops to zero there. Not only is it undesirable to have variable sensitivity, but the complete null in sensitivity leads to an inability to unambiguously track phase-difference excursions beyond ±&pgr;/2 from the point of maximum sensitivity. A reversal in the progress of a phase-difference occurring within the blind region of the interferometer could not be discerned from a continuation of the phase-difference into the next order.
The limitations of this canonical “homodyne” interferometer are widely recognized, and a number of methods have been developed to bypass these limitations. Chief among the methods used is the Doppler, or heterodyne, interferometer. In this form of an interferometric device, the same form of beamcombining described above may be used to combine the two test beams, however one of the beams to be interfered has had its frequency shifted with respect to the other beam (for example by the use of an acoustic-optic modulator or by using a dual-frequency laser). Because of this, when the two input beams are interfered, the optical frequency does not completely drop out of the equations describing the intensity-modulated output. Instead, the output intensity is modulated at the frequency shift employed (typically 10-50 MHz). Stated differently, the output appears to register a constantly increasing phase difference between the two input beams. In this way, an externally induced phase shift between the beams is detected as a momentary change in the rate of phase advance of the output intensities.
The advantages of Doppler interferometers include an ability to unambiguously detect phase shifts in either direction as well as shifts over ranges exceeding one interferometric order. Disadvantages of Doppler interferometers include the increased complexity since a dual frequency source must be used, and the additional RF electronic stages that are needed to track the phase of the detected signal. Furthermore, the rate of phase shift that can be tracked with a Doppler interferometer is limited by the frequency shift employed and the degree of filtering used in the phase detection electronics. A tradeoff between tracking speed and minimum detectable motion is required because of this. It is therefore impossible to detect very slow motions (e.g. small displacements with short periods) with high bandwidth. Likewise, very high speed motions can only be detected with limited accuracy. In no case should the rate of phase shift exceed the bias phase shift rate set by the frequency offset between the two beams. This places an upper limit on the the rate of phase shift between the two input beams (i.e. the speed of an object or surface being measured) which can be tracked by heterodyne interferometry. For light at 632 nm with a frequency bias of 50 MHz, this limit is 30 meters/second with practica
Duran Carlos
Hess Harald
Peale David
Irell & Manella LLP
Kim Richard
Kim Robert H.
KLA-Tencor Corporation
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