Optics: measuring and testing – By light interference – Having shearing
Reexamination Certificate
2002-08-23
2004-07-13
Turner, Samuel A. (Department: 2877)
Optics: measuring and testing
By light interference
Having shearing
C356S500000, C356S509000
Reexamination Certificate
active
06762845
ABSTRACT:
TECHNICAL FIELD
This description relates to multiple-pass interferometry.
BACKGROUND
Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
Referring to
FIG. 1
, a typical interferometry system
10
includes a source
20
, an interferometer
30
, a detector
40
, and an analyzer
50
. Source
20
includes a laser for providing an input beam
25
to interferometer
30
. In one example where heterodyne interferometry technique is used, input beam
25
includes two different frequency components having orthogonal polarizations. An acousto-optical modulator may be used to introduce frequency splitting to produce the two frequency components. Alternatively, source
25
may include a Zeeman-split laser to produce the frequency splitting. In another example, where homodyne interferometry technique is used, input beam
25
may have a single wavelength.
In a heterodyne interferometry system, the orthogonally polarized components are sent to interferometer
30
, where they are separated into measurement and reference beams. The reference beam travels along a reference path. The measurement beam travels along a measurement path. The reference and measurement beams are later combined to form an overlapping pair of exit beams
35
. The interference between the overlapping pair of exit beams contains information about the relative difference in optical path length between the reference and measurement paths. In a homodyne interferometry system, a non-polarizing beam splitter may be used to separate the input beam into the measurement and reference beams.
In one example, the reference path is fixed and the changes in the optical path length difference correspond to changes in the optical path length of the measurement path. In another example, the optical path length of both the reference and measurement paths may change, e.g., the reference path may contact a reference object that may move relative to interferometer
30
. In this case, changes in the optical path length difference correspond to changes in the position of the measurement object relative to the reference object.
When the reference and measurement beams have orthogonal polarizations, the intensity of at least one intermediate polarization of the overlapping pair of exit beams is selected to produce the optical interference. For example, a polarizer may be positioned within interferometer
30
to mix the polarizations of the overlapping pair of exit beams, which is then sent to detector
40
. Alternatively, the polarizer may be positioned within detector
40
.
Detector
40
measures the intensity of the selected polarization of the overlapping pair of exit beams to produce the interference signal. Detector
40
includes a photodetector that measures the intensity of the selected polarization of the overlapping pair of exit beams. Detector
40
may also include electronic components (e.g., an amplifier and an analog-to-digital converter) that amplifies the output from the photodetector and produces a digital signal corresponding to the optical interference.
In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarizing beam splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer.
The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams.
If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp/&lgr;, where v is the relative speed of the measurement and reference objects, &lgr; is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2&pgr; phase change substantially equal to a distance change L of &lgr;/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.
Unfortunately, this equality is not always exact. In addition, the amplitude of the measured interference signal may be variable. A variable amplitude may subsequently reduce the accuracy of measured phase changes. Many interferometers include non-linearities such as what are known as “cyclic errors.” The cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in optical path length pnL. In particular, the first harmonic cyclic error in phase has a sinusoidal dependence on (2&pgr;pnL)/&lgr; and the second harmonic cyclic error in phase has a sinusoidal dependence on 2 (2&pgr;pnL)/&lgr;. Higher harmonic cyclic errors can also be present.
There are also “non-cyclic non-linearities” such as those caused by a change in lateral displacement (i.e., “beam shear”) between the reference and measurement beam components of an output beam of an interferometer when the wavefronts of the reference and measurement beam components have wavefront errors. This can be explained as follows.
Inhomogeneities in the interferometer optics may cause wavefront errors in the reference and measurement beams. When the reference and measurement beams propagate collinearly with one another through such inhomogeneities, the resulting wavefront errors are identical and their contributions to the interferometric signal cancel each other. More typically, however, the reference and measurement beam components of the output beam are laterally displaced from one another, i.e., they have a relative beam shear. Such beam shear causes the wavefront errors to contribute an error to the interferometric signal derived from the output beam.
Moreover, in many interferometry systems beam shear changes as the position or angular orientation of the measurement object changes. For example, a change in relative beam shear can be introduced by a change in the angular orientation of a plane mirror measurement object. Accordingly, a change in the angular orientation of the measurement object produces a corresponding error in the interferometric signal.
The effect of the beam shear and wavefront errors will depend upon procedures used to mix components of the output beam with respect to component polarization states and to detect the mixed output beam to generate an electrical interference signal. The mixed output beam may for example be detected by a detector without any focusing
Connolly Patrick
Turner Samuel A.
Zygo Corporation
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