Interferometers commonly use polarization encoding to distinguish reference beams from measurement beams. In a plane-mirror interferometer 100 illustrated in FIG. 1, for example, an input beam IN contains two linearly polarized components having orthogonal linear polarizations. A polarizing beam splitter 110 in interferometer 100 separates the two components creating a reference beam and a measurement beam.
In FIG. 1, polarizing beam splitter 110 reflects the component corresponding to the reference beam. The reference beam thus travels down a path R1 through a quarter-wave plate 120 to a reference mirror 130. Reference mirror 130 has a fixed mounting relative to polarizing beam splitter 110 and is aligned perpendicular to path R1 so that the reference beam reflects from a reference mirror 130 and travels back through quarter-wave plate 120 along path R1. Passing twice through quarter-wave plate 120 effectively rotates the polarization of the reference beam by 90xc2x0 so that the reference beam returning on path R1 passes through polarizing beam splitter 110 and enters a cube corner reflector 140 along a path R2.
Cube corner reflector 140 reflects the reference beam onto an offset path R3, and the reference beam traverses polarizing beam splitter 110 directly to a collinear path R4. The reference beam then continues along a path R4 through quarter-wave plate 120 before again reflecting from reference mirror 130 and returning through quarter-wave plate 120 along path R4. The second pair of trips through quarter-wave plate 120 changes the polarization of the reference beam, so that polarizing beam splitter 110 reflects the reference beam from path R4 onto an output path ROUT.
Polarizing beam splitter 110 of FIG. 1 transmits the input polarization component corresponding to the measurement beam so that the measurement beam travels along a path M1 through a quarter-wave plate 150 to a measurement mirror 160. Measurement mirror 160 is on an object such as a translation stage in processing equipment for integrated circuit fabrication. Measurement mirror 160 is ideally perpendicular to path M1, but generally, measurement mirror 160 may have an angular orientation that is subject to variations as the object moves. FIG. 1 shows a configuration where measurement mirror 160 has a non-zero yaw angle relative to path M1. As a result, the measurement beam reflected from measurement mirror 160 returns along a path M1xe2x80x2 that forms a non-zero angle (i.e., twice the yaw angle) with path M1.
The measurement beam, which passes twice through quarter-wave plate 150, has its linear polarization rotated by 90xc2x0, so that polarizing beam splitter 110 reflects the measurement beam from path M1xe2x80x2 to a path M2 into cube corner 140. From cube corner 140, the measurement beam travels path M3, reflects in polarizing beam splitter 110 to a path M4 through quarter-wave plate 150 to measurement reflector 160. The measurement beam then returns from measurement reflector along a path M4xe2x80x2 through quarter-wave plate 150. Path M4xe2x80x2 forms an angle with path M4 according to the orientation of measurement mirror 160 and is parallel to path M1. Polarizing beam splitter 110 transmits the measurement beam from path M4xe2x80x2 to an output path MOUT.
Interferometer electronics (not shown) can analyze phase information from a combination of the reference and measurement beams to measure movement of measurement mirror 160. In particular, a merged beam resulting from merging the reference and measurement beams can be made to interfere to produce a measurement signal. When measurement mirror 160 is moving along the direction of the measurement beam, each reflection of the measurement beam from measurement mirror 160 causes a Doppler shift in the frequency of the measurement beam and a corresponding change in the beat frequency of the merged beam. In a DC interferometer where the measurement and reference beams initially have the same frequency, the beat frequency of the merged beam corresponds to the Doppler shift. In an AC interferometer where the measurement and reference beams initially have slightly different frequencies, the change in the beat frequency indicates the Doppler shift.
AC interferometers typically use an input beam having orthogonal, linear polarization components with slightly different frequencies. Imperfect polarization separation of the frequency components of the input beam can cause cyclic errors in the Doppler shift measurement. If the reference beam, for example, contains some light at the frequency intended for the measurement beam, the reference beam by itself gives rise to an error signal having the beat frequency depending on the frequencies of the input components. If the error signal becomes too large when compared to the measurement signal, accurate measurements become difficult. Accordingly, maximizing the measurement signal is important for accurate measurements.
Maximizing the measurement signal for AC or DC interferometers requires efficient combination of the measurement and reference beams, and combination of the reference and measurement beams is most efficient when the output paths ROUT and MOUT for the reference and measurement beams are collinear. Achieving collinear output beams from interferometer 100 depends on proper alignment of reference mirror 130 and measurement mirror 160.
In the properly aligned configuration, measurement mirror 160 is perpendicular to path M1, and reflected paths M1xe2x80x2 and M4xe2x80x2 are collinear with incident paths M1 and M4. As a result, measurement paths M2, M3, and MOUT respectively coincide with reference paths R2, R3, and ROUT when measurement mirror 160 is ideally aligned. If measurement mirror 160 is out of alignment, paths M1 and M1xe2x80x2 form an angle that depends on the misalignment of measurement mirror 160, and the reference and measurement paths are skewed relative to each other. The angular difference or separation between the measurement and reference paths continues until the second reflection from measurement mirror 160. After the second reflections, measurement path M4xe2x80x2 and output path MOUT become parallel to the output path ROUT for the reference beam. However, the angular variation of measurement mirror 160 still displaces the measurement beam output path MOUT relative to the reference beam output path ROUT. This phenomenon is commonly referred to as beam walk-off.
When the beam walk-off is negligible compared to the diameters for the reference and measurement beams, the merged beam provides a strong measurement signal. However, a misalignment of measurement mirror 160 by about 0.001 radians or more in concert with a large distance (on the order of 0.5 meters or more) between beam splitter 110 and mirror 160 in some precision interferometers causes a walk-off that is a significant fraction of the beam diameters. (The walk-off in a plane-mirror interferometer is generally about 4Lxcex1, where L is the distance between the interferometer and measurement mirror 160 and xcex1 is the angular misalignment in radians of measurement mirror 160.) The resulting decrease in the overlapped area of the measurement and reference beams causes a significant drop off in the measurement signal, making the cyclic error signal more significant and making accurate measurements difficult.
Another problem arising from beam walk-off is the dynamic range of measurement signal during operation of interferometer 100. In particular, the light intensity in the overlapped beam can vary from a best case having a maximum overlap to a worst-case have a relatively small overlap. The intensity of the measurement signal thus depends on the alignment of measurement mirror 160, and the alignment changes during operation of interferometer 100, particularly when the object being measured moves. The input beam must have sufficient power to provide a measurable signal in the worst-case alignment, which significantly reduces energy efficiency of interferometer 100. Additionally, the optical receiver and measurement electronics must have a dynamic range sufficient to handle both the worst case low measurement signal levels and the best case high measurement signal levels.
Yet another drawback of beam walk-off arises from non-uniformity of the wave fronts of the beams. Typically, beam curvature, wedge angles, and aberrations of the beams themselves and optical surfaces traversed by one beam but not the other can cause wave front phase differences. Measurement beam walk-off can change the overlap and specifically cause the measured phase of the signal to change even if the distance between mirror 160 and beam splitter 110 did not change.
Interferometer 100 employs cube corner reflector 140 to redirect the reference and measurement beams for additional reflections from respective plane-mirror reflectors 130 and 160. As noted above, cube corner reflector 140 and the additional reflections avoid angular separations between output beam paths ROUT and MOUT. The additional reflections also increase (i.e., double) the Doppler shift of the measurement beam and can increase the measurement resolution of the interferometer. A further cube corner reflector might be added to further increase the number of reflections of the measurement beam from measurement reflector 160 (and the number of reflections of the reference beam from the reference reflector 130). A shortcoming of using a cube corner reflector is the resulting increase in the beam walk-off (e.g., doubling beam walk-off when doubling the number of reflections).
A dynamic beam steering system could measure the relative position of the measurement and reference beams during operation of interferometer 100 and then dynamically adjust reference mirror 130 or another optical element in interferometer 100 to minimize the walk-off. Such dynamic steering systems tend to be complex, expensive, and vulnerable to failure. Accordingly, more efficient and less complex systems and methods for reducing or eliminating walk-off are desired. Ideally, the systems that reduce or eliminate walk-off will be compact and suitable for operation in limited working spaces.
In accordance with an aspect of the invention, an interferometer returns measurement and reference beams for an additional pass through the interferometer optics along paths that either retrace a first pass through the interferometer optics or follow paths parallel to the first pass. As a result, additional reflections of the measurement and reference beams from their respective reflectors eliminate walk-off between measurement and reference beams in a final merged output beam.
In an interferometer having multiple measurement axes, input beams for the different axes can be separated from each other after a combined beam undergoes a first pass through the interferometer optics. During the first pass, a combined measurement beam undergoes a first pair of reflections from a measurement mirror before being separated into separate measurement beams, one for each measurement axis. Each of the separated measurement beams separately pass a second time through the interferometer optics and undergoes a second pairs of reflections from the measurement mirror. Similarly, a combined reference beam makes a first pass through the interferometer optics before being split into separated reference beams that make a second pass through the interferometer optics.
The combination of the reflections of the combined measurement/reference beams from the measurement/reference reflectors during the first pass and the reflections of the separated measurement/reference beams from the measurement/reference reflectors during the second pass eliminates beam walk-off due to misalignment of the measurement or reference mirror. During each pass, a pair of reflections from the measurement mirror and a pair of reflections from the reference reflector eliminates angular separation between the measurement and reference beams.
A multi-axis interferometer having N measurement axes separates the combined beam into N separated beams. The combined beam and the separated beams have different paths through the interferometer optics and separated reflection areas on the measurement and reference mirrors. The areas of the measurement and reference mirrors accommodate N+1 pairs of reflections instead of 2N pairs of reflections, which may otherwise be required to separately generate output beams with no beam walk-off. The measurement and reference mirrors may thus be smaller. The reduction in the number of separate beam paths also reduces the size of the interferometer optics.
One specific embodiment of the invention is a multi-axis interferometer that includes a main beam splitter system, measurement and reference reflector systems, a return reflector, and a secondary beam splitter system. The main beam splitter system receives an input beam and separates the input beam, typically according to polarization, into a combined measurement beam and a combined reference beam. The measurement and reference reflector systems respectively receive and reflect back the combined measurement beam and the combined reference beam from the main beam splitter system. A retroreflector can then direct the combined measurement beam and the combined reference beam back for respective second reflections from the respective measurement and reference reflector systems. After the pairs of reflections, the main beam splitter system forms a combined output beam in which central axes of the combined measurement beam and the combined reference beam are parallel and walked-off from each other by a distance that depends on relative misalignment of the reflector systems.
The return reflector and the secondary beam splitter receive the combined output beam from the main beam splitter system, split the combined output beams into separated beams that are directed back into the main beam splitter system. When the return reflector reflects the combined beam before the secondary beam splitter system splits the combined beam into the separated beams, the interferometer can use a single return reflector for all of the measurement axes, instead of requiring one return reflector per measurement axis.
The main beam splitter system splits each of the separated input beams into separated measurement and reference beams that respectively reflect at least once from the measurement and reference reflector systems and then recombine in pairs to form separated output beams corresponding to the separated input beams. Retroreflectors corresponding to the separated beams can direct the respective separated measurement/reference beams back for second reflections from the measurement/reference reflector systems.
The main polarizing system generally includes a polarizing beam splitter that splits the input beam by polarization to form reference and measurement beams. The reference reflector system typically includes a first quarter-wave plate and a reference reflector; and the measurement reflector system typically includes a second quarter-wave plate and a measurement reflector for mounting on an object being measured by the interferometer. The secondary beam splitter system typically includes a non-polarizing beam splitter so that the separated beams returning to the main beam splitter system contain polarization components that the main beam splitter system can split to form separated measurement and reference beams.
Another specific embodiment of the invention is a multi-axis interferometer including interferometer optics, a beam splitter system, and a return reflector. The interferometer optics split an input beam into a reference beam and a measurement beam and direct the measurement beam for at least one reflection from a measurement reflector that is on an object being measured. The interferometer optics similarly direct the reference beam for at least one reflection from a reference reflector. In the interferometer optics, the reference and measurement beams merge into a combined beam in which the reference and measurement beams are parallel but subject to walk-off that depends on the alignments and positions of the measurement and reference reflectors. The return reflector receives the combined beam and directs the combined beam into the beam splitter system. The beam splitter system splits the combined beam into a plurality of separated beams and directs the separated beams into the interferometer optics. The interferometer optics then split each of the separated beams into a reference beam and a measurement beam and direct each of these measurement beams for at least one reflection from the measurement reflector. The interferometer optics similarly directs the separated reference beams for one or more reflections from a reference reflector or reflectors. For each of the separated beams, the interferometer optics recombine the reference and measurement beams to form a separated output beam in which the reference and measurement beams are collinear.
The return reflector is generally such that shifting of an incident path of the incident beam causes shifting of the reflected beam, and the shifting of the reflected beam is identical in magnitude and direction to the shifting of the incident beam. The return reflector can include, for example, an isosceles prism having a base oriented so that the base is perpendicular to the combined beam.
Yet another embodiment of the invention is a multi-axis plane-mirror interferometer including a polarizing beam splitter, a measurement reflector system, a reference reflector system, a return reflector, and a non-polarizing beam splitter system. The polarizing beam splitter splits an input beam into a combined measurement beam and a combined reference beam. The measurement and reference reflector systems including plane mirrors respectively receive and reflect back the combined measurement and reference beams from the polarizing beam splitter.
The return reflector receives the combined measurement beam and the combined reference beam from the polarizing beam splitter after the reflections from the measurement and reference reflectors and directs the combined beams into the non-polarizing beam splitter system. The return reflector generally reflects an incident beam such as the combined beams from the polarizing beam splitter in a manner such that shifting the incident beam results in a matching shift of a reflected beam.
The non-polarizing beam splitter system splits the combined measurement beam into a plurality of separated measurement beams that are directed into the polarizing beam splitter and splits the combined reference beam into a plurality of separated reference beams that are directed into the polarizing beam splitter.
Retroreflectors can receive the combined measurement beam, the combined reference beam, and the separated measurement and reference beams after first respective reflections from the respective measurement and reference reflector systems. The retroreflectors direct the combined measurement beam, the combined reference beam, and the separated measurement and reference beams for second reflections from the respective reflector systems. The pairs of reflections eliminate angular variations between the measurement and reference beams due to misalignment of the reflector systems. Walk-off between the combined measurement and reference beams cancels subsequent walk-off between the separated measurement and reference beams.
Still another embodiment of the invention is a method for operating an interferometer. The method includes directing an input beam into the interferometer, where interferometer optics split the input beam into a reference beam and a measurement beam, cause the measurement beam to reflect from a reflector mounted on an object being measured, directs the measurement and reference beams out of the interferometer optics as a combined beam. The combined beam is then split into a plurality of separated beams that are directed into the interferometer optics. For each separated beam, the interferometer optics splits the separated beam into a reference beam and a measurement beam, causes the measurement beam to reflect from the reflector mounted on the object being measured, and direct the reference and measurement beams out of the interferometer optics as an output beam corresponding to the separated beam. Analysis of the output beams determines measurements along multiple axes.