BACKGROUND OF THE INVENTION

The invention relates to electro-optical systems used to perform extremely accurate measurement of changes in either length or optical path length, e.g., interferometry systems. More particularly, the invention relates to an apparatus for use with an interferometry system in which the apparatus transforms a single frequency, linearly polarized laser beam into a beam with two frequency components that are orthogonally polarized.

The use of optical interferometry to measure changes in either length, distance, or optical path length has grown significantly due not only to technological advances in lasers, photosensors, and microelectronics but also to an ever increasing demand for high precision, high accuracy measurements [cf. N. Bobroff, “Recent advances in displacement measuring interferometry,”

Meas. Sci. Technol.,

4(9), 907-926 (1993)]. The prior art interferometers can be generally categorized into two types based on the signal processing technique used, i.e., either homodyne or heterodyne. The interferometers based on the heterodyne technique are generally preferred because (1) they are insensitive to low frequency drift and noise and (2) they can more readily have their resolution extended. Within the heterodyne type of interferometers, of particular interest are the ones based on the use of two optical frequencies.

In the prior art two-optical frequency heterodyne interferometers, the two optical frequencies are produced by one of the following techniques: (1) use of a Zeeman split laser, see for example, Bagley et al., U.S. Pat. No. 3,458,259, issued Jul. 29, 1969; G. Bouwhuis, “Interferometrie Mit Gaslasers,” Ned. T. Natuurk, 34, 225-232 (Aug. 1968); Bagley et al., U.S. Pat. No. 3,656,853, issued Apr. 18, 1972; and H. Matsumoto, “Recent interferometric measurements using stabilized lasers,”

Precision Engineering,

6(2), 87-94 (1984); (2) use of a pair of acousto-optical Bragg cells, see for example, Y. Ohtsuka and K. Itoh, “Two-frequency Laser Interferometer for Small Displacement Measurements in a Low Frequency Range,”

Applied Optics,

18(2), 219-224 (1979); N. Massie et al., “Measuring Laser Flow Fields With a 64-Channel Heterodyne Interferometer,”

Applied Optics,

22(14), 2141-2151 (1983); Y. Ohtsuka and M. Tsubokawa, “Dynamic Two-frequency Interferometry for Small Displacement Measurements,”

Optics and Laser Technology,

16, 25-29 (1984); H. Matsumoto, ibid.; P. Dirksen, et al., U.S. Pat. No. 5,485,272, issued Jan. 16, 1996; N. A. Riza and M. M. K. Howlader, “Acousto-optic system for the generation and control of tunable low-frequency signals,”

Opt. Eng.,

35(4), 920-925 (1996); (3) use of a single acousto-optic Bragg cell, see for example, G. E. Sommargren, commonly owned U.S. Pat. No. 4,684,828, issued Aug. 4, 1987; G. E. Sommargren, commonly owned U.S. Pat. No. 4,687,958, issued Aug. 18, 1987; P. Dirksen, et al., ibid.; or (4) use of two longitudinal modes of a randomly polarized HeNe laser, see for example, J. B. Ferguson and R. H. Morris, “Single Mode Collapse in 6328 Å HeNe Lasers,”

Applied Optics,

17(18), 2924-2929 (1978).

As for the prior art use of a Zeeman split laser to produce the two optical frequencies, this approach is only applicable to certain lasers (e.g., HeNe) and limits the frequency difference between the two optical frequencies to about 2 MHz. This imposes a limit on the maximum rate of change of the length or optical length being measured. In addition, the available power from a Zeeman split laser is less than 500 microwatts, which can be a serious limitation when one laser source must be used for the measurement of multiple axes, such as three to six axes.

The acousto-optical modulator with a single acousto-optical Bragg cell of Sommargren, commonly owned U.S. Pat. No. 4,684,828 and of Dirksen, et al., ibid., and the acousto-optical modulator with two acousto-optical Bragg cells of Dirksen, et al., ibid., are based on normal Bragg diffraction in both non birefringent and birefringent Bragg cells. The normal Bragg diffraction generates a diffracted beam wherein the state of linear polarization of the diffracted beam is the same state of linear polarization as the incident, undiffracted beam. However, the objectives of the heterodyne interfergmetry are usually best served when the two optical beam components from an acousto-optical modulator are frequency shifted one with respect to the other, orthogonally polarized, and collinear. The process of converting the output beam components generated by a normal Bragg diffraction acousto-optical modulator, i.e., two non collinear beams in the same linear polarization state into two collinear beams in orthogonally polarized beams, has had an efficiency significantly less than 100%.

Accompanying the increasing demand for improved high precision, high accuracy distance measurements is a demand to increase the number of axes being measured with distance measuring interferometry. The demand to increase the number of axes being measured translates to either increasing the number of laser source-acousto-optical modulator units, increasing the power of the laser source, and/or increasing the conversion efficiency with respect to power of the two frequency heterodyne source. An increase in the conversion efficiency is clearly an attractive option from a commercial point of view.

SUMMARY OF INVENTION

The present invention relates to an apparatus for providing light beams of orthogonal states of polarization and of different frequency for use in precision metrology applications such as in the measurement of length or length changes using interferometric techniques. The light beams of orthogonal states of polarization are typically parallel but may beneficially have a predetermined angle of divergence or convergence between them. Different embodiments of the invention are disclosed in the form of optical devices for efficiently converting an input optical beam comprising two components having differing frequency profiles, the same states of linear polarization, and directions of propagation differing by a small predetermined angle from a light source, typically comprising a single frequency laser and acousto-optical modulator, to an output beam having two principal, typically parallel, output beams of differing orthogonal states of polarization, one principal output beam comprising substantially the same frequency components as one of the input beam components and another principal output beam comprising substantially the same frequency components as another of the input beam components. The frequency profiles of the input beam components are typically different but may beneficially have the same frequency profiles for some applications. The energy flux profiles of the principal output beams may be spatially separated, partially coextensive, or substantially coextensive in accordance with the details of particular device embodiments. The input beam is introduced to a series of at least one phase retardation plate where it experiences phase retardations via optical birefringence of the at least one phase retardation plate to form two sets of orthogonally polarized internal beam components diverging by a small angle. The two sets of orthogonally polarized internal beam components subsequently become four external beams two of which, the principal ones, are available outside of the at least one phase retardation plate for use in anticipated downstream applications. The remaining two of the four output beams are typically reduced to nominally zero intensities compared to the intensity of the input beam so as to achieve a high efficiency conversion of the input beam into the principal output beams, thus rendering the two output beams with reduced intensities spurious. Spatial filtering may be used to further control any negative impact of the spurious beams.

Depending on the specific embodiment, progenitor beam components of selected ones of the external beams are either intercepted within or outside the series of at least one phase retardation plate so that the selected ones of the external beams are rendered typically parallel by a collimating means. The collimating means can be in the form of internal reflecting and/or integral refracting surfaces and/or external elements. However, if desired, the selected ones of the external beams can be non-parallel such that they have a predetermined angle of divergence or convergence between them.

The degree of overlap or spatial separation between the energy flux profiles of the principal, linearly-orthogonally polarized, external beams is controlled by various internal reflecting and refracting properties of the series of at least one phase retardation plate including the birefringence and optical properties of the material of the series of at least one phase retardation plate, the length of the physical path of travel experienced by the internal beam components, and/or the use of external control elements.

Thermal compensation can be provided via the use of thermal compensating birefringent elements or the arrangement of external components with respect to the series of at least one phase retardation plate or some combination of both. The surfaces of the series of at least one phase retardation plate, thermal compensating birefringent elements, the external elements, and the external control elements may be anti-reflection coated where appropriate to improve efficiency.

In general, in one aspect, the invention features an optical system including: a source which during operation generates two nonparallel propagating source beams; and a retarder element positioned to receive the two nonparallel propagating source beams and convert them into two nonparallel propagating output beams that are polarized substantially orthogonal to one another.

The optical system may include any of the following features. The nonparallel propagating source beams are diverging. The nonparallel propagating source beams are converging. The nonparallel propagating output beams are diverging. The nonparallel propagating output beams are converging. The retarder element is a retardation plate having substantially parallel entry and exit faces. The system further includes an additional retarder element positioned along a path defined by the source and output beams. The additional retarder element is positioned to receive the output beams and change their polarizations. The additional retarder is a half waveplate. The additional retarder is a quarter waveplate. The additional retarder element compensates for temperature dependent changes in the birefringence of the first mentioned retarder element. The additional retarder element is separate from the first mentioned retarder element. The additional retarder element is positioned to receive the nonparallel propagating output beams and generate nonparallel propagating output beams that exit from the additional retarder. The system further includes a third retarder element positioned to receive the nonparallel propagating output beams and generate substantially coextensive and collinear output beams that exit from the third retarder. The third retarder element is a birefringent prism. An optical axis of the retarder element lies substantially in a plane defined by the source beams. The retarder element is uniaxial. The optical frequencies of the two nonparallel propagating source beams differ from one another. The source includes: a laser generating a single-frequency, polarized beam; and a Bragg cell positioned to receive a beam derived from the polarized beam and generate the two nonparallel propagating source beams having optical frequencies that differ from one another. The source further includes: a source retarder element positioned to receive the beam derived from the polarized beam and transform it into ordinarily-polarized and extraordinarily-polarized beams, wherein immediately before exiting the source retarder element, the ordinarily-polarized and extraordinarily polarized beams generate a composite beam formed by a pair of overlapping beams, and wherein the Bragg cell is positioned to receive the composite beam and generate the two nonparallel propagating source beams having frequencies that differ from one another. The source further includes: a beam expander positioned to receive the beam derived from the polarized beam and expand the size of the polarized beam, and wherein the Bragg cell is positioned to receive the expanded beam and generate the two nonparallel propagating source beams having frequencies that differ from one another. The beam derived from the polarized beam is the polarized beam. The system further includes a beam contractor positioned to receive the nonparallel propagating output beams and contract the size of the nonparallel propagating output beams. The system is part of a distance measuring interferometry system, which also includes: an interferometer that directs at least a portion of one of the output beams along a reference optical path and at least a portion of the other of the output beams along a variable optical path and thereafter combines the portions of the output beams into a signal beam; and a detector for measuring an intensity of the signal beam. The detector includes a polarizer for producing a polarized signal beam having a polarization different from the polarizations of the output beams and the intensity of the signal beam measured by the detector is an intensity of the polarized signal beam. The interferometry system further includes measurement electronics for determining changes in the variable optical path from the measured intensity.

In general, in another aspect, the invention features a system including: a source which during operation generates first and second source beams propagating along nonparallel directions; and a retarder element positioned to receive the first and second source beams and to transform each of the first and second source beams into an ordinarily-polarized beam and an extraordinarily-polarized beam, wherein immediately before exiting the retarder element, the ordinarily-polarized and extraordinarily-polarized beams generated from the first source beam differ in optical phase by a first amount and the ordinarily-polarized and extraordinarily-polarized beams generated from the second source beam differ in optical phase by a second amount and wherein the first and second amounts differ by a value that is substantially equal to &pgr; radians (modulo 2&pgr;).

The system may include any of the following features. The first amount is substantially equal to &pgr; radians (modulo &pgr;). The first amount is substantially equal to &pgr;/2 radians (modulo &pgr;).

In general, in another aspect, the invention features a system including: a source which during operation generates first and second source beams propagating along nonparallel directions; and a retarder element positioned to receive the first and second source beams and transform each of the first and second source beams into overlapping ordinarily-polarized and extraordinarily-polarized beams, wherein upon exiting the retarder element the overlapping portions of the ordinarily-polarized and extraordinarily-polarized beams produced from the first source beam form a first output beam and the overlapping portions of the ordinarily-polarized and polarized beams produced from the second source beam form a second output beam and wherein the first and second output beams are polarized substantially orthogonal to one another.

The system may include any of the following features. An optical axis of the retarder element lies substantially in a plane defined by the first and second source beams. The optical axis makes an angle of about 45° with an axis collinear with the first source beam.

In general, in another aspect, the invention features a system including: a retarder element positioned to receive two nonparallel propagating input beams and convert them into two nonparallel propagating output beams that are polarized substantially orthogonal to one another; and a birefringent prism positioned to receive the two nonparallel propagating output beams from the retarder element and convert them into two substantially parallel optical beams that are polarized substantially orthogonal to one another.

The system may include any of the following features. The retarder element and the birefringent prism are integral with one another. One of the two nonparallel propagating output beams propagates within the birefringent prism as an ordinarily polarized beam and the other of the two nonparallel propagating output beams propagates within the birefringent prism as an extraordinarily polarized beam. The birefringent prism is made from a material in the group consisting of LiNbO

3

, KDP, quartz, and TeO

2

. The retarder element is made from a material in the group consisting of LiNbO

3

, KDP, quartz, and TeO

2

. The birefringent prism is a Wollaston prism. The system further includes a waveplate positioned between the retarder element and the birefringent prism.

In general, in another aspect, the invention features a system including: a source which during operation generates first and second source beams propagating along nonparallel directions; a retarder element positioned to receive the first and second source beams and produce first and second intermediate beams; and a birefringent prism positioned to receive the first and second intermediate beams and transform each of the first and second intermediate beams into ordinarily-polarized and extraordinarily-polarized beams, wherein the prism has a shape and a birefringence that causes the ordinarily-polarized beam produced from the first intermediate beam to produce a first output beam and the extraordinarily-polarized beam produced from the second intermediate beam to produce a second output beam, wherein the first and second output beams exit the prism substantially parallel to one another and wherein the combined energy of the first and second output beams is greater than half of the combined energy of the two source beams. In some embodiments, the polarizations of the first and second source beams are substantially the same.

In general, in another aspect, the invention features a system including: a source which during operation generates two nonparallel propagating source beams that are polarized substantially parallel to one another; a retarder plate positioned to receive the two nonparallel propagating source beams and produce two nonparallel propagating intermediate beams, wherein the retarder plate has a thickness, birefringence, and orientation that causes the two nonparallel propagating intermediate beams to be polarized substantially orthogonal to one another upon exiting the retarder plate; and a birefringent prism positioned to receive the two nonparallel propagating intermediate beams and produce two output beams that are polarized substantially orthogonal to one another, wherein the prism has a shape and a birefringence that causes the two output beams to be substantially parallel to one another.

The system may have any of the following features. The system further includes a half waveplate positioned between the retarder plate and the birefringent prism to change the polarizations of the two nonparallel propagating intermediate beams. An optical axis of the retarder plate is substantially orthogonal to an optical axis of the birefringent prism.

In general, in another aspect, the invention features a method including the steps of: generating first and second beams which propagate along nonparallel directions; separating each of the first and second beams into overlapping ordinarily-polarized and extraordinarily-polarized beams; retarding the extraordinarily-polarized and ordinarily-polarized beams produced from the first beam relative to one another, wherein the overlapping portions of the extraordinarily-polarized and ordinarily-polarized beams produced from the first beam form a first output beam; and retarding the extraordinarily-polarized and ordinarily-polarized beams produced from the second beam relative to one another, wherein the overlapping portions of the extraordinarily-polarized and ordinarily-polarized beams produced from the second beam form a second output beam, and wherein the first and second output beams are polarized substantially orthogonal to one another.

The method may include any of the following features. The method further includes the step of making the first and second output beams propagate parallel to one another. The method further includes the step of making the first and second output beams substantially coextensive with one another. The first and second output beams have optical frequencies that differ from one another.

The invention has many advantages. It provides systems and methods for efficiently generating two substantially coextensive and collinear beams having orthogonal polarizations. In particular, the present invention has a conversion efficiency of nominally 100% for conversion of input intensity into intensities of two orthogonally polarized exit beam components, and in certain end use applications the intensity of each of two orthogonally polarized exit beam components may be adjusted to nominally 50% of the input intensity.

The system is also compact and requires relatively few optics. Additional optics can be included to optimize the overlap of the orthogonally polarized beams and to compensate for temperature-dependent changes in the birefringence of the retarder elements.

Furthermore, in other embodiments, the invention provides an apparatus for generating orthogonally polarized beams of different frequency with a predetermined angle of divergence between them and a predetermined lateral separation between their energy flux profiles.

Also, the invention can provide the source beams for a heterodyne detection distance measuring interferometry system. Such systems can provide the precise position and orientation of objects being processed, such as in semiconductor wafer processing. Moreover, because of the efficient generation provided by the invention, a single laser source in the interferometry system can drive interferometric distance measurements over a large number of measurement axes. In some embodiments, the invention also uses an acousto-optic modulator to generate a relatively large frequency difference (e.g., about 20 MHz) in the orthogonally polarized beam. This large bandwidth enables relatively fast scan speeds in the distance measuring apparatus.

Other features and advantages of the invention will be apparent from the following detailed description, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The structure, operation, and methodology of the invention, together with other objects and advantages thereof, may best be understood by reading the detailed description in connection with the drawings in which each part has an assigned numeral that identifies it wherever it appears in the various drawings and wherein:

FIGS. 1

a

-

1

h

depict in schematic form the first embodiment and variants thereof of the present invention from the first category of embodiments and variants with

FIG. 1

a

depicting in schematic form the first embodiment;

FIG. 1

b

depicts in schematic form the first variant of the first embodiment of the present invention;

FIG. 1

c

depicts in schematic form the second variant of the first embodiment of the present invention;

FIG. 1

d

depicts in schematic form the third variant of the first embodiment of the present invention;

FIG. 1

e

depicts in schematic form the fourth variant of the first embodiment of the present invention;

FIG. 1

f

depicts in schematic form the fifth variant of the first embodiment of the present invention;

FIG. 1

g

depicts in schematic form and in greater detail the embodiment shown

FIG. 1

a;

FIG. 1

h

depicts a cross-sectional view of beams entering a birefringent prism;

FIGS. 2

a

-

2

c

depict in schematic form the second embodiment and variants thereof of the present invention from the second category of embodiments and variants with

FIG. 2

a

depicting in schematic form the second embodiment;

FIG. 2

b

depicts in schematic form the first variant of the second embodiment of the present invention;

FIG. 2

c

depicts in schematic form the second variant of the second embodiment of the present invention;

FIGS. 3

a

-

3

b

depict in schematic form the third embodiment and variant thereof of the present invention from the third category of embodiments and variants with

FIG. 3

a

depicting in schematic form the third embodiment;

FIG. 3

b

depicts in schematic form the first variant of the third embodiment of the present invention;

FIG. 4

depicts in schematic form the fourth embodiment of the present invention from the fourth category of embodiments and variants;

FIG. 5

depicts in schematic form an embodiment of a light source for use with the embodiments in the

FIGS. 1-4

;

FIG. 6

depicts in schematic form a distance measuring interferometry system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention relates to apparatus for providing light beams of orthogonal states of polarization and of different frequency for use in precision metrology applications such as in the measurement of length or length changes using interferometric techniques. A number of different embodiments of the invention are disclosed in the form of optical devices for efficiently transforming an input optical beam comprising two components having differing frequency profiles, the same states of linear polarization, and directions of propagation differing by a small predetermined angle from a light source to an output beam having two principal, typically parallel, output beams of differing states of polarization, one principal output beam comprising substantially the same frequency components as one of the input beam components and a second principal output beam comprising substantially the same frequency components as one other of the input beam components. The frequency profiles of the input beam components are typically displaced one from the other but may beneficially have the same frequency profiles. The energy flux profiles of the principal output beams may be spatially separated, partially coextensive, or substantially coextensive in accordance with the details of particular device embodiments and the requirements of the metrology or other contemplated application. In addition, thermal compensation may be made available through the use of thermal compensating elements.

Referring to the drawings in detail, and initially to

FIG. 1

a

,

FIG. 1

a

depicts, in diagrammatic form, the first embodiment of the present invention. The primary optical element in the first embodiment is a phase retardation plate

60

, shown in

FIG. 1

a

, typically made of a birefringent crystal, e.g. LiNbO

3

, potassium dihydrogen phosphate (KDP), or paratellurite (TeO

2

), or another birefringent material, e.g. liquid crystals. The input beam

41

, incident on a phase retardation plate

60

, comprises two components,

42

and

44

, with the two components having substantially the same but different frequencies, the same state of linear polarization, and directions of propagation differing by a small angle &dgr;, as shown in

FIG. 1

a

, from a light source

40

, comprising, for example, a single frequency laser and an acousto-optical modulator. The directions of polarizations of beams

42

and

44

are substantially at 45° to the plane of

FIG. 1

a

, the direction of the polarization of a beam relative to the plane of

FIG. 1

a

being indicated in

FIG. 1

a

as the angle in parentheses located next to the light beam number. For a given light beam, the angle is positive for a right-handed rotation from the x axis about a z axis, the x axis being contained in the plane of

FIG. 1

a

, the y axis pointing out of the plane of

FIG. 1

a

, and the z axis pointing in the direction of propagation of the given light beam. The optical axis

61

of the phase retardation plate

60

is orientated at an angle &agr;

1

with respect to a normal to the entrance facet of phase retardation plate

60

as illustrated in

FIG. 1

a

and orthogonal to a normal to the plane of

FIG. 1

a.

Upon entering crystal

60

, component

42

becomes first and second components

62

and

63

, respectively, of an internal beam, wherein internal beam components

62

and

63

are ordinarily (90°) and extraordinarily (0°) polarized, respectively. Similarly, the second component

44

of the input beam becomes on entering phase retardation plate

60

third and fourth components

64

and

65

, respectively, of the internal beam, wherein internal beam components

64

and

65

are ordinarily (90°) and extraordinarily (0°) polarized, respectively.

Since beam components

42

and

44

are incident on retardation plate

60

at different angles relative to optic axis

61

, extraordinarily polarized beam components

63

and

65

propagate within retardation plate

60

with phase velocities corresponding to different indices of refraction.

In general, the index of refraction n for an extraordinarily polarized beam propagating at an angle &thgr; with respect to an optical axis of a birefringent crystal is

1

n

2

=

cos

2

⁢

θ

n

o

2

+

sin

2

⁢

θ

n

e

2

(

1

)

where n

o

and n

e

are the ordinary and extraordinary principal indices of refraction of the birefringent crystal. The different indices of refraction for beam components

63

and

65

can be determined from Eq. 1. The index of refraction for ordinarily polarized beam components

62

and

64

is n

o

. According to these indices of refraction, the optic axis orientation (angle &agr;

1

) and the thickness d

1

of retardation plate

60

are chosen such that retardation plate

60

introduces a phase shift of p&pgr; radians in beam

63

relative to beam

62

and a phase shift of (p+1)&pgr; radians in beam

65

relative to beam

64

, p being an integer. Typically the angle &agr;

1

is set at a value substantially equal to 45°.

For example, for a divergence of about 3.5 mrad between beam components

42

and

44

, each having visible wavelengths and being incident substantially normal to a LiNbO

3

retardation plate

60

having an optic axis orientation of &agr;

1

=45°, a suitable thickness d

1

is about 2.4 mm, or odd multiples thereof. For a retardation plate made of a material more birefringent than LiNbO

3

, such as TeO

2

, a suitable thickness can be smaller. In the case of TeO

2

it would be about 1.4 mm.

Beams

62

,

63

,

64

, and

65

exit phase retardation plate

60

as beams

72

,

73

,

74

, and

75

, respectively. As a consequence of the phase shifts introduced in beams

62

,

63

,

64

, and

65

, the polarization of portions of beams

72

and

73

that overlap one another is substantially at 45° to the plane of

FIG. 1

a

and is substantially orthogonal to the polarization of portions of beams

74

and

75

that overlap one another, which is substantially 135° to the plane of

FIG. 1

a

. The directions of propagation of beams

72

and

73

are parallel and the directions of propagation of beams

74

and

75

are parallel, the entrance and exiting faces of retardation plate

60

being substantially parallel.

There is a small lateral shear S

b

between beams

72

and

73

and between beams

74

and

75

as shown in

FIG. 1

a

, the two lateral shears being substantially the same. The lateral shears are primarily a consequence of the difference in the direction of the respective energy flux vectors and the wave front vectors for extraordinarily polarized beams

63

and

65

in phase retardation plate

60

. The lateral shears between beams

72

and

73

and between beams

74

and

75

depicted in

FIG. 1

a

are exaggerated for the purpose of clearly illustrating the effects. Typically, the lateral shear S

b

is substantially smaller than the spot size of beam components

72

,

73

,

74

, and

75

, which is typically not smaller than about 1 mm. For example, if either of beam components

42

and

44

are incident on a 2.4 mm thick LiNbO

3

retardation plate

60

at approximately an angle of normal incidence and &agr;

1

is approximately 45°, the lateral shear S

b

between beam components

72

and

73

, or

74

and

75

is approximately 90 microns. Thus beams

72

and

73

and beams

74

and

75

substantially overlap in most cases.

Referring again to

FIG. 1

a

, beams

72

,

73

,

74

, and

75

enter a birefringent prism

120

made of a negative uniaxial crystal, e.g. LiNbO

3

or KDP. The optical axis of birefringent prism

120

is orientated at an angle of 45° to the plane of

FIG. 1

a

. Alternatively, for a birefringent prism

120

made of a positive uniaxial crystal, e.g. quartz or TeO

2

, the optical axis of birefringent prism

120

is orientated at an angle of 135° to the plane of

FIG. 1

a.

Upon entering birefringent prism

120

, each of beams

72

,

73

,

74

, and

75

separate into an ordinarily polarized beams (polarized at about 135°) and an extraordinarily polarized beams (polarized at about 45°). Because beams

72

and

73

substantially overlap one another and because of the phase difference between these two beams introduced by retardation plate

60

, the ordinarily polarized beams from beams

72

and

73

destructively interfere with one another, substantially canceling out each other. Thus, the ordinarily polarized beams from

72

and

73

are not shown in

FIG. 1

a

. Conversely, the extraordinarily polarized beams from beams

72

and

73

constructively interfere with one another and emerge from prism

120

as beams

92

and

93

, respectively, which substantially overlap and have polarizations of 45°. Similarly, the extraordinarily polarized beams from beams

74

and

75

destructively interfere with one another, substantially canceling out each other. Thus, the extraordinarily polarized beams from beams

74

and

75

are not shown in

FIG. 1

a

. The ordinarily polarized beams from beams

74

and

75

constructively interfere with one another and emerge from prism

120

as beams

94

and

95

, respectively, which substantially overlap and have polarizations of −45°.

The apex angle &agr;

2

of birefringent prism

120

is selected so that beams

92

and

93

exit birefringent prism

120

parallel to beams

94

and

95

. This is possible because beams

92

and

93

emerge from beams propagating as extraordinarily polarized beams in prism

120

and beams

94

and

95

emerge from beams propagating as ordinarily polarized beams in prism

120

. As a result, the system produces a pair of substantially equal-intensity output beams, beam

96

(formed from the superposition of beams

92

and

93

) and beam

97

(formed from the superposition of beams

94

and

95

), beams

42

and

44

being of substantially equal intensities, that propagate parallel to one another and have orthogonal polarizations (45° and −45°, respectively). There is a small non zero lateral shear between beams

92

and

94

, S

a

, which is exaggerated in

FIG. 1

a

. Typically this shear is less than about 100 microns. Beams

92

and

93

have the same frequency profile as the first input beam component

42

and beams

94

and

95

have the same frequency profile as the second input beam component

44

, which is different from that of beams

92

and

93

if, for example, beams

42

and

44

emerge from an acousto-optic modulator within light source

40

.

In some cases, such as when the lateral shear S

b

is not negligible, the destructive interference between portions of beams

72

and

73

that propagate as ordinarily polarized beams within prism

120

is not complete. Similarly, the destructive interference between portions of beams

74

and

75

that propagate as extraordinarily polarized beams within prism

120

can also be incomplete. However, even in these cases, birefringent prism

120

insures that beam

96

(which emerges from extraordinarily-polarized beams) has a polarization orthogonal to the polarization of beam

97

(which emerges from ordinarily-polarized beams). As shown in

FIG. 1

g

, portions of beams

72

and

73

that propagate as ordinarily polarized beams within prism

120

and do not completely cancel out because of destructive interference emerge as spurious beams

92

a

and

93

a

, which diverge away from beams

96

and

97

. Similarly, portions of beams

74

and

75

that propagate as extraordinarily polarized beams within prism

120

and do not completely cancel out because of destructive interference emerge as spurious beams

94

a

and

95

a

, which also diverge away from beams

96

and

97

. Because of the divergence, a spatial filter can be used to separate the spurious beams from output beams

96

and

97

.

The retardation imparted by retardation plate

60

minimizes the energy in spurious beams

96

a

(the combination of beams

92

a

and

93

a

) and

97

a

(the combination of beams

94

a

and

95

a

) by the destructive interference of beams

92

a

and

93

a

and beams

94

a

and

95

a

, respectively. And, the retardation imparted by retardation plate

60

maximizes the energy in beams

96

(the combination of beams

92

and

93

) and

97

(the combination of beams

94

and

95

) by the constructive interference of beams

92

and

93

and beams

94

and

95

, respectively.

FIG. 1

h

shows a cross-section of beams

72

,

73

,

74

, and

75

before entering birefringent prism

120

(intersecting reference plane

77

in

FIG. 1

g

). For purposes of illustration, the beams have exaggerated lateral shears S

a

and S

b

. The overlapping portions of beams

72

and

73

produce superposition beam

78

having a polarization of 45° and the non-overlapping portions,

86

and

87

, retain the polarizations of beams

72

and

73

, respectively. Similarly, the overlapping portions of beams

74

and

75

produce superposition beam

79

having a polarization of 135° and the non-overlapping portions,

88

and

89

, retain the polarizations of beams

74

and

75

, respectively. Superposition beams

78

and

79

contribute entirely to output beams

96

and

97

, respectively, after passing through prism

120

. In contrast, non-overlapping portions

86

,

87

,

88

,

89

contribute equally to output beams

96

and

97

and spurious beams

92

a

,

93

a

,

94

a

, and

95

a

after passing through prism

120

. Thus, for a retardation plate imparting the correct phase differences, the energy in the spurious beams decreases with lateral shear S

b

.

In some cases, small amounts of the overlapping portions of beams

72

and

73

, and beams

74

and

75

, also contribute to the spurious beams if the respective retardations imparted by retardation plate

60

are not homogeneous across the respective beam profiles or differ from the correct amount (i.e., a phase shift of p&pgr; radians in beam

63

relative to beam

62

where p is an integer and a phase shift of (p+1)&pgr; radians in beam

65

relative to beam

64

). However, even in such cases, birefringent prism

120

insures that output beams

96

and

97

have orthogonal polarizations. The efficiency of the transformation of input beam

41

into output beams

96

and

97

may be defined differently for different end use applications. One end use application may simply consider only the efficiency of transformation into an output beam without concern for degree of overlap or coextensiveness of output beam components whereas in another end use application, the degree of overlap or coextensiveness of output beam components is important such as in the creation of heterodyne interference signals. The efficiency of the transformation with respect to the creation of a heterodyne signal is dependent on a series of factors comprising the size of the lateral shear S

b

, the size of lateral shear S

a

, and the size of the small angle &dgr; relative to the size of the beam divergence of the input beam components

42

and

44

, the size of a beam divergence being related to the diameter of the beam.

The size of lateral shear S

a

effects the degree of overlap of the amplitudes of light beams with differing frequencies leading to the heterodyne signal. The size of a beam divergence relative to the size of the small angle &dgr; effects the size of the variation in the &pgr; phase shift introduced between the relative phase of beams

64

and

65

and the relative phase of beams

62

and

63

that can be achieved by the phase retardation plate

60

. Expressions for the efficiency are obtained for the case where the amplitudes of beams

72

,

73

,

74

, and

75

are constant across the respective wavefronts to illustrate in the simple form the properties of the invention without departing from the spirit and scope of the invention.

One expression for the efficiency Eff(S

a

, S

b

) is

Eff

⁡

(

S

a

=

0

,

S

b

)

=

⁢

1

π

⁢

(

ϑ

b1

⁢

cos

⁢

⁢

2

⁢

φ

+

ϑ

b2

)

-

⁢

S

b

2

⁢

R

⁢

1

π

⁢

(

sin

⁢

⁢

ϑ

b1

⁢

cos

⁢

⁢

2

⁢

φ

+

1

2

⁢

sin

⁢

⁢

ϑ

b2

)

(

2

)

where

ϑ

b1

=

cos

-

1

⁡

(

S

b

2

⁢

R

)

(

3

)

ϑ

b2

=

cos

-

1

⁡

(

S

b

4

⁢

R

)

(

4

)

φ

=

(

S

b

2

⁢

R

)

⁢

⁢

(

λ

0

2

⁢

R

)

⁢

π

δ

(

5

)

S

b

=(

r

−&thgr;)

d

1

  (6)

R is the radius of the output beam components, &lgr;

0

is the wavelength of the light beam in vacuum, d

1

is the thickness of phase retardation plate

60

as shown in

FIG. 1

a

, and r is the angle between the energy flux vector of a beam and the optical axis of phase retardation plate

60

and having the angle &thgr; between the normal to the wave front of the beam and the optical axis of phase retardation plate

60

.

A second expression for the efficiency Eff(S

a

, S

b

) is

Eff

⁡

(

S

a

,

S

b

=

0

)

=

2

π

⁢

(

ϑ

a

-

S

a

2

⁢

R

⁢

sin

⁢

⁢

ϑ

a

)

(

7

)

ϑ

a

=

cos

-

1

⁡

(

S

a

2

⁢

R

)

(

8

)

The angle r is related to &thgr; and the principal indices of refraction n

0

and n

e

of phase retardation plate

60

according to the formula

tan

⁢

⁢

r

=

n

o

2

n

e

2

⁢

tan

⁢

⁢

θ

(

9

)

[cf. Section 7 of Chapter 10 by J. Bennett and H. Bennett, “

Handbook of Optics

(McGraw-Hill, New York) 1978]. By mathematical manipulation of Eq. (9), the difference (r−&thgr;) can be expressed as

tan

⁡

(

r

-

θ

)

=

(

n

o

2

-

n

e