Method for aligning a cylindrical laser optical resonator

A method for aligning the optical surfaces of the high extraction annular ring resonator which includes a scraper mirror with a decentered aperture. A probe beam, from an external laser, is directed into the resonator cavity through the decentered aperture in the scraper mirror. The symmetrical properties of the probe beam near and far field intensity distribution patterns are used to align the optical surfaces within the cylindrical ring resonator.

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The present invention relates to a method for aligning a cylindrical laser
 optical resonator and more particularly to a method for aligning a high
 extraction decentered annular ring resonator (HEXDARR).
 2. Description of the Prior Art
 Various types of lasers are known in the art. For example, chemical lasers
 are known. Examples of such chemical lasers are disclosed in U.S. Pat.
 Nos. 3,575,669; 3,992,685; 4,237,429; 4,514,698; 5,099,492; and 5,624,564,
 hereby incorporated by reference. In order to provide relatively high
 power lasers in a relatively compact configuration, lasers utilizing a
 cylindrical gain generator and an annular ring resonator have been
 developed. In such lasers, the cylindrical gain generator is disposed
 within an annular ring resonator. In such a configuration, the gain medium
 flows radially outwardly from the cylindrical gain generator into an
 annular gain volume of the cylindrical resonator. In order to extract the
 maximum amount of power from the annular gain volume, high extraction
 annular ring resonators have been developed, for example, as disclosed in
 U.S. Pat. Nos. 4,598,408 and 4,744,090, assigned to the same assignee as
 the present invention hereby incorporated by reference. Examples of other
 annular ring resonators are also disclosed in U.S. Pat. Nos. 4,606,036 and
 4,516,214. The annular ring resonators, for example, as disclosed in the
 '408 patent, include a conical rear reflector, a waxicon, a reflaxicon, a
 scraper mirror with a decentered aperture and a plurality of flat beam
 steering mirrors forming a compact leg of the resonator. The decentered
 aperture in the scraper mirror allows a circular beam of light to be
 transmitted therethrough and reflected in the compact leg of the waxicon.
 The waxicon expands the circular beam into an annular light beam which
 makes a first pass through the annular gain volume. The annular beam is
 reflected by the conical rear reflector and thus makes a second pass
 through the annular gain volume. The annular beam reflected from the rear
 reflector is reflected to the reflaxicon, where the beam is compacted and
 a portion thereof reflected through the decentered aperture of the scraper
 mirror as feedback with the balance of the beam outcoupled as an output
 beam.
 While such annular ring resonators provide relatively high gain, such
 resonators are not without disadvantages. For example, the alignment of
 the various optical surfaces within the resonators have heretofore been
 relatively difficult and require much more precision than standard
 spherical optical surfaces. Unfortunately, relatively small amounts of
 misalignment of the optical surfaces causes significant degradation of the
 optical quality of the coupled laser beam.
 SUMMARY OF THE INVENTION
 It is an object of the present invention to solve various problems in the
 prior art.
 It is yet another object of the present invention to provide a simplified
 method for aligning the optical surfaces within a cylindrical ring
 resonator.
 Briefly, the present invention relates to a method for aligning the optical
 surfaces of the high extraction annular ring resonator which includes a
 scraper mirror with a decentered aperture. A probe beam from an external
 laser is directed into the resonator cavity through the decentered
 aperture in the scraper mirror. The symmetrical properties of the probe
 beam near and far field intensity distribution patterns after the probe
 beam undergoes a single round-trip passage through the resonator are used
 to align the optical surfaces within the cylindrical ring resonator.

DETAILED DESCRIPTION
 The present invention relates to a method for systematically aligning a
 cylindrical resonator, such as a high extraction decentered annular ring
 resonator (HEXDARR) to produce an output mode phase distribution quality
 not heretofore achieved consistently. The method in accordance with the
 present invention uses the near and far field patterns of a HEX-DARR laser
 which may be simulated, as illustrated in the accompanying figures, or may
 be generated experimentally to align the laser. For the purpose of
 visualizing these properties, the near and far fields may be simulated for
 a particular laser; however, as will be understood by those of ordinary
 skill in the art the principles of the present invention are applicable to
 other lasers. In particular, the alignment method in accordance with the
 present invention is based on observations of certain key types of
 misalignment, indicated by the appearance of certain features in the near
 and far field intensity distribution patterns of the alignment probe beam
 after it passes one round trip through the resonator. In addition, the
 probe beam if it is suitably masked upon exiting the aligned resonator can
 be made to have certain reflection symmetry properties which become
 important for determining the quality of the alignment.
 A high extraction decentered aperture ring resonator (HEXDARR) is
 illustrated in FIGS. 1 and 2 and generally identified with the reference
 numeral 20. The resonator 20 is adapted to be used with a high power
 continuous wave chemical lasers which include a cylindrical gain generator
 22. As illustrated in FIG. 1, the gain generator 22 may be eccentrically
 disposed within the generally cylindrical resonator 20. As mentioned
 above, the gain medium from the gain generator 22 flows radially outward
 from the gain generator 22 and into an annular gain volume 24, the inner
 radius of which is defined by the exterior radius of the cylindrical gain
 generator 22 and the outer radius of which is defined by a downstream
 boundary where the flowing gain medium becomes absorbing. As will be
 discussed in more detail below, the high power gain of the laser is
 accomplished by a folded mode path through the annular gain volume 24. A
 compact leg, generally identified with the reference numeral 26, is used
 to provide feedback of the laser power to the annular gain volume 24 of
 the resonator. The compact leg 26 includes a plurality of flat beam
 steering mirrors BSM1, BSM2, BSM3, BSM4 and BSM11. The system also
 includes a rear cone mirror BSM6. As will be discussed in more detail
 below, the compact leg 26 provides feedback and directs a portion of the
 output beam back into the annular gain volume 24 for further
 amplification. The resonator 20 also includes a beam compactor system,
 illustrated within the box 28. The beam compactor system 28 includes a
 waxicon inner cone (WIC), a waxicon outer cone (WOC), a reflaxicon inner
 cone (RIC), and a reflaxicon outer cone (ROC). The beam compactor system
 28 is used to expand and compact the light beams to and from the annular
 gain volume 24. The compacted beam is directed to and reflected from a
 large turning flat BSM8. The light reflected from the large turning flat
 BSM8 is directed to a scraper mirror BSM9 with a decentered aperture 30.
 All of the light beam directed to BSM9 but the portion which is incident
 on the decentered aperture 30 is reflected from BSM9 forming an output
 beam. The scraper hole 30 allows a portion of the light beam reflected
 from the large turning flat BSM8 to pass through BSM9 to the compact leg
 26.
 In operation, as best shown in FIG. 2, a portion of the light beam
 reflected from the large turning flat (BSM8) is directed through the
 decentered aperture 30 in the scraper mirror BSM9 as a light beam 32 and
 from there to the feedback beam path 31. The balance of the light beam
 from the large turning flat BSM8 forms an output light beam 34. The light
 beam 32, directed through the decentered aperture 30 in the scraper mirror
 BSM9, is reflected from the flat steering mirror BSM1 as a light beam 36.
 The light beam 36 is directed toward the flat beam steering mirror BSM 2
 and reflected therefrom as a light beam 38. The light beam 38 is reflected
 from the flat beam steering mirror BSM 3 as a light beam 40, which, in
 turn, is reflected from another flat beam steering mirror BSM11 as a light
 beam 42. The light beam 42 is directed to the flat beam steering mirror
 BSM4, which is optically aligned with the waxicon inner cone (WIC). The
 light beam 42, reflected from the flat beam steering mirror BSM4, is then
 reflected to the waxicon inner cone (WIC) as the light beam 44. The
 waxicon inner cone (WIC) transforms the light beam 44 into a radially
 expanding beam 46 and directs it to the waxicon outer cone (WOC), which
 forms an annular light beam which is reflected as a light beam 48 to the
 rear cone mirror BSM6, making a first pass through the annular gain volume
 24. The rear cone mirror BSM6 causes the annular beam to be reflected back
 as a light beam 50 making a second pass through the annular gain volume
 24. The annular light beam 50 is directed to the reflaxicon outer cone
 (ROC), which compacts the annular light beam 50, and directs it to the
 reflaxicon inner cone (RIC), where it is compacted as light beam 54. The
 compacted light beam 52 is reflected from the reflaxicon inner cone (RIC)
 as a compacted light beam 54 which, in turn, is directed and reflected
 from the large turning flat BSM8. As mentioned above, a portion of the
 light beam reflected from the large turning flat BSM8 is directed through
 the decentered aperture 30 in the scraper mirror BSM9 forming a feedback
 loop while the remaining portion is outcoupled from the resonator forming
 an output beam 34.
 In order to optimize the phase quality of the output beam 34, the various
 optical surfaces within the resonator 20 must be optically aligned. As
 will be discussed in more detail below, the alignment system in accordance
 with the present invention is adapted to provide a relatively simple and
 systematic method for aligning the various optical surfaces within the
 resonator 20.
 The four mirrored surfaces of the beam compactor mirror system 28 (WIC,
 WOC, ROC and RIC) are known to be manufactured on a large optics diamond
 turning machine as two sets of mirror surfaces (WIC-RIC and WOC-ROC).
 These two sets of mirror surfaces are permanently aligned and mounted
 together so that the beam compactor mirror system 28 can be considered as
 a rigid unit. In addition, it is known that during the manufacturing
 process, an annular reference surface is disposed in a plane normal to the
 figure axis of the beam compactor system 28 on the WOC-ROC set. The point
 where the figure axis intercepts this plane is illustrated in FIG. 2 as
 the point A.
 For the purpose of discussion, a reference Cartesian coordinate system is
 selected as illustrated in FIG. 2. The rotational figure axis of the
 WIC-RIC unit of a perfectly aligned HEXDARR (and therefore also of the
 prealigned beam compactor system 28) defines the z axis of the reference
 Cartesian coordinate system. The positive sense of the z axis is directed
 toward the gain generator 22 and the rear cone BSM6. The origin of this
 coordinate system is located on the rotational figure axis of the beam
 compactor system 25 at point A. The corresponding x and y axes form a
 right-handed coordinate system with the x axis oriented so that the x, z
 plane passes through the center of the scraper hole 30.
 Prior to implementing the alignment method in accordance with the present
 invention, the beam compactor system 28 and the rear cone BSM6 are
 considered to be aligned to each other and to the cylindrical gain
 generator (shown in FIG. 1) by separate lower-resolution alignment
 techniques. The beam compactor system 28 and the rear cone BSM6 are
 assumed to be perfectly aligned, except for a possible translation error
 in their relative position along the z axis, if the rotational figure axis
 of the rear cone passes through the RIC tip and point A (and thus also
 through the WIC tip), i.e., when the figure axis of the rear cone BSM6
 coincides with the z axis The rear cone BSM6 is manufactured with an
 annular reference surface, which is normal to its figure axis, similar to
 the reference surface of the beam compactor system 28. A point B on the
 rear cone figure axis is defined to be that point where the rear cone
 figure axis intercepts the plane defined by the annular reference surface
 (see FIG. 2). Therefore, by definition, when the rear cone BSM6 is
 perfectly aligned, point B lies on the z axis.
 The alignment tolerance for angular rotation of the rear cone about any
 axis located in the plane normal to the z axis and passing through point
 B, includes errors in the alignment angle (rear cone tilt) which can be of
 the order of a milliradian without seriously degrading optical performance
 of the HEXDARR 20. A separate angular alignment technique is assumed,
 which brings the rear cone tilt error to a value which meets this angular
 alignment criterion.
 The displacement of point B from the z axis (rear cone decentration) by a
 distance of the order of a millimeter in any direction in the plane normal
 to the z axis can seriously degrade the optical performance of the HEXDARR
 22. If a low-resolution rear cone positioning technique, such as simple
 physical measurement, is used to place point B within a few millimeters of
 its perfectly aligned position, the method in accordance with the present
 invention can be used to place point B to within a few tenths of a
 millimeter of its perfectly aligned position in the plane normal to the z
 axis,
 The method in accordance with the present invention makes use of a probe
 beam derived from an external laser (not shown). This laser is not shown
 in FIGS. 1 and 2, but the probe beam path itself is indicated. This probe
 beam is assumed to be a single mode TEM.sub.00 beam characterized by an
 azimuthally symmetric gaussian intensity distribution, although any single
 mode rotationally symmetric form of probe beam may be used instead.
 The probe beam is injected into the resonator 20 through the scraper hole
 30 by means of a probe beam injection mirror (not shown), placed between
 BSM8 and the scraper mirror BSM9 (not shown in the figures). The mirrors
 of the feedback beam path (BSM1, BSM2, BSM3, BSM11 and BSM4) in the figure
 arranged in space so that they not only guide the probe beam from the
 scraper hole 30 to the WIC mirror, but also induce an arbitrary rotation
 of the beam, usually 0.degree. or 90.degree., about the center of the
 gaussian intensity distribution (see FIGS. 1 and 2). The compact leg 26 is
 aligned by independent means for example to produce a centration error of
 the probe beam on the WIC tip which is less than a millimeter and a
 propagation direction error of the probe beam at the WIC tip (probe beam
 and/or compact leg tilt) which is less than a few tens of microradians.
 This allowable centration error for the probe beam can be shown by
 simulation, for example, to produce a negligible beam quality degradation
 for the mode. The beam quality is, however, more sensitive to probe beam
 and/or compact leg tilt error. The inventive alignment method can be used
 to reduce this tilt error to less than ten microradians.
 The method in accordance with the present invention is based upon the
 following:
 (1) The use of symmetry properties of the probe beam near and far field
 intensity distribution patterns to aid in the alignment process. The probe
 beam is initially rotationally symmetric about the center of its gaussian
 intensity distribution. If the probe beam is aligned, this center is
 coincident with the center of the scraper hole 30 as the probe beam
 propagates through the scraper hole 30 after injection into the resonator
 20. The edge of the hole 30 will clip the external portions of the
 gaussian distribution so that only a truncated gaussian distribution
 propagates past the scraper mirror and into the resonator. This truncated
 gaussian distribution is still rotationally symmetric about its center if
 the injected beam is properly aligned and centered in the scraper hole 30.
 After it is injected into the resonator 20 and propagated a single round
 trip through the aligned resonator 20, the probe beam intensity
 distribution, while no longer gaussian, is still rotationally symmetric
 about the center of its intensity distribution. This center is coincident
 with the RIC tip position after the beam is reflected from the RIC. This
 intensity distribution is then incident on and reflected by the scraper
 mirror BSM9, which contains a scraper hole 30 whose center is not
 coincident with the center of the incident intensity distribution The
 intensity distribution after reflection from the scraper mirror BSM9 is no
 longer rotationally symmetric about the original center (the center of the
 distribution before reflection from the scraper mirror) because the
 portion of the beam which was incident on the scraper hole 30 is missing
 in the reflected beam. Therefore, the reflected beam has an off-center
 hole, or region devoid of intensity, in it. The symmetry of the reflected
 beam is therefore reduced to only a simple reflection symmetry about the
 line connecting the center of this hole 30 in its distribution with what
 was originally its center before reflection from the scraper mirror.
 Referring to the Cartesian coordinate system described previously, the
 reflected beam will have reflection symmetry about the x,z plane (see FIG.
 2). The far field pattern obtained from this probe beam field distribution
 reflected from the scraper mirror BSM9 will also have this same reflection
 symmetry. The features of the far field pattern exhibiting this reflection
 symmetry can be enhanced by removing from the probe beam near field more
 than just the field distribution lying within the scraper hole 30. Removal
 of any area of the rotationally symmetric probe beam near field by an
 aperture which has reflection symmetry about the x,z plane, such as the
 scraper hole 30 itself, will result in a far field with the same
 reflection symmetry. In the resonator 20, illustrated in FIGS. 1 and 2,
 the probe beam injection mirror is such an aperture and the area of the
 near field of the probe beam blocked by the injection mirror is much
 larger than the area of the scraper hole 30. Therefore, the features of
 the associated far field will have more prominent reflection symmetry. Any
 aperture which intensifies the far field features having a particular,
 non-rotational symmetry will aid in the alignment process.
 (2) The far field reflection symmetry is destroyed by any misalignment
 which does not have the same symmetry. For example, if the rear cone BSM6
 is decentered by displacing point B from the z axis to any point not
 contained in the x,z plane, the resulting far field pattern of the probe
 beam reflected from the scraper will not have reflection symmetry about
 the x,z plane. To restore this symmetry, point B does not need to be
 brought back to its aligned position, but only to a point in the x,z
 plane. This can be accomplished by translating point B, and hence the rear
 cone, in the .+-.y direction until point B lies in the x,z plane.
 Conversely, if the rear cone BSM6 is translated in the .+-.y direction, a
 position can be found where the far field is symmetric about the x,z
 plane. Thus, by correcting the positions of resonator elements in only one
 dimension, an intermediate alignment state characterized by reflection
 symmetry in the far field intensity distribution can be reached. Then,
 from this intermediate alignment state, by correcting the positions of the
 resonator elements in the dimension orthogonal to the first dimension,
 i.e., in the .+-.x direction, the final fully aligned state can be
 reached. Thus, what was inherently a two-dimensional search for the
 aligned position of a resonator element is reduced to two one-dimensional
 searches.
 (3) The appearance of the far field pattern of the probe beam after it
 propagates one round trip through the resonator 20 may be determined
 primarily by the effects of decentration of the rear cone BSM6 when the
 resonator 20 is close to alignment, i.e., when it is aligned by separate
 means to within the low-resolution tolerances discussed previously. This
 is true even in the presence of small, otherwise arbitrary, misalignments
 of other resonator elements. Thus, if the far field lacks the required
 reflection symmetry, the first step in this alignment concept is to
 translate the rear cone along the .+-.y direction until the far field
 attains the "best" reflection symmetry attainable through this process. In
 a manual alignment exercise, this is a subjective judgment left to the
 individual aligning the resonator. In an automatic alignment system
 utilizing this alignment technique, e.g., sensors which, for example,
 calculate odd moments of the far field distribution about the x,z plane
 can be used and their outputs minimized to obtain the "best" reflection
 symmetry.
 (4) The next step in this alignment concept is to translate the rear cone
 along the .+-.x direction until the near field phase distribution
 root-mean-square deviation is minimized.
 (5) The next step in this alignment concept is predicated on the
 observation that the near field intensity distribution of the probe beam,
 after it is reflected from the scraper, contains nearly circular
 interference fringes which at this stage of the alignment process will not
 in general be centered in the intensity pattern, but rather eccentrically
 aligned, or skewed away from the center of the pattern. These fringes can
 be centered by introducing a corrective tilt into the probe beam until, in
 the subjective judgment of the individual aligning the resonator, the
 centration of the fringes appears to be optimized. The direction of the
 axis about which the corrective tilt of the probe beam should be carried
 out is that direction which is orthogonal to the direction in which the
 fringes are initially skewed.
 (6) The steps indicated in (3)-(5) may be repeated until no further
 corrections are indicated
 The method in accordance with the present invention depends in part on
 utilizing an important reflection symmetry property of the near and far
 field intensity distributions of the probe beam after the beam exits the
 resonator and is viewed on a scatter plate (not shown). Before injection
 into the resonator 20, the TEM.sub.00 gaussian probe beam is, or should
 be, rotationally symmetric about its direction of propagation. If the
 departure from rotational symmetry for the injected beam is known
 quantitatively, it can be factored into the observations and calculations
 which follow. If this injected beam is suitably aligned (propagation
 direction parallel to the figure axis of the beam compactor 28) and
 centered on the scraper hole 30 upon injection, the beam is still
 rotationally symmetric after it leaves the reflaxicon inner cone (RIC)
 after a one round-trip propagation through the aligned resonator. This
 probe beam rotational symmetry property is preserved even in the presence
 of an arbitrary number of degrees of mode rotation in the compact leg.
 If it is assumed that the tolerances on the tilt and decentration errors
 allowable for the injected probe beam are similar to those for the
 corresponding compact leg alignment phenomena, the required tolerances on
 the probe beam are found to be of the order of 10 microradians for the
 injected probe beam tilt error and 1 millimeter for the injected probe
 beam centration error.
 FIGS. 3a and 3b show the near field intensity and phase distributions and
 FIG. 3c shows the far field intensity distribution associated with an
 infrared probe beam field distribution immediately after reflection from
 the RIC of a perfectly aligned experimental or test resonator (not shown).
 (These figures show properties of the beam before it reflects from the
 scraper, i.e., no scraper hole is shown. In the near field figures, the
 various quadrants are indicated as follows: A single dot in the corner of
 the figure denotes the A quadrant, two dots denote the B quadrant, etc.)
 The rotational symmetry is evident. The dark Maltese cross pattern in the
 center of FIG. 3a and the square pattern feature in the center of FIG. 3b
 are believed to be due to rectangular plotting grid aliasing of what are
 essentially rotationally symmetric field distributions. In the near field
 intensity distribution of FIG. 3a, circular interference fringes can be
 observed which are associated with the two circular apertures intercepted
 by the probe beam in the cylindrical resonator system as modeled, viz.,
 the scraper hole 30 and the waxicon tip (eversion of the beam between the
 inner and outer cones of the waxicon maps the inner cone tip into a
 limiting aperture in the annular leg). If the resonator and probe beam are
 in an aligned condition, the probe beam intercepts both of these resonator
 apertures in an azimuthally symmetric manner, so the interference fringes
 are circular and aligned with the center of the pattern.
 Reduction of the initial full rotational symmetry property of the probe
 beam to only a simple reflection symmetry property about the
 .phi.=45.degree. axis will always occur after reflection of the beam from
 the scraper mirror because of the presence of the scraper hole ill the B
 quadrant. The intensity distribution features associated with this
 reflection symmetry are further enhanced in the alignment procedure by the
 fact that part of the exiting beam in the region of the scraper hole 30 is
 apertured in a similar manner as the scraper hole by the backside of a
 mirror (not shown) used to inject the beam into the scraper hole,
 resulting in an obscuration of a full quadrant of the beam, viz., the B
 quadrant, in the near field. The reflection symmetry about the
 .phi.=45.degree. axis caused by the shadow cast by the injection mirror
 will be perfect only insofar as the injection mirror shadow is perfectly
 aligned with the x and y axes within the B quadrant. These tolerances are
 not so tight that a visual inspection which indicates alignment of the
 shadow is not sufficient
 Besides the injection mirror obscuration pattern, there generally occurs in
 the near field a set of more-or-less concentric bright and dark
 approximately circular interference fringes. The origin of this feature
 was discussed above in reference to features shown in FIG. 3a. If the
 fringes are not exactly circular, concentric and centered, then they will
 appear to be more-or-less off center and eccentrically rather than
 concentrically, aligned with respect to each other. These fringes are
 important features for consideration in the alignment process.
 The alignment method in accordance with the present invention makes
 important use of certain observations of the appearance of the near and
 far field intensity distributions under different conditions of resonator
 misalignment, particularly the conditions of compact leg tilt and rear
 cone decentration. When the resonator is close to the aligned
 configuration, the near field intensity distribution appearance is
 primarily determined by the presence or absence of compact leg and/or
 probe beam tilt, while the far field intensity distribution appearance is
 primarily determined by the presence or absence of rear cone decentration
 under the same conditions This very useful isolation of the effect of
 compact leg and/or probe beam tilt from the effect of rear cone
 decentration when the resonator is nearly aligned depends upon removing
 the displacement of the far field spot (or spots), caused by compact leg
 and/or probe beam tilt, from the far field intensity distribution. This is
 accomplished experimentally by a locked-up fast steering mirror. In other
 words, the principal effect of compact leg and or probe/beam tilt on the
 far field intensity distribution is to displace spatially, but not change
 the relative appearance of, the far field spot pattern. Thus, in the
 presence of a fast steering mirror and for a resonator configuration which
 is nearly aligned, the near field intensity distribution becomes a
 diagnostic primarily for the presence of compact leg and/or probe beam
 tilt error while the far field intensity becomes a diagnostic primarily
 for the presence of rear cone decentration error. This allows the angular
 alignment of the compact leg/probe beam to be conducted separately from
 the positional alignment of the rear cone in the final stages of the
 alignment procedure These alignments are not strictly independent,
 however, but by iterating between them, a perfectly aligned condition can
 be reached. (The beam compactor is implicitly considered here to be the
 reference element in these alignment schemes, i.e., the beam compactor is
 aligned to some absolute reference condition as well as possible by some
 independent technique, and all other elements are then aligned relative to
 it by the technique described here.)
 There are two other misalignment modes to be considered. In the above
 discussion, it has been assumed that the rear cone figure axis has been
 perfectly aligned parallel to the beam compactor figure axis, i.e., that
 there is no rear cone tilt present. Rear cone tilt affects the probe beam
 near and far field intensity distributions minimally if the resonator is
 close to the aligned condition, i.e., noticeable changes in the appearance
 of the near and far field intensity distributions due to changes in the
 angular position of the rear cone occur only when the alignment error in
 the angular position is of the order of milliradians. For example, FIGS.
 4a and 4b show the near field intensity and phase distributions and FIG.
 4c shows the simulated far field intensity distribution when the rear cone
 is tilted by one milliradian about the .phi.=45.degree. axis. The nms
 wavefront error associated with this alignment condition is calculated to
 be 0.1656 .lambda., or 0.4637 microns. Most of this error results from the
 tilt component introduced into the wave front by this large rear cone
 tilt. The presence of this tilt is indicated by the fact that the far
 field central spot, shown in FIG. 4c, is shifted vertically from the
 center of the figure. The tilt component amounts to a tilt of the near
 field by only 5 microradians in the presence of a 1000 microradian rear
 cone tilt. If the tilt and focus components of this near field are
 removed, then the wavefront error is reduced to 0.0666 .lambda., or 0.1865
 microns.
 Also, from suitable simulations, the appearance of the output intensity
 distributions is observed to be similarly relatively insensitive to
 compact leg/probe beam decentration if the resonator is close to the
 aligned condition, i.e., noticeable changes in the appearance of the near
 and far field intensity distributions occur only when the alignment error
 in the compact leg/probe beam centration is of the order of a millimeter.
 FIGS. 5a and 5b shows the near field intensity and phase distributions and
 FIG. 5c shows the far field intensity distribution obtained from
 simulations of the laser performance when the compact leg is decentered by
 one millimeter along the .phi.=0.degree. axis at the waxicon inner cone
 (WIC) station. The nns wavefront error for this alignment condition is
 calculated to be 0.09914 .lambda., or 0.2776 microns, which is only
 slightly different than that for the aligned condition. The slight
 displacement of the spot in FIG. 5c to the right of the center of the
 figure is associated with the induced tilt. The rms near field wave front
 error after the tilt and focus are removed from FIG. 5b is 0.04743
 .lambda., or 0.1328 microns It is assumed here that independent alignment
 techniques are available to assure that the rear cone tilt and the compact
 leg/probe beam decentration can be held to within these tolerances.
 The symmetry property associated with the aligned resonator which is used
 in this alignment scheme is the reflection symmetry about the
 .phi.=0.degree. line passing through the near and far field intensity
 distributions, i.e., reflection symmetry about a line normal to the axis
 of the beam compactor and passing through the center of the scraper hole
 30 or, alternatively, the line passing through the external corners of the
 D and B quadrants.
 To illustrate the alignment method in accordance with the present invention
 using results from simulations of the performance of a HEX-DARR laser, for
 example, as illustrated in the figures, an initial misalignment state for
 a known resonator was selected and modeled as to what would be seen
 experimentally at the end of each step in the alignment process. The near
 and far field patterns obtained for that state of alignment did not posses
 the reflection symmetry about the .phi.=0.degree. that which must be
 obtained if the resonator is in a fully aligned state and, therefore, the
 resonator was not aligned. In addition, the associated near field wave
 front error was rather large, being approximately 1.2 microns.
 FIGS. 6a, 6b and 6c show a simulation of the effect of just a 30 .mu.r
 compact leg tilt about .phi.=0.degree. axis. The tilt axis orientation
 choice is arbitrary in this example. It is implicitly assumed that the
 probe beam is aligned. In FIGS. 6a and 6b, the near field intensity and
 phase distributions for a resonator with the compact leg tilted by 30 mr
 about .phi.=0.degree.. The B quadrant is blocked out in FIG. 6a
 corresponding to the presence of the injection mirror. In FIG. 6c we show
 the corresponding far field intensity distribution. The rms phase error
 associated with FIG. 6b is 0.2620 .lambda., or 0.7336 microns. Most of
 this phase error is caused by the tilt component caused by the compact leg
 tilt. In FIG. 6c, the far field spot is no longer circular as in the
 previous far field figures, but rather is elongated more or less along
 .phi.=0.degree.. The elongation is caused by the near field blockage of
 the B quadrant. In addition to this effect, the far field spot is
 displaced along the .phi.=135.degree. direction as a result of the compact
 leg tilt.
 FIGS. 7a and 7b show the near field intensity and phase distributions for
 the case of FIG. 6, except that the near field phase distribution has had
 tilt and focus removed. This affects only FIGS. 7b and 7c, of course, so
 FIG. 7a is the same as FIG. 6a. FIG. 7c shows the corresponding far field
 intensity distribution. Here the spot is centered in the figure. The
 wavefront error associated with FIG. 7b is 0.0500 .lambda., or 0.1400
 microns.
 All further far field intensity distributions will be shown with the near
 field tilt and focus removed. The near field phase distribution plots
 will, however, contain the tilt and focus components. The rms wavefront
 error both with and without these components removed will be given. Since
 the far field intensity distribution shown in FIG. 7c looks much less
 structured than that for FIG. 8c, the wavefront error for FIG. 8b is much
 larger than that for FIG. 7b. This is due to the fact that, in addition to
 compact leg tilt, some probe beam alignment error and some rear cone
 decentration error were present. In addition, a rear cone displacement of
 1.5 mm along the .phi.=-45.degree. was introduced.
 In FIGS. 8a and 8b, the near field intensity and phase distributions are
 shown for a case where a rear cone decentration in the .phi.=-45.degree.
 direction has been added to the conditions of FIG. 6. The ring-like
 interference fringe structure is seen in FIG. 8a to be displaced
 principally in the .phi.=135.degree. direction, as it was at the beginning
 of the alignment exercise. After removal of the tilt and focus from the
 phase distribution shown in FIG. 8b, the rms wavefront error is 0.2602
 .lambda., or 0.7286 microns. The far field shown in FIG. 8c is seen to be
 quite structured, possessing no symmetry about .phi.=45.degree..
 ALIGNMENT METHOD
 STEP 1
 The axes are defined in FIG. 2 with the corrector plate removed and above.
 The near field is observed on the scraper, BSM9. The associated far field
 is a well-defined term in optical science.
 The method for aligning the HEXDARR resonator is presented below If it is
 assumed that the lack of symmetry for the far field pattern in FIG. 8c is
 due primarily to a rear cone centration error, which is not located along
 the .phi.=0.degree., 180.degree., (it is not. of course, since we have
 decentered the rear cone 1.5 mm along the .phi.=-45.degree. axis), then
 the rear cone can be moved to a position where the centration error is
 along the .phi.=0.degree., 180.degree. axis by displacing the cone along
 the .phi.=90.degree. axis. (Displacement in the opposite direction, i.e.,
 along the .phi.=-90.degree. axis, can be shown to make the far field
 pattern and near field rms phase error "worse".) Adjusting the rear cone
 position is done first since there is no independent theodolite
 information that the compact leg tilt error is no more than 30 .mu.r.
 Also, the observed far field pattern is too structured to be caused by
 this compact leg tilt error alone. A similar argument can be made about
 the effect of probe beam tilt error on the far field pattern in the
 presence of the fast steering mirror. That is, for tilt errors less than
 about 150 .mu.r, the principal effect on the far field is displacement of
 the pattern and this is removed by the fast steering mirror. FIGS. 9a and
 9b show the near field intensity and phase patterns after the cone has
 been moved in the .phi.=90.degree. direction, so that the resulting rear
 cone decentration error coordinates are 1.06 mm along the .phi.=-0.degree.
 direction. FIG. 9c shows that the resulting far field pattern is
 relatively symmetric about the .phi.=0.degree. axis. The rms wavefront
 error for FIG. 9b, after removal of tilt and focus, is 0.1982 .lambda., or
 0.5550 microns, which is lower than that for FIG. 8b.
 Since experimentally it will not be known exactly when the rear cone
 centration error is along the .phi.=0.degree., 180.degree. axis, this
 condition is reached by making a subjective judgment about when the
 "quality" of the reflection symmetry is maximized. FIGS. 10a and 10b show
 the near field intensity and phase distributions when the decentration is
 1.077 mm along the .phi.=-10.degree. direction, which is a position along
 the trajectory of the rear cone decentration adjustment as the cone moves
 towards the .phi.=0.degree. axis. As may be seen, these figures do not
 look very different than the corresponding ones in FIG. 9. The rms
 wavefront error for FIG. 10b, however, is actually less than that for FIG.
 9b, being 0.1957 .lambda.. This lower wavefront error probably results
 from the simultaneous presence of the compact leg tilt. This lower
 wavefront error for a rear cone decentration which does not lie on the
 .phi.=0.degree., 180.degree. axis will not present a problem for the
 alignment scheme, however, since the alignment process will be one of
 iteration between correcting the rear cone position and correcting the
 compact leg and/or probe beam tilt errors. FIG. 10c shows the resulting
 far field pattern for this case. The differences between the appearances
 of FIG. 9c and FIG. 10c are subtle, but in practice it will not matter
 whether we choose the intermediate alignment condition to be that
 corresponding to FIGS. 9c or 10c. The iteration process will conclude at
 the same final alignment condition in either case.
 To complete the picture at this step, FIGS. 11a and 11b show the near field
 intensity and phase distributions for the case where the trajectory of the
 rear cone adjustment has gone beyond the .phi.=0.degree. axis, with the
 final decentration placed at 1.077 mm along the .phi.=10.degree.
 direction. Again, the near field patterns are minimally different from
 those of FIGS. 9 and 10. However, the rms wave front error has increased
 to 0.2067 .lambda.. The corresponding far field shown in FIG. 11c is not
 quite as symmetric as in FIGS. 9c and 10c, but even if this intermediate
 alignment condition is chosen at this step, the iteration process will
 still lead to the same final aligned condition.
 STEP 2
 In the second step in the method of alignment, it is assumed that the rear
 cone position is selected consistent with FIG. 9 at the end of the first
 step, i.e., a rear cone decentration of 1.06 mm along the .phi.=0.degree.
 degree direction. Of course, the correct position for the rear cone is not
 precisely known but, based upon symmetry, it should lie in either the
 .phi.=0.degree., 180.degree. direction from our position at the end of the
 first alignment step. FIGS. 12a and 12b show the near field intensity and
 phase distributions if the rear cone is moved in the .phi.=180.degree.
 direction half way to the position of perfect alignment for the rear cone,
 i.e., to a position 0.53 mm along the .phi.=0.degree. direction. The rms
 phase error associated with the near filed is reduced to 0.4420 .lambda.,
 or 0.1052 .lambda. microns after removal of tilt and focus. FIG. 12c shows
 the much improved far field pattern. In contrast to this improvement, if
 the rear cone BSM6 is moved instead the same distance in the
 .phi.=45.degree. direction, i.e., to a position 1.59 mm along the
 .phi.=45.degree. direction, the results are as shown in FIGS. 13a, 13b,
 and 13c. The wave front error associated with FIG. 13b is increased to
 0.3056 .lambda. with tilt and focus removed and the far field shown in
 FIG. 13c has markedly increased in structure (and in reflection symmetry
 about .phi.=0.degree. because the rear cone position is precisely on the
 .phi.=0.degree. line and is the dominant aberration).
 If, instead of the rear cone position associated with FIG. 9, the rear cone
 position associated with FIG. 10 is erroneously selected as the most
 reflection symmetric case, then as the rear cone BSM6 is moved in the
 .phi.=180.degree. direction, it will miss the perfectly aligned rear cone
 configuration. The "distance of the closest approach" to the perfectly
 centered rear cone, if we start with the case of FIG. 10, can easily be
 calculated to be a rear cone decentration of 0.1860 mm along the
 .phi.=-90.degree. direction. FIGS. 14a and 14b show the near field
 intensity and phase distributions, while FIG. 14c shows the far field
 intensity distribution. The rms phase error associated with FIG. 14b,
 after removal of tilt and focus, is 0.05431 .lambda., which is very close
 to that of FIG. 7b. Comparison of FIG. 14c with FIG. 7c shows only minor
 differences but the principal secondary feature of FIG. 14c is a sidelobe
 oriented in the .phi.=90.degree. direction. This could be considered to be
 a "pointer" that indicates that the aligned position for the rear cone
 lies a short distance in this direction. In other words, consider the case
 of choosing instead the rear cone position associated with FIG. 11 as
 yielding the most "symmetric" intermediate alignment position for the rear
 cone. Then "distance of closest approach" is calculated to be on the
 opposite side of the aligned position, i.e., at a rear cone decentration
 of 0.1860 mm along the .phi.=85.degree. direction. FIGS. 15a and 15b show
 the near field intensity and phase distributions for this case and FIG.
 15c shows the associated far field intensity distribution. The rms phase
 error associated with FIG. 15b is 0.0642 .lambda.. The sidelobe feature
 associated with FIG. 15c is now on the opposite side of the main lobe,
 indicating that the position of best cone alignment is in that direction.
 STEP THREE
 If the rear cone is moved to the aligned position, then the field patterns
 correspond to those shown in FIG. 7. For the third step in the alignment
 process, the "circular" interference pattern is observed to be oriented
 toward .phi.=90.degree. direction. To centrate the fringe pattern so that
 it looks like that of FIG. 4a, the compact leg mirrors are tilted -30
 .mu.rad about .phi.=0.degree. axis. In this theoretical example, or
 course, it is assumed that the probe beam has no alignment tilt error and
 the fringe pattern orientation is entirely due to compact leg tilt error.
 If the fringe pattern orientation is due to a combination of probe beam and
 compact leg tilt errors, then the following procedure can be used to
 separate the effects if the tilts are very different in magnitude. After
 the rear cone position has been adjusted as outlined above, any remaining
 skewing of the fringe pattern can be corrected by tilting the compact leg
 until the fringe pattern is centered. If the amount of tilt adjustment is
 much greater than the bounds for compact leg tilt error estimated from the
 theodolite measurement, then it can be assumed that the excess is due to
 probe beam tilt misalignment. In any case, if a value is obtained for
 compact leg tilt adjustment that exceeds the theodolite error estimate,
 the compact leg is restored to its original state, followed by adjusting
 the probe beam alignment to centrate the fringe pattern. Nevertheless,
 compact leg tilt error should not exceed the theodolite error estimate at
 the end of this alignment. Any remaining errors in the probe beam
 alignment will not be larger than the theodolite error estimate for the
 compact leg tilt, since in the above scheme the two tilts will sum to
 zero. Of course, the final alignment error in the probe beam will not
 directly affect the resonator performance. The compact leg tilt error, if
 small enough, primarily affects only the output wave tilt.
 Steps 1-3 outlined above can be iterated upon a few times until no further
 adjustments are indicated. Then the resonator 20 should be considered to
 be aligned. It should also be understood that the method discussed above
 can be done manually or can be automated.
 Obviously, many modifications and variations of the present invention are
 possible in light of the above teachings. Thus, it is to be understood
 that, within the scope of the appended claims, the invention may be
 practiced otherwise than as specifically described above.