Abstract:
Limiter optics for an ignition feedback regenerative free electron laser amplifier have a pickoff mirror direct a portion of the output from the free electron laser through a focusing assembler. After expanding this pickoff beam spatially and temporally, the focusing assembler first focuses the expanded pickoff beam to a focal point, the expanded focused pickoff beam is then passed through a movable limiter plate which serves as an off switch if the pickoff beam is above a predetermined intensity and then refocuses the expanded pickoff beam back into the free electron laser to enhance the emission intensity of the output beam. The expanded mirror may be a half silvered mirror or a phased mirror with a plurality of mesas. The pickoff mirror may be convex. The half silvered mirror produces two segments in the pickoff beam with a time lag dependent on the thickness of the mirror. The phased mirror creates a plurality of parallel beams for the expander beam with a predetermined time lag for each of said paralleled beams created. Orientation of a phased mirror may be rotated to control spatial separation of parallel beams.

Description:
RELATED APPLICATIONS 
     The benefit of U.S. Provisional Application Serial No. 60/178,531, filed Jan. 25, 2000 is claimed. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates in general to the control of high-powered lasers, and, in particular, to improving the reliability, safety and power output of free electron lasers. 
     2. Description of the Prior Art 
     Manmade space satellites are limited by their power requirements. Solar panels have long been used to provide power for satellites. Solar panels are limited for two reasons. First the energy received from the sun is relatively diffuse and is not adjustable. For a fixed surface area the power that can be created by the solar panel is limited. The greater the power, the larger the surface area required. Mirrors have been used in space to reflect more sunlight on a fixed area. This leads to the second limitation, the mass and volume of the solar panel needed to generate the required power level. For high power levels the mass and volume can force reductions in the remaining portions of the satellite. Even the use of mirrors reduces the mass and volume available for launch payloads. The power limitations force most satellites to be designed to operate on the power requirements of a small household appliance. 
     Electrical power has always been a limiting factor for satellites, and it restricts the services that they can perform. The need for additional transponders to satisfy the demand for satellite-supplied television, e-mail, worldwide web, long distance telephones, rapid computer data transfer, and many other types of telecommunication is increasing. The number of transponders has risen from about 24 active transponders per satellite in the late 1980&#39;s to 94 active transponders on the Hughes satellite launched in late 1997. The demand for additional power over the last few years fits an exponential curve and the end is not in sight. Instead it is increasing even faster. In response to the need for additional frequencies to carry the load the Federal Communications Commission has opened up the Ka band for satellite use. Recently completed National Aeronautics and Space Administration (NASA) studies indicate that the Ka band will on occasion require the availability of up to ten times the power requirements of the lower frequency L, C and Ku bands to counter rain fade. 
     The additional power needed for the Ka band is required to keep the television signals broadcast to earth at an acceptable level of quality. The Ka frequency band is 26.5 to 40 gigahertz (wavelength range of 11 millimeters to 7 millimeters). The size of raindrops is typically 1 to 3 millimeters with a maximum of 5 to 7 millimeters. Although the Ka band is in a water absorption region, much of the extinction of the signal is caused by the resonance in scattered energy resulting from the proximity of the wavelength to the raindrop size. The only practical source for the additional power required is additional electricity from the solar panels carried on the satellite. 
     At present the size of satellite solar panels is awkwardly large. Additional satellites in the same “space slot” can be deployed to increase the total solar panel area, and this is the direction that many satellite companies are going. A major drawback of this approach is that the output signals of the various satellites are not in phase, so interference between satellite transmissions can be a problem. The biggest drawback, however, is that the multiple satellite approach is very expensive. 
     One way to repower the satellites is laser power beaming, LPB. Laser beams can increase the power level an order of magnitude above that available from the sun. Further, since a laser can be tuned to a narrow frequency range, the efficiency of the solar panels can be maximized by using their optimum generating wavelength. Beaming from the earth&#39;s surface requires the laser beam to travel through our planet&#39;s atmosphere. For LPB to be effective the atmospheric path must be free of clouds. In addition, the atmosphere can cause various other problems associated with turbulence, scatter, and absorption. Sites with clear, smog-free air minimize the last two problem areas. Turbulence is handled by the use of adaptive optics. 
     Free electron lasers, FELs, are capable of high power without significant wavefront distortion since the light is generated in a vacuum. An ignition feedback regenerative free electron laser (FEL) amplifier (IFRA FEL) designed by Kim, Zholents and Zolotrev does not need cavity mirrors, a power-limiting feature of most types of lasers. It provides greater output power than prior FELs. By feeding a portion of the output power back through the undulator and a portion to the photocathode emitting electrons, optical power grows without the necessity of cavities. Their invention is disclosed in U.S. pat. application Ser. No. 09/361,675. Other prior art patents for free electron lasers include Sheffield U.S. Pat. No. 5,960,013 and Edighoffer U.S. Pat. No. 5,029,172. One problem with IFRA FEL is that the portion of the beam fed back can grow in power, increasing the output of the laser and going into a runaway situation. A further problem with IFRA FEL is that the generated optical pulse is of the same duration as the electron bunch that emitted the pulse. This causes phasing problems unless the optical feedback loop can be accurately controlled. Any portion of an electron bunch out of phase with the optical pulse is wasted. This invention provides a means for phasing of the feedback loop and a means for control of the internal efficiency within the undulator so positive feedback producing a runaway condition does not occur. This invention provides a method and mechanism to lengthen the duration of the optical pulse fed back to the IFRA FEL. 
     SUMMARY OF THE INVENTION 
     Limiter optics for an ignition feedback regenerative free electron laser (FEL) amplifier, IFRA FEL, are made by using a very small pickoff mirror to direct a portion of the IFRA FEL&#39;s output beam to a pulse expander mirror. Light reflected from the expander mirror is then passed through focusing optics, which refocuses this pulse expanded light beam to a predetermined location within the undulator of the IFRA. FEL. Since it lengthens the duration of the IFRA FEL laser pulse, the next electron bunch is assured of being completely illuminated by the returned optical pulse. 
     The focusing optics has two Cassegrainian mirror systems. The first Cassegrainian mirror focuses the parallel light beam incident on a convex pickoff mirror to a focal point. The second Cassegrainian mirror then refocuses the light beam into a nearly parallel beam to a focal point in a predetermined location in the undulator. Mounted near the focal point between the two Cassegrainian mirrors is a movable limiter plate which controls the cutoff intensity of the pickoff beam. 
     In order to meet the phasing conditions, the optical pulse-length exiting the undulator must be expanded. In this way the optical pulse is not required to exactly match the electron bunch length time-wise. The feedback loop average power is planned in the IFRA FEL to be 4 kilowatt. A cooled mirror can handle over 2 kilowatts per square millimeter of surface area. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a state of the art IFRA FEL; 
     FIG. 2 is a drawing of one embodiment of the present invention; 
     FIGS. 3A,  3 B,  3 C are views of optically equivalent pulse expander mirrors; 
     FIG. 4 is an alternate embodiment of the present invention; 
     FIG. 5 is a comparison of light reflected from a phased step mirror and from a phased half-silvered mirror; and 
     FIG. 6 shows light reflected from a phased mesa mirror for FIG.  3 C. 
     FIG. 7 shows a perspective view of the phased mesa mirror that creates the reflected light pattern of FIG.  6 . 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENT 
     FIG. 1 is an example of a typical ignition feedback regenerative free electron laser (FEL) amplifier, IFRA FEL, suitable for laser power beaming, LPB. An optical pulse laser  10  has an up-converter  12  take an initial ignition pulse and convert it to a suitable wavelength before it is used to illuminate photocathode  14 . Up-converter  12  will not change quality or intensity of light passing through it, but does convert to the best frequency for emission of photons with a given quality and intensity. Photocathode  14  in turn emits a bunch of electrons  15  with a pulse width determined by the design parameters of laser  10  and photocathode  14 . This electron bunch is immediately accelerated by an initial accelerator  16 . The electron bunch is now directed through a linear accelerator  18 , which may have a large number of cooled RF cavities  20  operating near room temperature. Electron bunch  15  is now accelerated by the RF cavities to a speed very close to the speed of light. Electron bunch  15  now enters a bunch compressor  21 , which reduces the electron bunch length from about 5 millimeters to about 1 millimeter with a corresponding increase in bunch height. The electron bunch is directed by steering magnets, which may be part of bunch compressor  21 , to an undulator  22 . Undulator  22  may contain both a linear undulator and a tapered undulator also known as a tapered wiggler. The electron bunch loses about 2 percent of its energy by emitting light, which exits undulator  22  as optical pulse  24 . Electron, bunch  15  is directed back into linear accelerator  18  out of phase with RF cavities  20 . The bunch decelerates, giving up its energy to the RF cavities  20 . Electron bunch  15  is then directed to a beam dump system  26 , which is comprised of a further decelerator  28  to avoid radiation hazards and a beam dump  30 . 
     Two pickoff mirrors  32  and  34  are placed in the path of optical pulse  24 . Pickoff mirror  32  feeds a portion of optical pulse  24 , approximately 5 percent, back through up-converter  12  onto photocathode  14  to generate a new electron bunch. As the energy level of optical pulse  24  increases, the feedback to photocathode  14  increases and in turn this increases the energy level of the electron bunch emitted by the photocathode to a level higher than the initial electron bunch  15 . The speed at which the system operates means the output of undulator  22  may be described as a pulsed optical beam. Sample functioning levels can have pulse lengths of approximately 24 picoseconds separated by 8.4 nanoseconds. 
     Pickoff mirror  34  feeds a second portion, approximately 2 percent, of each optical pulse  24  via mirrors  36  back into undulator  22 . If this feedback is timed to coincide with a new electron bunch, illumination by the optical pulse induces in-phase stimulated emission from the electron bunch, increasing the amount of light emitted from the electron bunch in undulator  22 . As this cycle repeats, pickoff mirror  34  continually sends back greater optical power, which in turn increases the optical power output from undulator  22 . That is more than 2 percent of the energy is given up by the electron bunch because of the presence of the feedback light. If the feedback is unchecked, far more than 2 percent of the energy in the electron bunch will be emitted. Levels that will destroy the system can be reached very quickly, thus the concern over a runaway effect. The IFRA FEL has output increased by the effects of both pickoff beams. 
     The problems with the prior art of FIG. 1 are (1) to phase the reentrant optical pulse  24  to the new electron bunch entering undulator  22  and (2) to prevent a runaway situation. To avoid problem (2), a mode filter, also known as a limiter plate  38 , has been placed in the feedback loop from pickoff mirror  34  to function as an automatic cutoff. 
     The bunch width of the electron bunches is of the order of 24 picoseconds. The optical pulses are also of this same 24 picoseconds width. To solve problem (1) matching the electron bunch and the optical pulse so they pass through undulator  22  together is critical. To complicate matters the feedback loop can develop divergence problems, especially after passing through a limiter plate. 
     FIG. 2 is one embodiment of the present invention. Light excited in undulator  22  is parallel, very coherent, and thus can be thought of as originating from a point source. About 2 percent of it is picked off by a pickoff means such as small (possibly as small as 2 millimeters on a side) convex mirror  42 . Convex mirror  42  may be cooled by any known cooling techniques for mirrors. These techniques are well known and not shown. The portion picked off, beam  40  expands and strikes a pulse-expander-folding mirror  44 . Expander mirror  44  is mounted at the entrance pupil of two focusing optics  48  and  54 . Expander mirror  44  is designed to expand the pulse width by a desired factor, two is practical, so that when the returned pulse arrives nearly in phase with the incoming pulse from accelerator  18  the return pulse is twice as wide as the incoming pulse. As a result, even if there is a small phasing error, each point on the incoming pulse is covered by part of the returned pulse and stimulated emission will occur in phase with the emitted light beam. In this way the need for an optical cavity such as that used in most lasers is eliminated. Very high power operation of the laser is then possible since there are no cavity mirrors to damage. 
     Limiter assembly  46  has expander mirror  44 , focusing optics  48 , limiter plate  50 , adjusting means  52 , and refocusing optics  54 . The effect of limiter assembly  46  is to tune pickoff beam  40  so it has spatial and temporal uniformity of a preselected pulse duration. 
     Focusing optics  48  may be a pair of mirrors such as the Cassegrainian arrangement with a central aperture  56  to allow pickoff beam  40  to first be diverged and then refocused to a preselected location, focal point  58 . Placed near this location is limiter plate  50  which is mounted on adjusting means  52 . Limiter plate  50  is a plate of lead phthalocyanine or one of the azulenic compounds or other similar material which becomes increasingly opaque when the energy density of light passing through exceeds design parameters. Adjusting means  52  may be a vernier drive or other similar means which moves limiter plate  50  either closer to or farther away from focal point  58  of refocused pickoff beam  40 . As limiter plate  50  is moved farther from preselected focal point  58 , the energy density decreases. As it moves closer, the energy density increases. Thus moving limiter plate  50  functions as an on-off control to prevent a runaway problem. 
     Further information can be found regarding lead phthalocyanine in “Ultrafast Transient White Light Absorption Spectroscopy of Novel Materials for Optical Limiting”, S. M. Kirkpatrick et al. pp 123-127 and further information regarding Azulenic compounds “Optical Power Limiting in Some Azulenic Compounds” B. R. Kimball et al., pp 32-38. Both are in the publication  Power Limiting Materials and Devices , SPIE Proc v. 3798 July 1999. Other better materials may be used in place of lead phthalocyanine as they become available. 
     Light that does pass through limiter plate  50  is then refocused again. This time the imaging plane of focal point  58  is refocused to point  60  within undulator  22  of IFRA FEL. The location of point  60  is chosen to maximize the efficiency of stimulated emission. The object is to provide high efficiency for further light emission. By a fundamental theorem in optics every point in a parallel beam from a point source is superimposed on the image of the point source, so temporal mixing of the two different phases of light developed by mirror  42  at focal point  58  is complete and the pulse length of the image formed in the undulator is greater in length than the pulse length beam  24 . A plurality of mirrors  70  are placed as desired to direct the refocused beam, exit beam  69 , into undulator  22 . Mirrors  70  then redirect exit beam  69  to an optimum point  60  in undulator  22 . The exact location of point  60  is a matter of design. Ideally, point  60  is near the entrance to undulator  22 . Mirrors  70  may be mounted on an optical table, not shown, which may be moved by an adjustment means, also not shown. Commercially available adjustment means include the Inchworm by Burleigh Instruments Inc., or the Nanomover Micropositioner by Melles Griot. Mirrors  70  are shifted along the optical path to assure that exit beam  69  arrives at focal point  60  at the same time as an electron bunch reaches the same point in undulator  22 . Focal point  60  may be at any location in undulator  22  desired. This stimulates greater light emission, which in turn leads to a higher intensity pickoff beam  40  for the next cycle. The present invention is designed to prevent any runaway effect. 
     Ideally, a pulse expander-folding mirror would be a single parallel plate about 1-2 millimeters thick as shown in FIG.  3 A. In FIG. 3 several mirror variations for use as expander mirror  44  are shown. In FIG. 3A, expander mirror  44  is a half-silvered mirror  45 . It is half-silvered so that half of the incident beam  40  is reflected from the first surface  73  and the rest of it from the second surface  74 . This is a possible configuration for a pulse expander-folding mirror. However beam  40  is very intense, and it is difficult to cool a glass plate. For a 200 kilowatt laser it will be possible to use, but as the laser output power increases, possibly to a megawatt, it becomes more difficult to cool. Fortunately there are alternatives which are nearly as good as a refractive glass plate. They are mesa-like structures with reflecting surfaces top and bottom, as shown in FIG.  3 B and FIG.  3 C. The vertical separation between the parallel reflecting surfaces is about 5 millimeters. Since they are mirrors, they can be cooled efficiently by known techniques. The light beams reflected from the top and bottom of the mesa are laterally displaced, but if the beams are focused, they become superimposed and the resulting pulse-length is twice what the incoming pulse length of the electron beam is. The mirror structure is mounted at the entrance pupil of the focusing optics  48 , and it focuses the return beam near the entrance of undulator  22 , where the electron pulse train and the regenerative optical pulse are combined as discussed above. At that point the doubled pulse width from the reflective optics is optically equivalent to that from the half-silvered mirror. Nearby the overlap is nearly as good, and phase-matched stimulated emission will occur. 
     The simplest all-mirror configuration is shown in FIGS. 3B and 5A. The mesa direction may be lined up parallel to the beam direction or rotated 90 degrees as shown. The mesa height L would be about 5 mm. A better system with multiple mesas lying parallel to the beam direction is shown in FIG.  3 C and FIG.  6 . Since the mesas are closer to each other the effective overlap of the top and bottom of the mesa would extend farther from the focal point of the Cassegrain system than in the case of a single mesa. By orienting the mesas parallel to the beam rather than perpendicular to it vignetting of the beam by the edge of the mesa is eliminated. 
     FIG. 5A shows a mirror  46  used as the expander mirror  44  with one mesa of depth L. Beam  40  is now shown as a single pulse  79  of pulse length t traveling along optical path  80 . Part of pulse  79  reflects off of raised mesa  64  as pulse  84  travels along optical path  81 . The rest of pulse  79  reflects off of unraised portion  62  of mirror  46  as pulse  85  travels along optical path  83 . By design the portion of pulse  79  reflected from unraised portion  62  is delayed one pulse length t so pulse  79  exits mirror  46  with a double pulse length. With mirror  46  oriented as shown, vignetting occurs due to the gap  82  between optical paths  81  and  83 . 
     The height of mesa  64  may be of any thickness. For FIG. 5A, the thickness L is set at a height so that the leading edge of pulse  85  is timed to match the trailing edge of pulse  84 . If step  64  is greater, there will be a time gap after pulse  84  passes before pulse  85  arrives. If step  64  is less, pulses  84  and  85  will partially overlap in time despite being physically offset. Each pulse has a duration time t. For the two pulses to match so the leading edge of pulse  85  matches the trailing edge of pulse  84  the step thickness can be calculated from the relation distance equals velocity times time. 
     If a phased step mirror  46  is used as in FIG. 5A, then pulse  84  and pulse  85  pass through aperture  56  shown in FIG. 2, each in a different portion of space as well as different time intervals. Pulses  84  and  85  are focused to focal point  58 , which becomes the first place where the pulses combine spatially after being separated by mirror  46 . By making the plane through focal point  58 , the imaging plane for refocusing optics  54 , pulses  84  and  85  are brought to the same spatial point  60  solely separated by the time lag caused by phased mirror  46 . 
     In FIG. 5B, half silvered mirror  45  has front surface  73  and back surface  74  as previously described. Optical pulse  90  of period t, again a parallel coherent light pulse, will have approximately 50 percent of pulse  90  reflected off of front surface  73  and the remainder reflected off of the rear surface  74 . Light reflected off of front surface  73  will depart as optical pulse  92 . Light reflected off of rear surface  74  will depart as optical pulse  94 . Thickness T of half silvered mirror  45  will determine the time lag between the leading edges of pulse  92  and pulse  94 . For purposes of example in FIG. 5B, thickness T produces a time lag sufficient to cause the trailing edge of pulse  92  to coincide with the leading edge of pulse  94 . Adjusting thickness T can cause a gap between pulses  92  and  94  or cause them to partially overlap. While this is an alternate embodiment for an expander mirror, it is not the current preferred method because the light reflecting off of back surface  74  does cause internal heating which degrades the mirror performance. 
     If the one step mesa configuration shown in FIGS. 3B and 5A is rotated 90 degrees so it is parallel to beam  40  then the side view would be similar to FIG. 3C except gap  82  is eliminated so vignetting is removed as a possible complication. However, by rotating to be parallel to the beam, a further option is now possible, strips of mesas. FIG. 7 is a perspective of a strip mesa expander mirror  61  suitable for use as expander mirror  44 . FIG. 3C is a side view of striped mesa expander mirror  61 . Striped mesa expander mirror  61  has reflecting surfaces  62  alternated with raised reflecting surfaces  64 . Because all reflecting surfaces  62  and  64  form a single mirror, mirror  61  may be easily cooled by known techniques. 
     FIG. 6 is an oblique view showing the back and side of mirror  61 , in contrast to the side views of FIG.  3  and FIG.  5 . Beam  40  is coming from below in FIG.  6 . Mirror  61  is angled as shown in FIG.  3 C. Beam  40  has pulse t which now is reflected in the delayed pattern shown. Because no gap spatially arise between these optical paths vignetting is avoided. Because there is a layering effect of the expanded pulse components and refocusing problems are reduced because smaller spatial recombination problems are present between adjoining delayed pulse components. Many more varieties for an expander mirror are clearly possible. 
     Whichever of these options or others is shown for expander mirror  44 , mirror  44  is at the focus of focusing optics and serves at a pupil  56 . As shown in FIG. 2, focusing optics  48  may be a Cassegrain mirror system. Refocusing optics  54  is also shown as a Cassegrain mirror system. Since mirror  44  is at the focal point of focusing optics  48 , refocusing optics  54  will focus this pupil to undulator  22  where the igniter laser pulse and the regenerative pulse are combined. Since focusing optics  48  focuses the pickoff portion of convex mirror  42  onto focal point  58 , the beam then expands to fill refocusing optics  54 . A spatial filter, not shown, may be placed before focus  58  if desired. Since focus  58  is at the focal point of refocusing optics  54 , parallel light beam  69  is emitted by refocusing optics  54 , shaped and is sent to pass through undulator  22 . Since light from any point on a pupil, here expander mirror  44 , passes through every point on any image formed by the optical system, here the parallel beam through undulator  22 , lateral phase nonuniformities in the expander mirror  44  caused by the top or bottom reflectors are smoothed out and the stretched pulse from the regenerative loop is laterally uniform. 
     A major advantage of the stepped mirror configuration is that the possibility of damage to the pickoff system and distortion of the wavefront of the reflected beam is greatly reduced. The laser output of IFRA FEL has an initial power of 200 kilowatts and an ultimate power of a megawatt or more. The diameter of the output beam is approximately one centimeter. It then begins to expand. Approximately 2 percent of the output beam is deflected back into the feedback system by mirror  42 . Fully reflective mirrors can be cooled and if properly designed have been shown experimentally to be able to handle over 2 kilowatts per square millimeter of power without mirror distortion. (See R. M. Wood Laser Damage in Optical Materials (Adam Hilger, Bristol, 1986), pp. 113 and 121.) 
     An additional advantage of the stepped mirror configuration is the absence of transmission through an optical component. Not only does transmission make it difficult to adequately cool the component but defects in the material can cause hot spots which may not only scatter light and deform the transmitted wavefront but may also weaken the material and become a site for catastrophic damage. The thickness of materials used in any mirror may cause scatter as the beam is both reflected and partially transmitted from the front surface of the material and the transmitted portion is then reflected from the back surface of the mirror. 
     If a phased mirror is used, the amount of separation L is set at a distance needed to produce adjoining pulses of a desired time lag. As an example, if a 24 picosecond pulse is desired, focus the existing beam at the optimum position within undulator  22 . Separation L is then about 5 millimeter. The previously described adjustment means, not shown can move the pair of mirrors  70  to adjust the phase of the pulse. 
     If a half silvered pickoff mirror  45  is used as the pickoff means, the thickness T, as shown in FIG. 5B, will determine the amount of delay the transmitted light through top surface  73  will have after reflecting off of bottom surface  74 . Front surface  73  is coated with a semitransparent material that reflects 50 percent or so of the light. The remaining light transmits to back surface  74 , which is coated with a fully reflective coating. For incident light at 45° as shown in FIG. 5B, the light is refracted for a given index of refraction. The light then travels a distance in mirror  45 , reflects off of the back surface and travels the same distance in mirror  45  before exiting. These paths are shown in dashed lines in FIG.  5 B. Light reflecting off of the upper surface at the same location as the exit point for light from the back surface has traveled a different distance. Using the geometric relations shown in FIG. 5B with 34 picosecond pulses and a mirror  45  with an index of refraction of 1.5 1.5 yields a thickness 1.28 millimeters for T. For a stepped mirror as shown in FIG. 5A, the height L of the mesa for similar conditions is 5.09 millimeters. Such half silvered expander mirrors are commercially available. 
     FIG. 4 is an alternate embodiment of the present invention. Half silvered mirror  45  is shown as the expander means. Mirror  45  is used to redirect the pickoff beam  40  into focusing optics  48 . Refocusing optics  54 , which may also be a Cassegrainian arrangement, now produce an exit beam  69 . The choice of whether exit beam  69  is a parallel or converging beam is the designer&#39;s choice and is not effected by the manner in which the expander beam is created. A plurality of mirrors, here shown as two concave mirrors  71  and  72 , bring exit beam  69  to a focus at point  60  as shown before. These mirrors become part of refocusing optics  54  needed to refocus the imagining plane to point  60 . There are many other arrangements to refocus the imaging plane through focus point  58  to point  60  in undulator  22 . Also, in FIG. 4, mirrors  70 ,  71 , and  72  may be mounted on an optical table not shown which is adjustable in three dimensions along the optical path for the same reasons as discussed above. The adjustment of concave mirror  71  is illustrated by double headed arrows. The other mirrors can be similarly adjusted in three dimensions, if desired.