# Patent

## Title
Resonant Fourier scanning

## Abstract

A scanning beam assembly comprising: a beam generator to generate a beam of radiation, and two or more oscillating reflectors configured to deflect the beam in sequence, each reflector being driven to contribute an incremental deflection of the beam so as to achieve a desired scanning beam waveform, at least one oscillating reflector aligned to receive the beam from the beam generator and deflect the beam to a second oscillating reflector, each oscillating reflector operating in a sinusoidal mode having a frequency and amplitude, and a controller for controlling the phase and/or frequency and/or amplitude of the oscillation of the reflectors so as to provide a desired scanning beam waveform.

## Background
FIELD OF INVENTION
This invention relates to improvements in scanning beam assemblies of the type that employ an oscillating reflector to control the scanning beam, as well as to scanning beam imaging systems incorporating such scanning assemblies and to corresponding improvements in devices, particularly medical devices, including resonant fourier scanning device.
BACKGROUND OF THE INVENTION
U.S. Published Application 2005/0020926A1 discloses a scanning beam imager which is reproduced in FIG. 1 herein. This imager can be used in applications in which cameras have been used in the past. In particular it can be used in medical devices such as video endoscopes, laparoscopes, etc.
FIG. 1 shows a block diagram of one example of a scanned beam imager 102. An illuminator 104 creates a first beam of light 106. A scanner 108 deflects the first beam of light across a field-of-view (FOV) to produce a second scanned beam of light 110, shown in two positions 110a and 110b. The scanned beam of light 110 sequentially illuminates spots 112 in the FOV, shown as positions 112a and 112b, corresponding to beam positions 110a and 110b, respectively. While the beam 110 illuminates the spots 112, the illuminating light beam 110 is reflected, absorbed, scattered, refracted, or otherwise affected by the object or material in the FOV to produce scattered light energy. A portion of the scattered light energy 114, shown emanating from spot positions 112a and 112b as scattered energy rays 114a and 114b, respectively, travels to one or more detectors 116 that receive the light and produce electrical signals corresponding to the amount of light energy received. Image information is provided as an array of data, where each location in the array corresponds to a position in the scan pattern. The electrical signals drive a controller 118 that builds up a digital image and transmits it for further processing, decoding, archiving, printing, display, or other treatment or use via interface 120.
Illuminator 104 may include multiple emitters such as, for instance, light emitting diodes (LEDs), lasers, thermal sources, arc sources, fluorescent sources, gas discharge sources, or other types of illuminators. In some embodiments, illuminator 104 comprises a red laser diode having a wavelength of approximately 635 to 670 nanometers (nm). In another embodiment, illuminator 104 comprises three lasers: a red diode laser, a green diode-pumped solid state (DPSS) laser, and a blue DPSS laser at approximately 635 nm, 532 nm, and 473 nm, respectively. Light source 104 may include, in the case of multiple emitters, beam combining optics to combine some or all of the emitters into a single beam. Light source 104 may also include beam-shaping optics such as one or more collimating lenses and/or apertures. Additionally, while the wavelengths described in the previous embodiments have been in the optically visible range, other wavelengths may be within the scope of the invention. Light beam 106, while illustrated as a single beam, may comprise a plurality of beams converging on a single scanner 108 or onto separate scanners 108.
One example of these scanners employs a MEMS scanner capable of deflection about two orthogonal scan axes, in which both scan axes are driven at a frequency near their natural mechanical resonant frequencies. In another example, one axis is operated near resonance while the other is operated substantially off resonance. Such a case would include, for example, the nonresonant axis being driven to achieve a triangular, or a sawtooth, velocity profile as is commonly utilized in cathode ray tube (CRT) devices and discussed in more detail later. In such cases, there are additional demands on the driving circuit, as it must apply force throughout the scan excursion to enforce the desired velocity profile, as compared to the resonant scan where a small amount of force applied for a small part of the cycle may suffice to maintain its sinusoidal velocity profile.
In a resonant scanning beam imager (SBI), the scanning reflector or reflectors oscillate such that their angular deflection in time is approximately a sinusoid, at a mechanical resonant frequency determined by the suspension stiffness and the moment of inertia of the MEMS device incorporating the reflector. Herein this mechanical resonant frequency is referred to as the “fundamental frequency.” Motion can be sustained with little energy and the devices can be made robust when they are operated at the fundamental frequency. However, sinusoidal angular deflection is less than optimal for certain applications. The varying velocity inherent in a sinusoidal scan gives varying exposure at a given point in the FOV, thus sensitivity varies with position. Achieving a desired dynamic range and resolution is most problematic in the center of the scan domain because the beam angular velocity is greatest there, requiring higher signal processing bandwidth in order to sustain a required spatial resolution at the target or scene. Therapy based on energy delivery may be least effective there and require compensating modulation. Finally, if the illumination is by laser, the power allowed when the beam reverses position at each extreme of its position is much less than that allowed when it is racing through the center.
By comparison, for some applications a “sawtooth” waveform might be employed, where the beam is translated at uniform velocity over the scene, with a much faster “retrace” at the end of each scan. Alternatively, a “triangle” waveform beam displacement might be employed, where the retrace occurs at the same rate as the scan in the opposite direction. FIG. 4A illustrates how beam position and angular velocity vary a sawtooth approach, and FIG. 4B illustrates the position and velocity vary in a triangular approach. In either approach, the beam velocity is uniform as it moves across the field of view, reducing the bandwidth required in the controller 118, providing more uniform performance over the field of view, and allowing a higher illuminating power level.
SUMMARY
In accordance with this disclosure, scanning beam imagers are provided that include a combination of resonant scanning reflectors that operate at different but coordinated frequencies, phases and/or amplitudes to approximate (within the mathematical limits of a Fourier series) a user designed waveform over the field of view.
Those skilled in the art will appreciate that when an SBI includes multiple reflectors, using Fourier techniques, a wide array of diverse waveforms can be produced. As a result, the SBI becomes a much more flexible tool as waveforms can be tailored to the requisites of a particular application. In one embodiment, a waveform is provided that provides essentially constant velocity with time, similar to a sawtooth waveform, in another embodiment a waveform is adopted that is essentially constant over predetermined velocity similar to a triangular scan. The term “velocity” as used herein can be either the angular velocity of the reflector or the scanning velocity of the beam across any point in the FOV. In still another embodiment, a waveform may be designed that is uniquely adapted to compensate for undesirable or intrinsically interfering aspects of the optical elements in a scan path. In still another embodiment, a waveform can be programmed into the SBI using fourier analysis that accommodates the shape of a target area, e.g., the surface of a tissue or organ.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic illustration of a scanning beam imager known in the art from Published Application 2005/0020926A1.
FIG. 2 is a schematic diagram of a combination of reflectors useful in one embodiment of the invention.
FIG. 3 is a schematic diagram of a combination of reflectors useful in another embodiment of the invention.
FIG. 4 is a series of graphs illustrating the angular beam velocities associated with sawtooth (A) and triangular (B) scans.
FIGS. 5 & 6 are flow charts showing processes for controlling drive circuits for SBI reflectors with feedback (FIG. 5) and without (FIG. 6).
FIG. 7 is a schematic diagram of the effect of rotation of the reflector by an angle α on the displacement of the incident beam.



DETAILED DESCRIPTION
Before explaining the several embodiments of the present invention in detail, it should be noted that each embodiment is not limited in its application or use to the details of construction and arrangement of parts and steps illustrated in the accompanying drawings and description. The illustrative embodiments of the invention may be implemented or incorporated in other embodiments, variations and modifications, and may be practiced or carried out in various ways. Furthermore, unless otherwise indicated, the terms and expressions employed herein have been chosen for the purpose of describing the illustrative embodiments of the present invention for the convenience of the reader and are not for the purpose of limiting the invention.
It is further understood that any one or more of the following-described embodiments, examples, etc. can be combined with any one or more of the other following-described embodiments, examples, etc.
FIG. 2 illustrates one embodiment of the invention 10 which employs a “cascade” of reflectors 12, 14, 16, 18, and, more particularly, MEMS scanners. In this figure, the reflectors are shown as projecting out of the plane, and rotating in the plane (about perpendiculars erected to the plane and containing the reflector). This figure shows a single axis of deflection: it may be possible to incorporate both axes of deflection (for example, rotation in the plane and also about the line representing the reflector). Each reflector oscillates/scans at a different rate. In a particular embodiment, each reflector is configured, by appropriate choice of mass, geometry, and suspension stiffness, to have a natural resonance near the frequency (“fundamental frequency”) at which it will be driven. Each reflector is then driven to deflect the beam in a sinusoidal pattern having a magnitude, frequency and phase selected to achieve the desired deflection and hence the desired ultimate velocity waveform. In the embodiment shown in FIG. 2, four reflectors are used but those skilled in the art will recognize that the objective, namely, achieving a desired scan velocity waveform, can be achieved using as few as two or as many reflectors as may be desired. Those skilled in the art will recognize that in theory, assuming no attenuation of the scanning beam upon reflection, there is no limit on the number of reflectors; and under Fourier theory, the more reflectors that are available, the more accurately or closely one can approximate the user designed waveform. In practice where the size of the imager is limited, the number of reflectors will generally be 2 to about 6, and typically 2 to 4.
It is assumed for the purposes of this discussion, and in accordance with one embodiment, the reflectors are driven near their fundamental frequencies, as described above, because of the high efficiency possible: large excursions can thereby be achieved with less drive power. Of course if one desires to drive the reflectors at a different and likely less efficient frequency, it will not avoid this invention.
In order to achieve the desired scan, the reflectors are driven by a drive circuit. Near resonance, the relationships between the amplitude and phase of the driving waveform (e.g., the waveform that drives a MEMS reflector device) and the amplitude and phase of the resulting motion may vary strongly, and nonlinearly, with frequency. Among the factors that can affect the relationship between the driving waveform and the angular velocity waveform of the MEMS are temperature, external vibration, strain, atmosphere and other factors.
Accordingly, in one embodiment as illustrated in FIG. 5A feedback is employed to enable the driving circuit 50 to force the reflector 52 movement to the desired phase and amplitude. This feedback may be implemented by measurement of reflector position (for example by capacitive displacement sensor, strain gauges on the suspensory elements, etc.) or actual measurement of beam position (for example using an auxiliary pixilated sensor or a silicon strip sensor 54 similar to that as described in Nuclear Science Symposium Conference Record, 2005 IEEE 23-29 Oct. 2005 Volume: 2, page(s) 781-785). FIG. 5B illustrates a control circuit in accordance with another embodiment of the invention in which the controller compares the net beam position as detected at 54 and uses Fourier analysis to make appropriate adjustments in one or more of the oscillating reflectors 54.
In applications where the relationship between the driving waveform and the reflector waveform is fairly stable (that is, where factors such as the temperature, external vibration, strain, atmosphere do not vary significantly), as illustrated in FIG. 6 it may be possible to characterize the phase and amplitude relationship and operate the system “open loop,” without feedback. In this embodiment, a simple lookup table (LUT) 60 outputs the actual drive amplitude and phase 62 required for the reflector 64 when given the desired amplitude and phase.
Those skilled in the art will appreciate that reflector control can be approached from different perspectives. In one embodiment of the invention involves closed loop control wherein one may program the controller with a target waveform and measure the net beam deflection, perform a Fourier analysis of it, and then adjust the phases and amplitudes of the drive signals for the reflectors in the directions that minimize the phase and amplitude error from what it mathematically should be for the target waveform. In another embodiment one drives the individual reflectors according to the fourier analysis of the target waveform.
Each reflector contributes an additive angular displacement to the beam, as illustrated in FIG. 7. Here, the incident beam 70 is reflected an additional amount as 2α a result of the rotation of the reflector 72 by then angle α in a global coordinate system.
It will be clear, then, that each succesive reflection adds a deflection (alpha) proportional to that reflector's angular excursion. Since each reflector's excursion is sinusoidal, the total deflection is a sum of sinusoidal quantities. Any periodic waveform can be approximated by a sum of appropriately-weighted sinusoids whose frequencies are harmonics of the original waveform. The method of Fourier analysis is used to arrive at the weightings, and the set of weights defines a Fourier series. Furthermore, since both sine and cosine terms are the typical result of such analyses, the requisite phase for each sinusoid is also obtained.
For example, Fourier analysis indicates that a triangle wave with argument x may be approximated by the series




  
    sin
    ⁡
    
      (
      x
      )
    
  
  -
  
    
      sin
      ⁡
      
        (
        
          3
          ⁢
          x
        
        )
      
    
    
      3
      2
    
  
  +
  
    
      sin
      ⁡
      
        (
        
          5
          ⁢
          x
        
        )
      
    
    
      5
      2
    
  
  -
  ⋯




and a sawtooth wave (with zero retrace time) by the series





  
    sin
    ⁡
    
      (
      x
      )
    
  
  -
  
    
      sin
      ⁡
      
        (
        
          2
          ⁢
          x
        
        )
      
    
    2
  
  +
  
    
      sin
      ⁡
      
        (
        
          3
          ⁢
          x
        
        )
      
    
    3
  
  -
  
    
      sin
      ⁡
      
        (
        
          4
          ⁢
          x
        
        )
      
    
    4
  
  +
  
    
      sin
      ⁡
      
        (
        
          5
          ⁢
          x
        
        )
      
    
    5
  
  -
  ⋯




The error in the approximation depends on the number of terms and, except where the waveform changes abruptly, can be reduced to any required degree. Therefore, even when the individual reflectors are moving in sinusoidal fashion, it is possible to approximate any desired velocity profile, and in particular a uniform velocity profile across the field of view.
FIG. 3 illustrates a further embodiment of the invention in which the reflectors 12, 14, 16 and 18 are aligned in a common plane and the light is reflected from a fixed reflector 20. The same considerations govern the design and operation of this scanner as govern the design and operation of the scanner in FIG. 2.
MEMS scanners can be designed fabricated using any of the techniques known in the art as summarized in the following patent references. Some embodiments use a MEMS scanner. A MEMS scanner may be of a type described in, for example; U.S. Pat. No. 6,140,979, U.S. Pat. No. 6,245,590, U.S. Pat. No. 6,285,489, U.S. Pat. No. 6,331,909, U.S. Pat. No. 6,362,912, U.S. Pat. No. 6,384,406, U.S. Pat. No. 6,433,907, U.S. Pat. No. 6,512,622, U.S. Pat. No. 6,515,278, U.S. Pat. No. 6,515,781, and/or U.S. Pat. No. 6,525,310, all hereby incorporated by reference. In one embodiment, the reflectors are magnetically resonant scanners as described in U.S. Pat. No. 6,151,167 of Melville or a micromachined scanner as described in U.S. Pat. No. 6,245,590 to Wine et al.
While the present invention has been illustrated by descriptions of a method, several expressions of embodiments, and examples, etc. thereof, it is not the intention of the applicants to restrict or limit the spirit and scope of the appended claims to such detail. Numerous other variations, changes, and substitutions will occur to those skilled in the art without departing from the scope of the invention. It will be understood that the foregoing description is provided by way of example, and that other modifications may occur to those skilled in the art without departing from the scope and spirit of the appended Claims.

## Claims

1. In a scanning beam assembly comprising:
a beam generator to generate a beam of radiation, and
two or more oscillating reflectors configured to deflect the beam in sequence, each reflector being driven to contribute an incremental deflection of the beam so as to achieve a desired scanning beam waveform, at least one oscillating reflector aligned to receive the beam from the beam generator and deflect the beam to a second oscillating reflector, each oscillating reflector operating in a sinusoidal mode having a frequency and amplitude, and
a controller for controlling the phase and/or frequency and/or amplitude of the oscillation of the reflectors so as to provide a desired scanning beam waveform.

2. The scanning beam assembly of claim 1 wherein the resultant waveform is approximately linear for a portion of its period.

3. The scanning beam assembly of claim 1 wherein the at least two of the reflectors oscillate about substantially parallel axes.

4. The scanning beam assembly of claim 1 wherein one of the oscillating reflectors has a fundamental frequency of resonance and the other reflectors operate at odd harmonics of the fundamental resonance frequency.

5. The scanning beam assembly of claim 1 wherein the amplitude of a successive reflector's deflection is the inverse square of the harmonic number.

6. The scanning beam assembly of claim 1 wherein the oscillating reflectors rotate about axes that are parallel and in a common plane and each oscillating reflector directs light to a fixed reflector which redirects the light sequentially to the next sinusoidally oscillating reflector.

7. The scanning beam assembly of claim 1 wherein the beam generator illuminates an optical fiber which transmits the beam to at least one of the reflectors.

8. The scanning beam assembly of claim 1 wherein the scanning beam assembly additionally includes at least one detector positioned to receive light reflected from the field of view.

9. The scanning beam assembly of claim 1 wherein the reflector includes a MEMS scanner.

10. The scanning beam assembly of claim 1 wherein the assembly includes a detector capable of generating a signal indicative of the position, frequency or amplitude of at least one reflector and the signal provides an output that is fed back to the controller to control the oscillation of at least one of the reflectors.

11. The scanning beam assembly of claim 1 wherein the controller is programmable with the desired waveform.

12. The scanning beam assembly of claim 11 wherein the controller performs a Fourier analysis based upon the desired waveform to control the oscillation of at least two oscillating reflectors.

13. The scanning beam assembly of claim 11 wherein the assembly includes a detector capable of generating a signal indicative of the position, frequency or amplitude of at least one reflector and the signal provides an output that is fed back to the controller to control the oscillation of at least one of the reflectors.

14. A scanned beam endoscope comprising:
an endoscope, and a scanning beam assembly including:
a beam generator to generate a beam of radiation, and
two or more oscillating reflectors configured to deflect the beam in sequence, each reflector being driven to contribute an incremental deflection of the beam so as to achieve a scanning beam waveform, at least one oscillating reflector aligned to receive the beam from the beam generator and deflect the beam to a second oscillating reflector, each oscillating reflector operating in a sinusoidal mode having a frequency and amplitude, and

a controller for controlling the frequency and/or amplitude an/or phase of the oscillation of the reflectors so as to provide a desired scanning beam waveform.

15. A scanning endoscope tip comprising:
a beam generator to generate a beam of radiation, and
two or more oscillating reflectors configured to deflect the beam in sequence, each reflector being driven to contribute an incremental deflection of the beam so as to achieve a scanning beam waveform, at least one oscillating reflector aligned to receive the beam from the beam generator and deflect the beam to a second oscillating reflector, each oscillating reflector operating in a sinusoidal mode having a frequency and amplitude, and

a controller for controlling the frequency and/or amplitude and/or phase of the oscillation of the reflectors so as to provide a desired scanning beam waveform.

16. The scanning endoscope tip of claim 15 wherein the at least two of the reflectors oscillate about substantially parallel axes.

17. The scanning endoscope tip of claim 15 wherein one of the oscillating reflectors has a fundamental frequency of resonance and the other reflectors operate at odd harmonics of the fundamental resonance frequency.

18. The scanning endoscope tip of claim 15 wherein the amplitude of a successive reflector's deflection is the inverse square of the harmonic number.

19. The scanning endoscope tip of claim 15 wherein the oscillating reflectors rotate about axes that are parallel and in a common plane and each oscillating reflector directs light to a fixed reflector which redirects the light sequentially to the next sinusoidally oscillating reflector.

20. The scanning endoscope tip of claim 15 wherein the beam generator illuminates an optical fiber which transmits the beam to at least one of the reflectors.