Optical Design Work for a Laser-Fiber Scanned

1
Optical Design Work for a Laser-Fiber
Scanned Image Source for the Crusader Helmet
Janet Crossman-Bosworth Research Engineer
Optical Design Human Interface Technology
Laboratory University of Washington January 16,
2003
2
Introduction

• Three optical designs will be presented.
• First Design -
• Low frequency fiber resonance input
• Second Design -
• High frequency fiber resonance input
• Third Design -
• High frequency fiber resonance input

3
First Design
4
Goals for First Design

• Point Source Re-imaging
• Circular Scan
• 19mm Screen
• 20µm RMS Spot Sizes
• 532nm Wavelength
• Low frequency fiber resonance input (2.5kHz)
• from endoscope prototype
• Axial Length of System lt 100mm

5
Fiber Input for First Design

• Plotted fiber tip positions
• from model data for
• endoscope prototype
• (linear mode shape)
• Optical Node Length
• 4.5mm average
• Maximum fiber tip
• displacement 2mm
• N.A. 0.11 (single mode fiber)

Optical Node Length The distance between the
fiber tip and the position along the axis
from which the light appears to emanate.
6
Optical Layout for First Design

• File Name HMD I
• All Custom Lenses
• Display Diameter 18mm
• Lens System Length 23mm
• (fiber tip to screen)
• Estimated Weight 0.5g

7
At the Screen (Image Plane)

• File Name HMD I
• Central Region
• RMS Spot Diameter 31.19µm
• 32 spots/mm
• 64 resolvable spots/mm approx.
• Peripheral Region
• RMS Spot Diameter 303.05µm
• 3 spots/mm
• 6 resolvable spots/mm approx.

We have been able to resolve approximately
twice as many spots/mm as that calculated
from the RMS spot diameter.
8
Resolution Diffraction Limited Example

• Rayleigh Criterion
• The maximum illumination of one
• diffraction pattern coincides with the
  first
• dark ring of the other diffraction
  pattern.
• Separation 1.22 ? (F/)
• (This is also called the Airy Disk
  Radius.)
• Sparrow Criterion
• There is no minimum between the
• maxima from the two diffraction
  patterns.
• Separation ? (F/)
• Our measurements use a criterion
• between that of Rayleigh and Sparrow.

9
Summary for First Design

• Fiber tip displacements of 2mm do not
• occur for video rate frequencies.
• The first design will not work for video
• rates.
• There is not sufficient resolution in the
• periphery of the first design.

10
Second Design
11
Goals for Second Design

• 15µm RMS Spot Size
• 2mm to 4mm Optical Node Length
• Maximum Fiber Tip Displacement 1mm
• (Representative of higher frequency
  systems)
• Axial Length of System lt 80mm

12
Fiber Input for Second Design

• Simplified model
• (Not actual measurements)
• 4mm Optical Node Length
• Maximum fiber tip
• displacement 1mm
• across a spherical curve
• N.A. 0.11 (single mode fiber)

13
Optical Layout for Second Design

• File Name HMD ZK3e
• All Custom Lenses
• Display Diameter 20mm
• Lens System Length 52mm
• (fiber tip to screen)
• Estimated Weight 1.0g

14
At the Screen (Image Plane)

• File Name HMD ZK3e
• Central Region
• RMS Spot Diameter 61.99µm
• 16 spots/mm
• 32 resolvable spots/mm approx.
• Peripheral Region
• RMS Spot Diameter 107.30µm
• 9 spots/mm
• 18 resolvable spots/mm approx.

15
Summary for Second Design

• The required field of view has been achieved.
• The illumination across the field of view is more
• uniform.
• A spot size of 15µm is not achievable across a
• 19mm field of view, using a 0.11 N.A.
  fiber
• with a maximum displacement of 1mm,
• according to the Optical Invariant.
• For more information about the Optical
  Invariant, see Appendix A.

16
Third Design
17
Goals for Third Design

• Increase the fiber N.A. to 0.4 or 0.5
• 50µm RMS Spot Size
• 0.95mm Optical Node Length
• Maximum Fiber Tip Displacement 0.5mm
• (Representative of higher frequency
  systems)
• Axial Length of Lens System lt 80mm
• 5 Lenses or Less
• All Commercial Lenses to Reduce Cost

18
Fiber Input for Third Design

• Simplified model
• (not actual measurements)
• 0.95mm Optical Node Length
• Flat object plane using a
• Noliac ring bender
• Maximum fiber tip
• displacement 0.5mm
• across a flat plane
• N.A. 0.4 (custom fiber)

19
Third Design Prototype Design

• File Name HMD ZZH1c4
• 1 Custom Lens, 4 Commercial Lenses, and 1 Fiber
  Optic Taper
• Display Diameter 20mm
• (at large end of 2x magnification fiber
  optic taper)
• Intermediate Image Plane Diameter 10mm (at
  small end of taper)
• System Length 69mm (fiber tip to taper) 19mm
  (taper) 88mm
• Estimated Weight 6g (lenses) 16g (taper) 22g

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Fiber Optic Taper

• Schott Fiber Optic Taper
• 2x Magnification
• Large end diameter 20mm
• Small end diameter 10mm
• Taper Length 19mm
• Fiber diameter at large end 6µm
• Estimated Weight 16g

21
Image at Small End of Taper

• File Name HMD ZZH1c4
• Central Region
• Airy Disk Diameter 15.65µm
• (Diffraction Limited)
• 64 spots/mm
• 128 resolvable spots/mm approx.
• Mid-Peripheral Region
• RMS Spot Diameter 25.87µm
• 39 spots/mm
• 78 resolvable spots/mm approx.
• Peripheral Region
• Airy Disk Diameter 22.43µm
• (Diffraction Limited)
• 45 spots/mm
• 90 resolvable spots/mm approx.

22
Image at Large End of Taper

• File Name HMD ZZH1c4
• Central Region Spot Diameter 31.30µm
• 32 spots/mm
• 64 resolvable spots/mm approx.
• Mid-Peripheral Region Spot Diameter 51.74µm
• 19 spots/mm
• 39 resolvable spots/mm approx.
• Peripheral Region Spot Diameter 44.86µm
• 22 spots/mm
• 45 resolvable spots/mm approx.
• A design goal of 50µm diameter spots yields 20
  spots/mm and
• approximately 40 resolvable spots/mm.

23
Tolerance Analysis of the Third Design(Tolerance
Analysis for the Intermediate Image Plane)

• 40 tolerances were used which, each by
  themselves, would
• allow no more than a 100?m RMS spot
  diameter at the
• intermediate image plane for any field
  point, but with a
• ?1 minimum tolerance on all tolerances
  except the
• decenters and tilts.
• 10 Radius of Curvature Tolerances
• 5 Spacing Tolerances
• 5 Center Thickness Tolerances
• 10 Decenter Tolerances, ranging from ?0.05mm to
  ?0.20mm
• 10 Tilt Tolerances, which were either ?0.6? or
  ?1.0?
• The optical design program uses the final spacing
  to the intermediate
• image plane to adjust the back focus
  during tolerancing.

24
Tolerance Analysis (continued)

• Results
• A Monte Carlo tolerance analysis was run, which
• simulates the effect of all the
  tolerance errors
• simultaneously.
• The mean RMS spot diameter was 134µm.
• This translates to approximately 15 resolvable
  spots/mm.
• After being magnified by the 2x taper, there
  would be
• approximately 7 resolvable spots/mm.
• This design is highly sensitive to tolerance
  errors.
• Very tight tolerances are required to maintain
  intended
• design performance.

25
Third Design with Curved Source

• Vignetting
• High field curvature
• Peripheral RMS spot size diameters 1.022mm

26
Third Design with IR Source

• Wavelength 1.31µm
• RMS spot size diameters 2.7mm to 3.2mm
• Nearly parallel light impinges upon the screen.
• Distance between last lens and taper 35mm
• (A beamsplitter could be placed here.)

Light from 2 object points
Light from 11 object points
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Summary for Third Design

• The image meets the 50µm spot diameter goal,
  except in
• the mid-periphery where the spot
  diameter is
• approximately 52 microns.
• The system exceeds the 80mm length goal by 8mm.
• Only 5 lenses were used.
• 1 custom lens was needed.
• Tight tolerances are required for this design.
• A flat image source is required for this design.
• A beamsplitter could be used with this design for
  IR light.
• Will the crosshatching of the taper be visible?

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Conclusions

• The original goal was a 19mm screen with 809
  resolvable
• spots, or approximately 43 resolvable
  spots/mm.
• The third design very nearly meets this original
  goal across
• the field of view. The first and
  second designs do not.
• An analysis of the optical invariant is needed to
  determine
• what characteristics are needed in the
  optical fiber.
• Methods to increase the fiber N.A. and increase
  the fiber
• tip displacement for a standard fiber
  are known here at
• the HIT Lab.

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Conclusions (continued)

• Fiber scanners are being designed and fabricated
  to meet
• these optical specifications.
• Large fiber tip displacements at high resonant
  frequencies
• are difficult to achieve.
• Just as there is an optical invariant, there may
  also be an
• invariant for resonant fiber scanning.
• Designs are limited to geometrical size
  limitations of the
• Crusader Helmet. (i.e. 20mm flat
  screen 100mm
• length)

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Possibilities forFuture Design Work

• Use Other Fiber Input Characteristics
• Further Aberration Control
• Circular or Rectilinear Scan
• Gradient Index Optics
• Diffractive Optics
• Doublets and/or Triplets
• Most or All Custom Lenses
• No Fiber Optic Taper
• No Field Flattening
• Eight or More Lenses

31
Appendix A

• Optical Invariant

32
Optical Invariant

• Optical Invariant ypnu ynup
• y yp Axial Principal Ray Heights
• u up Axial Principal Ray Angles
• n Index of Refraction

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Optical Invariant at Object Image Surfaces

• ypnu ynup ypnu ynup
• y y 0 and n n 1
• So ypu ypu
• yp represents half of screen diameter -9.5mm
• u represents the angle needed to produce an Airy
• Disk diameter of 15 µm. u -2.48 º
• ypu (-9.5)(-2.48) Optical Invariant

34

• ypu (-9.5)(-2.48) Optical Invariant
• yp represents maximum fiber displacement
• u represents axial ray angle from fiber tip
• An unmodified fiber may have a Numerical
• Aperture (N.A.) of 0.11, where N.A.
  sin u
• If N.A. 0.11, then u 6.32, and yp 3.73mm
• If yp 1, then u 23.56, and N.A. 0.40

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The End