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 -

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 < 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. = (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 = µm
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 λ (F/#)
(This is also called the Airy Disk Radius.)
Sparrow Criterion:
There is no minimum between the
maxima from the two diffraction patterns.
Separation = λ (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 < 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. = (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 = µm
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 50µm RMS Spot Size
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 < 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

20. 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
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

27. 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?

28. 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.

29. 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)

30. Possibilities for Future 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

33. Optical Invariant at Object & Image Surfaces
ypnu – ynup = yp’n’u’ – y’n’up’
y = y’ = 0 and n = n’ = 1
So ypu = yp’u’
yp’ represents half of screen diameter = -9.5mm
u’ represents the angle needed to produce an Airy
Disk diameter of 15 µm. u’ = 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

35. The End