optical design work for a laser-fiber scanned image source for the crusader helmet janet...
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Optical Design Work for a Optical Design Work for a
Laser-Fiber ScannedLaser-Fiber Scanned
Image Source forImage Source for
the Crusader Helmetthe Crusader HelmetJanet Crossman-BosworthResearch Engineer – Optical DesignHuman Interface Technology Laboratory
University of WashingtonJanuary 16, 2003
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
First DesignFirst Design
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
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.
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
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.
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.
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.
Second DesignSecond Design
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
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)
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
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.
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.
Third DesignThird Design
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 < 80mm• 5 Lenses or Less• All Commercial Lenses to Reduce Cost
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)
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
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
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.
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.
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 100m 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.
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.
Third Design with Curved Source
• Vignetting• High field curvature• Peripheral RMS spot size diameters = 1.022mm
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 11object points
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?
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.
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)
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
Appendix A
Optical Invariant
Optical Invariant
• Optical Invariant = ypnu – ynup
• y & yp = Axial & Principal Ray Heights• u & up = Axial & Principal Ray Angles• n = Index of Refraction
Optical Invariant at Object & Image Surfaces
• ypnu – ynup = yp’n’u’ – y’n’up’
• y = y’ = 0 and n = n’ = 1
• So yyppu = yu = ypp’u’’u’
• 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
• yyppu = (-9.5)(-2.48)u = (-9.5)(-2.48) = Optical Invariant= Optical Invariant
• yyppu = (-9.5)(-2.48)u = (-9.5)(-2.48) = Optical Invariant= 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. = 0.11N.A. = 0.11, then u = 6.32°, and yypp = 3.73mm = 3.73mm
• If yypp = 1 = 1, then u = 23.56°, and N.A. = 0.40N.A. = 0.40
The EndThe End