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