Stefan Machleidt

Leslie Klein

Michail Yordanov

Virtual Engineering: Design of Optical See-Through Displays

Stefan Machleidt

Virtual Engineering: Design of Optical See-Through Displays 3

Overview

Principles of OpticsBasic ApproachImplementationSummaryFuture WorkDemo

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Fermat´s principle (principle of least time)

The path taken between two points by a ray of light is the path that can be traversed in the least time.

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i

ii dnOPL

ni: refractive index of material i

di: distance of part i

Law of refraction (Snell´s law)

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1

2

2

1

)sin(

)sin(

n

n

1

2

1n

2n

Law of reflection

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21 1 2

Convex Lens

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Convex Lens

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Convex Lens

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Convex Lens

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Convex Lens

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Important for design of optical see-through displays

Concave Mirror

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Thin Lens Formula

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fSS

111

21

Spherical Aberration

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Distortion

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cushionshaped

barrelshaped

object

Human Eye

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Overview

Principles of OpticsBasic ApproachImplementationSummaryFuture WorkDemo

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Objectives / Basic Approaches

• Intuitive manipulation of optical elements• Real-time calculation

=> Sequential arrangement of optical elements• Potential for extension of the range of optical elements

=> Uniform structure for optical elements

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Structure / Algorithm

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Eye

Overview

Principles of OpticsBasic ApproachImplementationSummaryFuture WorkDemo

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Mirror / Combiner

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Mirror / Combiner

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Mirror / Combiner

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Mirror / Combiner

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Mirror / Combiner

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Convex Lens

First Approach: Approximation (Thin Lens Formula)

Pro:• Fast calculation• Independent from lens size

Contra:• No distortion• Inaccurate

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Convex Lens

Second Approach: Accurate Calculation of the Optical Path

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QxYnxYxXnxPXnxxOPL )()()()(),( 212121121

Convex Lens

Second Approach: Accurate Calculation of the Optical Path

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QYnYXnPXnOPL )()()()(),( 212121121

2

1

Convex Lens

Second Approach: Accurate Calculation of the Optical Path

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...2

arccoscos2),(221

2

2

2

21

2

1122

22

2

2121

PMMM

PMMMPMPMrrPMnOPL

Convex Lens

Second Approach: Accurate Calculation of the Optical Path

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QhYnhYhXnhPXnhhOPL )()()()(),( 212121121

Convex Lens

Second Approach: Accurate Calculation of the Optical Path

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QhYnhYhXnhPXnhhOPL )()()()(),( 212121121

242

2

3221

222

2

521

222

221

2

121121 ),( ahahnhhahhnahahnhhOPL

Convex Lens

Second Approach: Accurate Calculation of the Optical Path

Pro• Accurate placement of focal plane

Contra• enormous complexity• no unique solution:

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Convex Lens

Third Approach: Approximation (Ray Tracing)

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Concave Mirror

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Summary

• Linked list algorithm• Ray tracing approximation

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Future Work

• Occlusion / side effects• Additional objects:

- Aspherical lenses- Aspherical curved mirrors (windshield)

• Binocular systems

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Demo

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Discussion

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