physical-optics analysis of optical interferometers€¦ · laser diode. laser components...

Physical-Optics Analysis of Optical Interferometers

S. Zhang*, H. Zhong**, Rui Shi**, C. Hellmann*, F. Wyrowski***University of Jena, ** LightTrans GmbH

DGaO 2019, Darmstadt, June 13, 2019

Applied Computational Optics Group

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Applied Computational Optics Group and LightTrans

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Connecting Optical Technologies

Physical-Optics System Modeling by Connecting Field Solvers

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Field Solver Lenses, …

Field Solver Prisms, …

Field Solver Gratings, …

Field Solver Micro-and Nano-structures Field Solver Fibers,

…

Physical-Optics System Modeling: Regional Field Solvers

free space

prisms, plates, cubes, ...

lenses & freeforms

apertures & boundaries

gratings

diffractive, Fresnel, meta lenses

HOE, CGH, DOEmicro lens & freeform

arrays

SLM & adaptive components

diffractive beam splitters

diffusers

scatterer

waveguides & fibers

crystals & anisotropic components

nonlinear components

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Field Solvers

Physical-Optics System Modeling by Connecting Field Solvers

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Connection of solvers via I/O channel concept which enables non-sequential physical-optics

system modeling

free space prisms,

plates, cubes, ...

lenses & freeforms


gratings

diffractive, Fresnel, meta

lensesHOE, CGH,

DOEmicro lens &

freeform arrays

SLM & adaptive

components

diffractive beam

splitters

diffusers

scatterer

waveguides & fibers



Field Solvers

Surface Channels: Example of Plate/Etalon

7

+/+

Surface +/+ +/- -/- -/+1st ×2nd ×

Setting A


8

+/+

Surface +/+ +/- -/- -/+1st ×2nd ×

Setting Afree

space prisms, plates,

cubes, ...

lenses & freeforms


gratings


lensesHOE, CGH,

DOEmicro lens &

freeform arrays

SLM & adaptive

components

diffractive beam

splitters

diffusers

scatterer

waveguides & fibers



Field Solvers

12

1 112

2


9

+/+

Surface +/+ +/- -/- -/+1st ×2nd ×

Setting A


10

+/+

Surface +/+ +/- -/- -/+1st ×2nd ×

+/+

Surface +/+ +/- -/- -/+1st × ×2nd ×

Surface +/+ +/- -/- -/+1st × ×2nd ×

Setting A Setting CSetting B


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Surface +/+ +/- -/- -/+1st × × ×2nd ×

+/+

Surface +/+ +/- -/- -/+1st × × × ×2nd × × × ×

+/+

+/+

Setting D Setting E


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planar-planar (parallel) - varying thickness from 100 to 99 µm

+/+

Surface +/+ +/- -/- -/+1st × × × ×2nd × × × ×

+/+

+/+


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planar-planar (parallel) - varying thickness from 100 to 99 µm

+/+

Surface +/+ +/- -/- -/+1st × × × ×2nd × × × ×

+/+

+/+

Constructive and destructive interference alternatively shows up when the thickness of plate varies.


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planar-planar (non-parallel) - center thickness 100 µm- tilt of first surface

+/+

Surface +/+ +/- -/- -/+1st × × × ×2nd × × × ×

+/+

+/+

no tilt

x [mm]

y[m

m]

Surface Channels: Example of Plate

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planar-planar (non-parallel) - center thickness 100 µm- tilt of first surface

Linear interference fringes appear due to linear change

of etalon thickness.

tilt by 0.1°

x [mm]

y[m

m]+/+

Surface +/+ +/- -/- -/+1st × × × ×2nd × × × ×

+/+

+/+

x [mm]

y[m

m]

input polarization along x1.35

x [mm]

y[m

m]

input polarization along y

1.0


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cylindrical-planar- center thickness 100 µm- cylindrical surface radius 1 m

Polarization-dependent effect on the interference is considered.

+/+

Surface +/+ +/- -/- -/+1st × × × ×2nd × × × ×

+/+

+/+


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planar-spherical- center thickness 100 µm- spherical surface radius -1 m

+/+

Surface +/+ +/- -/- -/+1st × × × ×2nd × × × ×

+/+

+/+

Non-sequential simulation time of etalon with curved surfaces: few seconds and less

Collimation System: Sequential Simulation

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#1 #2#3 #4 #5 #6

Perfect AR coating is assumed, so sequential modeling is used.

collimating objective lens (NA=0.63)

high-NAlaser diode

Laser ComponentsWSLD-1064-050m-1-PD- fundamental Gaussian- wavelength 1064 nm- divergence (FWHM) 20° x 10°- astigmatism 11.6 µm between

x- and y-plane

Collimation System: Non-Sequential Simulation

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high-NAlaser diode

Laser ComponentsWSLD-1064-050m-1-PD- fundamental Gaussian- wavelength 1064 nm- divergence (FWHM) 20° x 10°- astigmatism 11.6 µm between

x- and y-plane

#1 #2#3 #4 #5 #6

multiple reflections between uncoated surfaces #4 and #5, other surfaces are well

coated.

Physical-Optics Modeling of Interferometer

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Maximum flexibility in source modeling: profile, multimode, polarization, coherence

Maximum flexibility to select detector, e.g. e.m. field components, irradiance, intensity, polarization

He-Ne laser- fundamental Gaussian- wavelength 632.8 nm

3x beam expanderbeam splitter

beam splitter

2 mm

2 mm

BK7BK7

reference path

test path(test object may tilt and/or shift)

?

How to calculate interference fringe with the possible shift and tilt of components considered?

Flexible inclusion of different types of components

free space prisms,

plates, cubes, ...

lenses & freeforms


gratings


lensesHOE, CGH,

DOEmicro lens &

freeform arrays

SLM & adaptive

components

diffractive beam

splitters

diffusers

scatterer

waveguides & fibers



Connecting Field Solvers: Example

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Field Solvers

13

2

2

1

3

# idealized component

2

1 1

1

2

2

3 3

High flexibility for different interferometer setups.

Modeling and Design Examples in VirtualLab Fusion

• Michelson interferometer• Mach-Zehnder interferometer• Fizeau interferometer• Coherence measurement• White light interferometry• Coherence scanning interferometry• Spectroscopy with Etalon • Locally polarized fields by interference• Gouy phase shift demonstration

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Laser-Based Michelson Interferometer and Interference Fringe Exploration

Modeling Task

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monomode laser- wavelength: 635nm

- half-angle divergence: 2°

?interference

pattern

detector How does the interference fringe change with respect to the shift and tilt of the movable mirror?

movablemirror

fixed mirror

1 mm 1 mm

shift

tilt

shift

tilt

beam splitter

Result with Equivalent Optical Path

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detector

movablemirror

fixed mirror

beam splittermonomode

laser

Coherent superposition of two fields reflected from planar mirrors at equivalent-path

positions gives no interference fringes.

Result with Shifted Movable Mirror

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detector

movablemirror

fixed mirror


laser

Shift of the movable mirror introduces defocus, and therefore ring fringes are

observed at the detector plane.

Result with Tilted Movable Mirror

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detector

movablemirror

fixed mirror


laser

Tilt of the movable mirror leads to parallel striped interference fringes are

seen at the detector plane.

Result with Shifted and Tilted Movable Mirror

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detector

movablemirror

fixed mirror


laser

Combination of both shift and tilt of the movable mirror gives rise to shifted ring

pattern in the interference fringes.



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Mach-Zehnder Interferometer

Modeling Task

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He-Ne laser- fundamental Gaussian- wavelength 632.8 nm


beam splitter

2 mm

2 mm

BK7BK7

reference path

test path(test object may tilt and/or shift)

?

How to calculate interference fringe with the possible shift and tilt of components considered?

Interference Fringe Due to Component Tilt

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tilt angle

Calculation of interference pattern including element tilt

takes less than 2 seconds!

0° tilt

x [mm]

y[m

m]

3° tilt

x [mm]

y[m

m]

5° tilt

x [mm]

y[m

m]

10° tilt

x [mm]

y[m

m]

0 shift

x [mm]

y[m

m]

300µm shift

x [mm]

y[m

m]

500µm shift

x [mm]

y[m

m]

1000µm shift

x [mm]

y[m

m]

Interference Fringe Due to Component Shift

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shiftCalculation of interference

pattern including element shift takes less than 2 seconds!



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Fizeau Interferometer for Optical Testing

Modeling Task

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spherical wave- wavelength 532nm- half-opening angle

26.6°

collimation lens

beam splitter

imaging lens

referenceflat

test flat

detector ?How does the interference fringe change for different test flats?

Tilted Planar Surface under Observation

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reference flat

detector

tilted planar surface

Reflection from the test planar surface remain as plane waves, but only with slightly different direction, and therefore leading to parallel striped fringes.

Cylindrical Surface under Observation

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reference flat

detector

cylindrical surface

Reflected wavefront from the test cylindrical surface gets curved in one direction, therefore leading to parallel striped fringes but with varying pitch.

Spherical Surface under Observation

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reference flat

detector

spherical surface

Spherical surface changes the reflected wavefront in radial direction, thus the interference fringes appears as concentric rings.



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Coherence Measurement Using Michelson Interferometer and Fourier Transform Spectroscopy

Modeling Task

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fundamental Gaussian(central wavelength 635 nm)

a) bandwidth 50 nmb) bandwidth 100 nm(24 samples frequency)

detector

change of the lateral interference fringes for different d values

movablemirror

fixed mirror

shift distance d

point-wise measurement with respect to d values

…

Lateral Interference Fringes – 50 nm Bandwidth

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fundamental Gaussian(central wavelength 635 nm)

a) bandwidth 50 nm shift distance d

d=0 d=1µm d= 2µm

Lateral Interference Fringes – 100 nm Bandwidth

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shift distance d

d=0 d=1µm d= 2µm

fundamental Gaussian(central wavelength 635 nm)b) bandwidth: 100 nm

Broader spectral bandwidth leads to shorter coherent length; and therefore the interference fringe starts to vanish sooner in comparison to the case with

narrower bandwidth.

Pointwise Measurement

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detector

movablemirror

fixed mirror

shift distance d

50nm bandwidth

100nm bandwidthfundamental Gaussian

(central wavelength 635 nm)a) bandwidth 50 nm

b) bandwidth 100 nm



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White-Light Michelson Interferometer

Modeling Task

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Xenon lampblack body spectrum6200K temperature

41 frequency samples

achromatEdmund optics

No. 49-664

fixed mirror

movable mirror (slightly tilted)

?interference

fringe

How to calculate the interference fringes with consideration of the finite coherence length of the source and the mirror movement?

detector

power spectrum

Change in Interference Fringes

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no shift 1µm shift 2µm shift

When the movable mirror moves from 0 µm to 2 µm, the contrast of interference pattern decreases, due to

limited coherence length of the light source.

shift

fixed mirror

detector

Xenon lamp



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Full-Field Optical Coherence Scanning Interferometry

Modeling Task

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?interference

fringe

detector

beamsplitter

fixed mirror

specimen(movable)

How to calculate the interference pattern and even to derive the height profile of the specimen under test?

Xenon lampblack body spectrum6200K temperature

41 frequency samples

1.0

0.9

0.8

380nm 750nm

power spectrum

achromatEdmund optics

No. 49-664

height contour0

6 µm

25 µm

Simulated Interference Fringes

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Contour lines of interference fringes corresponds to the height contour of the specimen under measurement.

height contour0

6 µm

25 µm

1 µm shift of specimenno shift of specimen 2 µm shift of specimen

Xenon lamp

detector

fixed mirror

specimen(movable)



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Examination of Sodium D Lines with Etalon

Modeling Task

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input spherical wave- sodium D lines

@ 588.995 nm & 589.592 nm- linearly polaried

along x direction- half divergent angle is 2.3°

d1 = 70mm

d2 = 1.686mm

d3 = 10mm d5 = f = 100mm

d4 = 4.3mm

fused silica

silica-spaced etalonHR - coating- reflectance ≈ 90 % - thickness ≈ 700 nm- material: Silicon Dioxide

& Titanium Dioxide

spherical lens- type: plano – convex- radius = 51.94mm- material: N-BK7 ?

Visualization of Both Spectrum Lines

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input spherical wave- sodium D lines

@ 588.995 nm & 589.592 nm

588.995nm

589.592nm

field in front of the etalon

field on the focal plane

Finesse vs. Coating Reflectance

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input spherical wave- single spectrum line

@ 589.592 nm

HR - coating- reflectance ≈90%,

80%, 60%

R ≈ 90% R ≈ 80% R ≈ 60%

Sharpness of the interference fringes depends on the reflectance

of the coatings on the etalon.


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extracting 1D data along the diagonal direction

R ≈ 90%

R ≈ 80%

R ≈ 60%

the higher reflectance, the higher finesse


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extracting 1D data along the diagonal direction

R ≈ 90%

R ≈ 80%

R ≈ 60%

the higher reflectance, the higher finesse



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Generation of Spatially Varying Polarization byInterference with Polarized Light

Modeling Task

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He-Ne laser- fundamental Gaussian- wavelength 632.8 nm- circularly polarized


beam splitter

2 mm

2 mm

BK7BK7

?

interference

polarizer(fixed)

polarizer(rotatable)

How does the interference pattern change with respect

to the polarization states of two arms?

Interference Pattern Changes with Polarizer Rotation

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polarizer(fixed)

polarizer rotation by 0° polarizer rotation by 45°

polarizer rotation by 75° polarizer rotation by 90°

Interference fringes start to disappear, when polarizer

rotates from parallel to orthogonal orientation.

Interference Pattern Changes with Polarizer Rotation

65


polarizer(fixed)

polarizer rotation by 0°

polarizer rotation by 75°

Fringe contrast changes with

polarizer rotation.

Interference Pattern

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polarizer(x-direction)

polarizer(x-direction)

polarizer(y-direction)

parallel polarizers

crossed polarizers

Interference information is encoded

in polarization state



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Observation of Gouy Phase Shift in a Mach-Zehnder Interferometer

Modeling Task

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Gaussian beam- waist radius 1 mm- wavelength 680 nm

beam splitter beam combiner1 mm

1 mm

BK7BK7

?Interference

(in front of focus)

?Interference

(behind focus)

9.5 mm 9.5 mm


70

By observing the center of the fringes, the change from

constructive to destructive interference implies a 𝜋𝜋 −shift in the

phase of the spherical wave.

constructive interference

destructive interference


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Conclusion

• Connecting field solvers enables fast physical-optics modeling • Channel concept allows non-sequential physical-optics modeling

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High flexibility for physical-optics analysis of optical interferometers!

EOS Topical Meeting on Diffractive Optics 2019

16. – 19. September 2019

Jena, Germany

Submit your paper to EOS Topics Meeting


16. – 19. September 2019

Jena, Germany

Guest of Honor & Plenary Speaker:Bernard Kress (Microsoft, USA)

Invited SpeakersBenfeng Bai, Tsinghua University, China

Sven Burger, Zuse Institute Berlin, Germany

Andreas Erdmann, Fraunhofer IISB Erlangen, Germany

Patrice Genevet, Université côted’azur, France

Michael A. Golub, Tel Aviv University, Israel

Tommi Hakala, University of Eastern Finland, Finland

Jürgen Jahns, Fernuniversität in Hagen, Germany

Uwe Zeitner, Fraunhofer IOF Jena, Germany


16. – 19. September 2019

Jena, Germany

Submit your paper to EOS Topics Meeting

Thank You!

76

Physical-Optics Analysis of Optical InterferometersApplied Computational Optics Group Applied Computational Optics Group and LightTrans Physical-Optics System Modeling by Connecting Field SolversPhysical-Optics System Modeling: Regional Field SolversPhysical-Optics System Modeling by Connecting Field SolversSurface Channels: Example of Plate/EtalonSurface Channels: Example of Plate/EtalonSurface Channels: Example of Plate/EtalonSurface Channels: Example of Plate/EtalonSurface Channels: Example of Plate/EtalonSurface Channels: Example of Plate/EtalonSurface Channels: Example of Plate/EtalonSurface Channels: Example of Plate/EtalonSurface Channels: Example of PlateSurface Channels: Example of PlateSurface Channels: Example of PlateCollimation System: Sequential SimulationCollimation System: Non-Sequential SimulationPhysical-Optics Modeling of InterferometerConnecting Field Solvers: ExampleModeling and Design Examples in VirtualLab FusionLaser-Based Michelson Interferometer and Interference Fringe ExplorationModeling TaskResult with Equivalent Optical Path Result with Shifted Movable MirrorResult with Tilted Movable MirrorResult with Shifted and Tilted Movable MirrorModeling and Design Examples in VirtualLab FusionMach-Zehnder InterferometerModeling TaskInterference Fringe Due to Component TiltInterference Fringe Due to Component ShiftModeling and Design Examples in VirtualLab FusionFizeau Interferometer for Optical TestingModeling TaskTilted Planar Surface under ObservationCylindrical Surface under ObservationSpherical Surface under ObservationModeling and Design Examples in VirtualLab FusionCoherence Measurement Using Michelson Interferometer and Fourier Transform SpectroscopyModeling TaskLateral Interference Fringes – 50 nm BandwidthLateral Interference Fringes – 100 nm BandwidthPointwise Measurement Modeling and Design Examples in VirtualLab FusionWhite-Light Michelson InterferometerModeling TaskChange in Interference FringesModeling and Design Examples in VirtualLab FusionFull-Field Optical Coherence Scanning InterferometryModeling TaskSimulated Interference FringesModeling and Design Examples in VirtualLab FusionExamination of Sodium D Lines with EtalonModeling TaskVisualization of Both Spectrum LinesFinesse vs. Coating ReflectanceFinesse vs. Coating ReflectanceFinesse vs. Coating ReflectanceModeling and Design Examples in VirtualLab FusionGeneration of Spatially Varying Polarization by Interference with Polarized LightModeling TaskInterference Pattern Changes with Polarizer RotationInterference Pattern Changes with Polarizer RotationInterference PatternModeling and Design Examples in VirtualLab FusionObservation of Gouy Phase Shift in a Mach-Zehnder InterferometerModeling TaskInterference Pattern Interference Pattern ConclusionFoliennummer 73Foliennummer 74Foliennummer 75Thank You!

physical-optics analysis of optical interferometers€¦ · laser diode. laser components...

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