professor j. gopinath - university of colorado...

Professor J. GopinathUniversity of Colorado at Boulder

ECEN 4606, Undergraduate Optics Lab

ECEN 4606Undergraduate Optics Lab

Interferometry

Professor J. Gopinath



Administrative Details• Prelab #4 due now!• CU Learn ?, either 0 or 10 points

- Credit for completion• Lab #1

- average was 80- can drop one lab score

• Handout: Lab #5 and Lecture #6• Prelab redos

- Turn in by time lab report is due• MATLAB required for Prelab #5

- Access1. EECS Shell2. SRC3. Office hours4. Access to ECEE 282

Buff card activated at front deskLab access EXCEPT following times:

Tues: 8 – 10 am, 12 – 2 pm, 6-8 pmWed: 3 – 5 pmThurs: 10 am – 3 pm

5. ITS Labs in Engineering



Fringe Visibility

Hecht, Optics, p. 561



Interference: Spherical Waves

• Professor McLeod, CU-Boulder



Spherical Aberration4

040ρWW =∆

Wavefront error in pupilW040 = 1

Interferogram

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W∆

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x• Professor McLeod, CU-Boulder• Wyant and Creath, Basic WavefrontAberration Theory for Optical Metrology



Coma

20131

30131 cos ρθρ xxWxWW ==∆


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• Professor G. Yoon, University of Rochester, Aberration Theory •Professor McLeod, CU-Boulder

Interferogram

Coma is absent on axis, and increases with field angle



Astigmatism

220222

2220222 cos xxWxWW ==∆ θρ


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Interferogram

• Professor McLeod, CU-Boulder• Professor G. Yoon, University of Rochester, Aberration Theory



Field Curvature

220220 ρxWW =∆


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• Professor McLeod, CU-Boulder•Professor G. Yoon, University of Rochester, Aberration Theory

Interferogram

Image appears on curved surface



Distortion

xxWxWW 30311

30311 cos ==∆ θρ


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Interferogram

• Professor McLeod, CU-Boulder• Wyant and Creath, Basic Wavefront Aberration Theory for Optical Metrology



Summary of aberrations

Wyant and Creath, Basic WavefrontAberration Theory for Optical Metrology

The spatial coherence length is the transverse distance over which the beam wave-fronts remain flat:

The temporal coherence time and the spatial coherence lengthThe temporal coherence time is how long the beam remains sinusoidal at a single wavelength:

Since there are two transverse dimensions, we can define a spatial

coherence area, Ac.

Temporal Coherence

Time, τc

Spatial Coherence

Length, xc

τc

Wave-fronts

xc

k

k

Wave-fronts

Trebino, Georgia Tech, UG optics course

Spatial and Temporal Coherence

Beams can be coherent or

only partially coherent

(indeed, even incoherent)

in both space and time.

Spatial andTemporal

Coherence:

TemporalCoherence;

Spatial Incoherence

Spatial Coherence;

TemporalIncoherence

Spatial andTemporal

Incoherence

xc

τc

τc

Wave-fronts

τc

τc

xc

xc

xc


How quickly will a light wave deviate from a perfect sine wave in time?

0 21 21 0exp exp ( )( , ) Re{ }( )tot E i k xE E i k x tx tt ωω−= −+

So the phase will drift on a time scale of: ~ 2π/∆ω = 1/∆ν

Suppose the light wave has two frequencies:

τ

Ε

The two frequencies will become significantly out of phase with each other in a time, tc:

2

2

1

1

22 / ( )

c c

c

τ τ πτ ωπ

ω ωω

− =⇒ = −

1 2 2ω π νωω∆ = − = ∆where:Trebino, Georgia Tech, UG optics course

The coherence time is the reciprocal of the bandwidth.

The largest frequency difference in the light wave will yield the shortest phase-drift time, which we call the coherence time:

1/c vτ = ∆

where Dn is the light bandwidth (the width of the spectrum).

Sunlight and light bulbs are temporally very incoherent—and have very small coherences times (a few fs)—because their bandwidths are very large (the entire visible spectrum).

Lasers can have much longer coherence times—as long as about a second, which is amazing; that's >1014 cycles!




Astigmatism at Circle of Least Confusion


Interferogram

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( ) ( )2212

212

02222

21222

0222 cos yxxWxWW −=−=∆ ρθρ

• Professor McLeod, CU-Boulder• Wyant and Creath, Basic Wavefront Aberration Theory for Optical Metrology



Spherical aberration at Circle of Least Confusion

( )2234

040 ρρ −=∆ WW


Interferogram

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• Professor McLeod, CU-Boulder

professor j. gopinath - university of colorado...

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