Test and Measurement for Optical Devices and Systems
outline
4.1 Introduction
4.2 the Michelson interferometer wavelength meter
Chapter 4 Wavelength Meters
4.3 wavelength meters in multiple signal environments
4.4 absolute wavelength accuracy considerations for
Michelson-interferometer wavelength meters
4.5 Michelson wavelength-meter measurement
considerations
Huilian Ma
[email protected]
4.6 alternative wavelength meter techniques
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4.1 Introduction
4.1 Introduction
 methods of accurate wavelength measurement
 the vacuum wavelength to air wavelength conversion
vacuum  nair air
nair  1.00027 (in standard dry air)
① Optical bandpass filter techniques: F-P filters, wavelength calibrator
cells （波长校准器 ）
The wavelength difference in air and vacuum is 270ppm. A 1550nm vacuum
wavelength source would have a wavelength of 1549.58nm in standard dry air.
 wavelength meters can measure power versus wavelength
② Interferometric fringe-counting （条纹计数 ）techniques are commonly
used for high accuracy applications
③ Wavelength discriminator （波长鉴别器 ）techniques.
 distinguish grating-based OSA by making very accurate measurements
of wavelength
 grating-based OSA with 0.1nm absolute-wavelength accuracy
 Wavelength meter: more than  0.001nm accuracy
 examples require very accurate measurement of wavelength
a WDM lasers, Chromatic dispersion measurements, Wavelength-resolved
insertion loss measurements on a fiber-Bragg grating filter
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 波长测量原理
4.2 The Michelson interferometer wavelength meter
d
单色光
 干涉光路原理图
反射镜 M1
M' 2
M1
G1
M1  M 2
M1移动导轨
G
M2
2
M1与M2垂直：等倾干涉条纹（同心圆环），中心处两束相干光的光程差为
单色光源
扩束镜
若中心处为明条纹，则
反
射
镜
  2d
1  2d  k1
若改变反射镜的位置，使中心仍为明条纹，则  2  2(d  d )  k2 
M2
分光板 G1
G1//G2并与M1, M2 成45度
补偿板 G2
 
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2 d
 k1  k2 
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只要测出干涉仪中M1移动的距离∆d,并数出相应的“吞吐”环数∆k,就可求出λ.
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4.2.1 Fringe-counting description of wavelength meter operation
4.2 The Michelson interferometer wavelength meter
The form for the photocurrent generated
from the interferometer detector:
4.2.1 Fringe-counting description of wavelength meter operation
I  L   1  cos  2L / u   
4.2.2 Doppler-shift approach to understanding wavelength meter
operation
L
u   
 N 
4.2.3 accurate measurement of distance and wavelength measurement
with respect to wavelength standard
4.2.4 summary of Michelson-interferometer wavelength-meter operation
Block diagram for a Michelson Interferometer
L : optical path length difference between the two interferometer arms
(is twice the mirror movement distance because the double transit through each interferometer arm)
u : unknow wavelength of the light in the medium of the interferometer
 : phase-shift difference for equal path length delays between the two arms
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4.2.1 Fringe-counting description of wavelength meter operation
the number of counted fringes  条纹  in the length L is N
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4.2.1 Fringe-counting description of wavelength meter operation
Terminology associated with the spectral width of a signal:
 Coherence length Lc: defined as the distance where the coherence
function drops to 1/e of its maximum value.
Coherence length Lc:
(a) Interferogram for a 1550nm DFB laser. (b) optical spectrum of the 1550nm DFB laser
Lc
velocity
c 
 f1 
 spectral width of a signal:
2
1
 c
For a broadband source with a Gaussian power versus wavelength distribution
I  L   1  exp
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(a) Interferogram for a 1550nm LED. (b) optical spectrum of the 1550nm LED
4.2.2 Doppler-shift approach to understanding wavelength meter operation
   4 L 2 
1/ 2


 
 4 2   2 1/2 2  


 2L 

 cos 
 

Two limitations: (1) The position of the mirror must be known very accurately.
(2)The index of refraction of the interferometer environment has to be known
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accurately.
4.2.2 Doppler-shift approach to understanding wavelength meter operation
 多普勒效应或多普勒频移:
The detector will measure the beat frequency between the fixed and
moving arm paths. If the detector is measuring the beat frequency
signal for the time period, T, the number of zero crossings, M,
measured during the period, T, will be:
当光源或声源相对于接收器不是静止而是运动的时候,且相对运动速
度vx<<c，则接收到的频率由光源或声源发出的原始频率f0变成
f  f 0 1  vx / c 
M  f  T
当光源向着接收器运动时vx取正,反之取负
The moving mirror will cause a Doppler frequency shift on the light in
the moving arm. The Doppler frequency shift will be:
The unknown frequency of the input signal can then be measured as:
f 0   vi M  /  2vmT 
f   2vm f 0 / i 
vm: mirror velocity, vi: speed of light in the medium of the interferometer
a typical Doppler frequency shift:
vm  1.5m / s, f 0  193.5THz  f  1.93MHz
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4.2.3 accurate measurement of distance and wavelength measurement
with respect to a wavelength standard
 Measurement of distance:
4.2.4 summary of Michelson-interferometer wavelength-meter operation
L  known  N
1. The reference laser and the unknown laser signals must take
identical path lengths for the measurement to be valid.
 wavelength measurement with respect to a wavelength standard
2. The accuracy of the measurement is limited by the wavelength
accuracy of the reference laser.
3. It is important to know the ratio of the index of refraction between
the measurement wavelength and the known wavelength. The
absolute index of refraction is not needed, just the ratio.
4. The coherence of a source affects the shape of the interferogram.
Wide spectral width sources show interference only over a narrow
range of path-length differences in the interferometer.
u   N r / N u    nu / nr   r
Reference wavelength: 633nm
An unknown arm wavelength of 1550nm
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4.3 wavelength meters in multiple signal environments
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4.3 wavelength meters in multiple signal environments
The input signal for this interferogram includes a DFB laser
at 1300 am and 1550nm with equal powers
The interferogram does not show the regular period.
L 

 N 
u  
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(a) The interferogram for a combined 1300, 1550, and 1650nm
signal with equal power. (b) results of a Fourier transform
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operation on the interferogram data.
4.4 absolute wavelength accuracy considerations for Michelson-
4.3 wavelength meters in multiple signal environments
interferometer wavelength meters
 Fourier transform wavelength meters are very useful for WDM
communication system measurements
Some of the important variables that influences wavelength meter accuracy:
(1) Maximum path-length change in the variable arm of the
interferometer. The longer the interferometer path-length difference,
the better the accuracy. Related to this subject is the ability to count
fractional fringes.
(2) knowledge of the ratio of the index of refraction at the reference
wavelength to the index of refraction at the unknown wavelength.
(3) the wavelength accuracy of the reference source will ultimately limit
the accuracy of the measurement of the unknown.
The signal processing block diagram of Fourier-transform
wavelength meter.
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parameter
Uncertainty contribution
comments
Fractional fringe counting error
0.17ppm
Assume a 1/10 fringe resolution
in 600,000 sample interferogram
Index of refraction dispersion vs
wavelength
0.2 ppm
Assumes that elevation is known
and tem is stabilized 10C
Reference laser accuracy
0.1ppm-1ppm
Depends on wavelength
stabilization of He-Ne laser
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4.4 absolute wavelength accuracy considerations for Michelsoninterferometer wavelength meters
4.4 absolute wavelength accuracy considerations for Michelsoninterferometer wavelength meters
 the ability of count many fringes and to count them accurately
 index of refraction and dispersion of air
For electronic zero-counters to measure the number of fringes: the fraction
of a fringe found at the beginning and end of sweep will be ignored.
u   N r / N u    nu / nr   r
L 3cm  2
 L 
example: u  

 38709.68
 N 
u 1550nm
 N 
 L  3cm  2
if the 0.68 fringe fraction is not counted: u  
 1550.027 nm

 N  38709
vac  nair  air
2406030
15997 

for standard dry air: ns  1  108  8342.13 


130  1/  2 38.9  1/  2 

Increase the scanning distance
 Devising methods for
fractional fringe counting:
multiplied interference fringes
Standard dry air
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4.6 alternative wavelength meter techniques
 the index of refraction is a function of temperature, pressure,
and gas composition.
n T , P   1 
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 ns  1  0.00138823P
 Fabry-Perot filters
1  0.003671T
0.0457  8

n T , P, h   n T , P   h*  5.722 
10
 2 

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4.6 alternative wavelength meter techniques
 Static F-P interferometer
wavelength meter
F-P filter transmission versus wavelength for a mirror spacing of 50 m
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4.6 alternative wavelength meter techniques
 wavelength decimators
 Static Fizeau interferometer
wavelength meter
F-P作为鉴频器，产生的是环状条纹 Fizeau（菲索）条纹是线条纹，有利
于采用线列探测器直接探测条纹移动。
A wavelength discriminator uses a filter that has its insertion-loss
versus wavelength well-characterized.
Very simple and maybe adequate for many applications.
Typical accuracy:~650 ppm
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(can cover a single telecommunication wavelength band.)
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