Download Power Meters with Thermal Detectors

Chapter Two – Optical Power Measurement
Contents
1. Power Meters with Thermal Detectors
2. Power Meters with Photodetectors
3. LED-Power Measurement
4. High-Power Measurement
5. Uncertainties in Power Measurement
6. Responsivity Calibration
7. Linearity Calibration
1
Introduction
Two types of power measurements:
Absolute power measurement – Needed in conjunction with optical sources, detectors
and receiver
Relative power measurement – Important for the measurement of attenuation, gain and
return loss
Two main groups of optical power meters:
Power meters with thermal detectors – the temperature rise caused by optical
radiation
Power meters with photodetectors – the incident photons generate electron-hole pairs
Question
How to measure the power with a thermal detector?
2
Introduction
Comparison of thermal power meters and photodetector power meters
Characteristics
Power meters with thermal
detectors
Power meters with
photodetectors
Wavelength
dependence
+ wavelength-independent
+ wide wavelength range
- wavelength dependence
- wavelength range 2:1
Self-calibration
+ available
- not available (calibration
indispensable)
Sensitivity
- very low (typically 10 μW)
+ very high (down to less than 1
pW)
Accuracy
±1% depending on calibration
method
±2% depending on calibration
method
Although photodetector-type power meters suffer from a relatively small wavelength
coverage and the need for absolute calibration, their astounding sensitivity usually makes
them the preferred choice.
Nevertheless, power meters with thermal detectors are sometimes preferred in the
calibration laboratories because of their wide and flat wavelength characteristics. In
addition, thermal detectors can be directly traceable to electrical power measurements.
Altogether, there is good reason for the existence of both types of power meters.
3
Power Meters with Thermal Detectors
Example thermal detector: Substitution radiometry (Self-calibration method)
Substitution radiometry:
First exposed to the optical radiation
Then the radiation is switched off (with a shutter of chopper) and replaced by
electrically generated power
Questions
What is the parameter to be controlled to achieve time-independent temperature?
What provides the basis for the accuracy of this method?
Important elements of a thermal detector with electrical substitution
An absorptive layer – collects the incident light
A heating resistor – perform substitution, thermally well coupled to the absorptive layer
An isolated sheet of silver – equalizing any temperature differences, coated with black
paint
A thermopile (a series connection of thermocouples) – measures temperature rise, in
close proximity to the silver
4
Power Meters with Thermal Detectors
The figure shows the thermal detector with electrical substitution
Question
What is the series of apertures for?
5
Power Meters with Thermal Detectors
For highest accuracy
Reference plane on large thermal mass – to maintain constant temperature during the
relatively long measurement times
Blocking of background radiation and stray light – using a jacket with thermal isolation
Optimization of heat flow – a negligible thermal resistance between the absorptive
layer and the heater
High absorptance – reduce reflection, which does not contribute to the temperature rise
Accurate measurement of the electrical power – eliminate heat dissipation from the
resistor lead
Alternative operation
Continuously heated by electrical power which is slightly larger than the optical power
to be measured
The sensor voltage is recorded without the optical power applied
Then the sensor is exposed to the optical power, and a feedback loop reduces the
electrical power until the sensor voltage is the same as before (on-line calibration)
The desired optical power measurement result is simply the difference of electrical
powers between the two steps
6
Power Meters with Thermal Detectors
Principal problems
Low sensitivity
The correspondent long measurement time
Possible improvement
Replacing pyroelectric sensors or thermopiles with semiconductor material
Typical characteristics of thermal power meters
Sensitivity down to 1 μW
Uncertainty as low as ±1%
Spectral range from ultraviolet to far infrared
Time constant of several seconds to minutes depending on the detector size
Question
Why does the thermal power meters need a long measurement time?
Question
Using the alternative measurement procedure mentioned in the previous slide, is it
possible to have initial electrical power lower than the optical power to be measured?
Explain why.
7
Power Meters with Thermal Detectors
Cryoradiometer
A thermal detector that is placed into vacuum and cooled to approximately 6 K using
liquid helium
The most precise optical power meters due to
At 6 K, the thermal mass (the energy needed to raise the temperature by 1 K) of the
absorbing material is drastically reduced
Heat loss due to radiation is virtually eliminated because the radiated energy is
proportional to T4 (T in K)
Heat contributions from the resistor leads can be eliminated by making them
superconducting
Convection losses are eliminated
Questions
What is the consequence of having low thermal mass?
How do the superconducting resistor leads help?
How do the convection losses eliminated?
8
Power Meters with Photodetectors
Principal advantages
Great sensitivity – can measure power levels down to less than 1 pW (-90 dBm)
High modulation frequency response – fast measurement time
Ease of use
Principal disadvantages
Exhibits a relatively strong wavelength dependence
No self-calibration
Categories
Small-area power meters – only measures power from a fibre
Large-area power meters – open beams and fibre applications
Important elements in a large-area power meter
Antireflective coating on the connector adapter
Pinhole and angled position of the detector
9
Power Meters with Photodetectors
The figure shows a cross-section through a commercial large-area optical sensor head
based on a photodetector
Question
Why is the photodetector angled positioned?
Operations
Temperature stabilization using a thermoelectric cooler ensures stable measurement
results
The photodetector is operated at zero-bias voltage in order to eliminate any offset
currents
10
Power Meters with Photodetectors
The most important contributions to accurate power measurements are
Individual correction of wavelength dependence
Temperature stabilization
Wide power range with good linearity
Good spatial homogeneity
Low polarization dependence
Low reflections
Compatibility with different types of fibre
PIN diode
The figure shows a cross-sectional view of a planar InGaAs PIN diode
11
Power Meters with Photodetectors
PIN diode
Operation
Each incident photon is absorbed in the intrinsic (i-) layer
An electron-hole pair is created – the photon energy ≥ bandgap energy (materialdependent
The holes and electrons are swept out of the i-region by the large built-in electric field –
photocurrent
Terms which describe the conversion efficiency
Quantum efficiency η, defined as the number of electrons per photon
Responsivity r, defined as the photocurrent per unit of optical power
Question
What is the value for η in the ideal case?
12
Power Meters with Photodetectors
PIN diode
From the definition, the responsivity r is given by,
I
r =
P
Each photon represents the energy Eph,
E ph = hu =
hc
l
where h = Planck’s constant, ν = optical frequency, and c = speed of light in vacuum
The optical power which corresponds to one photon is,
Pph =
E ph
Dt
=
hc
l Dt
The correspondent electrical current is one electron charge q per time span Δt,
I ph =
q
Dt
The linear spectral responsivity of an ideal photodetector with η = 1,
ql
r =
hc
13
Power Meters with Photodetectors
PIN diode
Practical photodetectors deviate from this ideal wavelength dependence in several ways:
A long wavelength limit (cutoff wavelength) – photon energy becomes lower than the
bandgap energy, determined by the detector material
At short wavelength – absorption outside of the i-region reduces the number of
electron-hole pairs
The responsivity may also be reduced by recombination: when the electrons
recombine with the holes before they reach the electrodes
Reflections from the detector surface can produce substantial inaccuracies in optical
power and insertion loss measurement
Question
Pure InGaAs has a refractive index of 3.5. Calculate the reflectivity (or Fresnel
reflection) at the detector surface. [Answer = 31%]
A periodic structure of the responsivity may be observed due to optical interference in the
diode
Antireflective coatings
Single-layer, quarter-wavelength coating are most often used
Multi-layer coating – low reflectivity over a wider wavelength range
14
Power Meters with Photodetectors
Spectral Responsivity
The figure shows typical responsivity measurement results for three types of
photodetectors
Short wavelength range (500 -1000 nm) – silicon
Long wavelength region – both Germanium and InGaAs
15
Power Meters with Photodetectors
Spectral Responsivity
Germanium
Lower cost solution
Recommended when the sources to be measured are spectrally narrow and the
wavelength is well known (around 1550 nm)
1% error when the power meter’s wavelength setting is incorrect by 1 nm
InGaAs
Flat around 1550 nm
Better than 0.1% per nm wavelength error
Well suited for optical amplifier (EDFA) applications
More expensive technology
Question
What is the property that makes InGaAs detectors suitable for EDFA applications?
16
Power Meters with Photodetectors
Temperature Stabilization
Temperature-stabilized detectors – generate reproducible measurement results
The figure shows the responsivity of a germanium detector
It exhibits a relatively small temperature dependence for most of the wavelength range
There is substantial change beyond the cutoff wavelength – shift of cutoff wavelength, ~
1nm/K
17
Power Meters with Photodetectors
Spatial Homogeneity
The responsivity of photodetectors can vary across the detector surface
The figure shows the relative responsivity of an InGaAs photodetector at 1550 nm
Inhomogeneous photodetector surfaces create measurement uncertainties – the position
and diameter of the incident beam cannot be perfectly controlled
18
Power Meters with Photodetectors
Spatial Homogeneity
Multimode fibre
A dark and light “speckle pattern” is formed if illuminated with a narrow spectral-width
optical source
This will cause the power distribution in the fibre cross-section to fluctuate
Questions
How is the speckle pattern formed?
What will happen if a wide spectral source is used?
19
Power Meters with Photodetectors
Power Range and Nonlinearity
Sources of nonlinearity – Photodetector nonlinearity, electronic nonlinearity
The photodetector nonlinearity:
Noise at low power levels
Supralinearity at medium power levels
Saturation at high power levels
The electronic nonlinearity
In-range nonlinearity of the analogue amplifier
Ranging discontinuity – non-matching amplifier gains
Question
What causes nonlinearity in the analogue amplifier at high power levels?
The nonlinearity is defined as
N (P ) =
r (P ) - r (P0 )
r (P0 )
Where r(P) is the power meter’s responsivity at an arbitrary power level, and r(P0) is the
20
responsivity at the reference level (usually 10 μm)
Power Meters with Photodetectors
Power Range and Nonlinearity
The nonlinearity is usually wavelength dependent – wavelength-dependent photodetector
The figure illustrates the possible nonlinearity effects of an optical power meter
Dark current
Limits the low end of the power range
Depends on the active area and on the semiconductor material
The shot noise current is given by, in 2 = 2qB n ´ 2I d éA 2 ù
ë û
21
Power Meters with Photodetectors
Power Range and Nonlinearity
2
Total short noise in = 2qB n (2I d + rPopt )
where r = responsivity and Popt = received optical power
Noise equivalent power (NEP)
NEP =
1
r
in 2 =
1
2qB n (2I d + rPopt )
r
Signal-to-noise ratio (SNR)
SNR =
éW ù
ê
ú
êë Hz ú
û
Popt
NEP
SNR improvements
Reduce dark current – either by cooling or by reducing the detector’s active area (the
dark current is proportional to the active area)
Longer averaging time
Question
What will happen to the SNR as the Popt increases?
22
Power Meters with Photodetectors
Power Range and Nonlinearity
The figure shows the power dependence of the SNR
Question
Why is the SNR linear for low Popt?
23
Power Meters with Photodetectors
Power Range and Nonlinearity
Range discontinuity
The power meter does not display exactly the same power level when switching
between power ranges
Caused by the necessity to switch the gain of the electronic amplifier, depending on the
input power level
Supralinearity
An increase in responsivity typically starting at power levels ~ 100 μW
Due to “traps” in the semiconductor material causing increased recombination at low
power levels
When the power reaches higher levels, then these traps become saturated, the
recombination decreases, and the responsivity increases
Saturation
Caused by reduction of the electric field across the pn-junction along with
recombination in the active region
24
Power Meters with Photodetectors
Polarization Dependence
Causes for polarization dependence
Crystalline structure in the semiconductor material and in the photodetector’s coating
Mechanical stress in the detector
Tilting against the beam axis (to reduce multiple reflections)
A relatively strong wavelength dependence of the polarization characteristics can also be
observed and is usually caused by the quality of the antireflective coating
25
Power Meters with Photodetectors
Optical Reflectivity and Interference Effects
Without antireflective coating, optical detectors exhibit reflectivities up to 30% - cause
multiple reflection and optical interference problems
Examples of antireflective coating
Silica on silicon detectors
Silicon nitride on InGaAs detectors
The figure shows the measured reflectance of an InGaAs photodetector with a single-layer
antireflective coating made from silicon nitride with a thickness of a quarter wavelength
26
Power Meters with Photodetectors
Optical Reflectivity and Interference Effects
Silicon nitride has a refractive index n = 1.95 and acts as an impedance transformer
matching the refractive index of InP (n = 3.2) with air (n = 1)
The quarter-wavelength layer is responsible for the overall minimum around 1250 nm for
this specific diode
The additional ripple is caused by the upper InP layer which forms an additional resonator
due to the fact that InP has a refractive index of 3.2, in contrast to the refractive index of 3.52
fro the intrinsic InGaAs layer.
The reflectance varies substantially from detector to detector
A slight thickness change of the InP layer shifts the pattern to different wavelength
Question
Why is the pattern shifted to different wavelength when the thickness changes?
The detector surface or the glass cap may cause reflections
If the detector is sufficiently large, the unwanted power fraction on the detector = the
photodetector reflectance x the reflectance of the optical interface
To reduce this problems, the adapter is coated with an antireflective coating on the
inside, and a pinhole shields the highly reflective connector end
27
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Single-mode Fibres
The far-field power density (irradiance) from a single-mode fibre, H(z) is usually
described by a gaussian beam
æ 2r 2 ÷
ö
H (z ) = H 0 exp çç÷
èç w (z )2 ÷
ø
where z = distance from the source on the beam axis, w = radius of the beam waist at
which the power has dropped to 1/e2, at the distance z, and r = radial distance from the
optical axis
The numerical aperture (NA) of the fibre is defined by the 5% angle of the far field.
If the detector diameter coincides with the circle created by the numerical aperture,
then the detector misses 5% of the total beam power
The corresponding 95% detector radius is
rdet = z
NA
1 - NA
2
@ zNA
Generally, when the power density at the detector radius has decayed to x%, then
there is x% of the total power outside the detector. This is a property of the gaussian
beam
28
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Single-mode Fibres
The coupling efficiency is given by
æ 2rdet 2 ÷
ö
h = 1 - exp çç÷
çè w 2 ÷
ø
It is advisable to replace w, the 1/e2 beam radius, by the 5% beam radius which
corresponds to the fibre’s numerical aperture. The gaussian beam profile yields,
w = 0.817r5% = 0.817 ´ zNA
Then the coupling efficiency can be expressed on the basis of the numerical aperture
é
h = 1 - exp êê
ë
2
æ1.71rdet ÷
öù
ú
çç
÷
è zNA ø ú
û
Question
If the detector radius is 2.5 mm, the distance between the fibre end and the detector is
8 mm, and the numerical aperture of the single-mode fibre is 0.3, calculate the coupling
efficiency. [Answer = 96%]
29
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Angled Fibre Ends
Angled fibre ends are aimed at reducing reflections
The figure shows a single-mode fibre, both with straight and angled fibre end
Assume that, in the case of the straight fibre end, the detector captures the beam fully,
and that in the angled case the detector misses a part of the beam
30
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Angled Fibre Ends
In both cases, the numerical aperture of the fibre is defined by the 5% angle γ of the far
field
In the angled case, the tilt of the beam axis β can be calculated using Snell’s law,
b = arcsin (n sin (a )) @(n - 1)a
The effective numerical aperture for the angled case is
NAeff = sin (g + b )
Question
What is the effective numerical aperture for the straight case?
To capture the beam fully
A shorter distance to the detector would be needed
Tilting the fibre, so that the beam axis is realigned to hit the centre of the detector
Using a lens to reduce the effective beam diameter
31
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Fibres of High NA
In situations with high numerical aperture, a power meter may not present the same
responsivity to all parts of the beam
Solution 1 – Decreasing the distance between fibre end and photodetector
Problems
Reflection becomes significant
The photodetector’s responsivity is lower for those parts of the beam that hit the
detector at larger angles
Question
Why is the reflection problems may occur if the distance between fibre end and
photodetector decreases?
32
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Fibres of High NA
Solution 2 – Using a lens with high numerical aperture in order to collimate the beam
Problems
Light emitted at larger angles will be more strongly reflected off the lens than the
on-axis beams
Question
Suggest one improvement to this solution?
The figure shows the power meter with a lens inserted into the beam path
33
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Fibres of High NA
Solution 3 – Using an integrating sphere in combination with the photodetector
Ideally, the integrating sphere should perfectly scatter all incident light
The detector should not be exposed to either direct beams from the source or to
beams after only one reflection
Beams forming large angle (high numerical aperture) against the connector axis
go through different attenuations than the near axis beams
In addition, some of the materials used to scatter the beam inside the integrating
sphere tend to absorb moisture, so that the scattering characteristics change with
the relative humidity
34
Power Meters with Photodetectors
Compatibility with Different Fibres
Compatibility with Multi-mode Fibres
A narrow linewidth source will generate irregular far-field patterns (speckle patterns),
which are caused by optical interference between the different fibre modes
Speckle patterns go through rapid changes when the fibre is moved, because changing
the path lengths of the individual modes by only fractions of the wavelength creates a
different speckle pattern
Speckle patterns create additional uncertainties because the photocurrent is a
convolution of the speckle pattern with the detector’s spatial homogeneity
35
LED Power Measurement
LED power is difficult to measure because
LED’s wide spectral width
The photodetector’s responsivity changes within the spectral range
Correction
Possible if the detector’s spectral responsivity and the LED’s spectral power density
are known
The figure shows the situation for a 1550 nm and a germanium detector
λ0 = arbitrarily chosen wavelength (preferably the LED peak wavelength) for which the power
meter is corrected
rrel(λ) = responsivity relative to λ0 , where rrel(λ0) = 1
p0 = spectral power density of the LED at the wavelength λ0, in watts/nm
f(λ) = factor describing the LED’s spectral emission, where f(λ0) = 1
36
LED Power Measurement
The correct LED power is
P = p0 ò f (l ) dl
The uncorrected measurement result is
Pm = p0 ò f (l )rrel (l ) dl
A correction factor can be calculated to be
P
K =
=
Pm
ò f (l ) dl
ò f (l )r
rel
(l ) d l
Question
What if the LED spectrum is symmetrical and the detector’s responsivity is linearly
changing with respect to wavelength?
37
LED Power Measurement
The following measurement procedure is suggested
Determine the LED’s centre wavelength, for example, from its data sheet
Set the power meter to the LED’s wavelength λ0 and measure the LED power
If the LED spectrum is essentially symmetrical and the photodetector’s responsivity is
nearly linear within the LED’s spectral band, use the measured power as the result
If one of the above condition is not met,
Calculate the correction factor as in the previous slide
Multiply the measured power with the correction factor to obtain the correct power
Question
Is the correction factor needed for laser power measurement? Explain why.
38
High Power Measurement
Optical power meters based on photodetectors can measure maximum power levels of a
few milliwatts
Beyond this power level, the photodetector goes into saturation
Possible output power exceeding the measurement range of conventional power meters
The amplifier pump lasers, which produce 100 mW
All optical amplifiers, which may exceed 1 watt (except for preamplifiers – a few
milliwatts)
The figure shows a commercial high-power optical head with a 5 mm InGaAs detector and a
window made from absorbing glass, to reduce the incident optical power to a suitable level
39
High Power Measurement
Local overheating of the absorber
Occurs when the incident optical power levels exceed 100 mW
Prevention – create a spot diameter of not less than 3 mm on the detector (measured
at the 5% points)
Question
At the given distance of 8 mm between the end of a standard single-mode fibre and the
detector, determine whether it is adequate to prevent the local overheating of the
absorber when the numerical aperture of the fibre is 0.1. [Answer = No]
Solutions for high-power measurement
Inserting a scattering filter between the fibre end and the detector
Wide wavelength range
High-power capability
Scattering introduces depolarization – reduces the polarization dependence of the
optical head
Different beam geometries (fibre types) will cause different attenuations – this
technique splits power away from the detector
40
High Power Measurement
Solutions for high-power measurement
Inserting a mesh-type filter consisting of thin wires between the fibre end and the detector
Wide wavelength range
High-power capability – increased wire temperature will not influence the attenuation
Splitting some power away before the measurement
Limited to certain fibre types because the coupler fibres must be of the same types as
the fibre to be measure
Inserting an integrating sphere between the fibre end and the detector
Usually an expensive solution
Some angle dependence & dependence on relative humidity
Several of these techniques can be combined
A collimating lens may have to be inserted before these filters to ensure that beam
diameter remains smaller than the detector diameter
41
High Power Measurement
Common to all of these techniques is the need for calibrating the filter attenuation
The figure shows the calibration setup
An optical attenuator may have to be inserted between the source and the detector to
ensure stable output power
42
High Power Measurement
The calibration is for the specific fibre and wavelength
Procedure
Set a power level that can be handled by the unattenuated sensor
Measure the power P1
Attach the filter
Measure the power again P2
The desired filter attenuation is the ratio of the two power levels
43
Uncertainties in Absolute Power Measurement
Random uncertainty due to power instability
Power instabilities could be inherent to the source or caused by external reflection
travelling back to the source
Systematic uncertainty due to power-meter calibration
It is assumed that the power meter is regularly calibrated following the
manufacturer’s recommendations and that the wavelength correction is set to the
wavelength of the source
The absolute uncertainty and the conditions for which this uncertainty applied should be
obtained from the power meter’s data sheet
Systematic uncertainty due to the spectral width of the source
Laser diodes measurement – negligible
LED measurement
No error if the spectrum is symmmetrical about the centre wavelength and the
power meter’s responsivity is linear within the wavelength range of interest
Otherwise, a correction factor or an uncertainty can be calculated
44
Uncertainties in Absolute Power Measurement
Systematic uncertainty due to wavelength
The wavelength of the source (centre wavelength) should be accurately known
Otherwise, the partial uncertainties will be the wavelength uncertainty multiplied by the
power meter’s responsivity versus wavelength slope (%/nm) at that wavelength
Systematic uncertainty due to beam geometry
In the best case, the beam is centred on the detector and the beam diameter is about
2/3 of the detector diameter
If this is not the case, then an appropriate uncertainty may have to be calculated
Particularly, problems can be expected when the fibre end is angled and the beam
partly misses the detector
45
Uncertainties in Absolute Power Measurement
Systematic uncertainty due to power level
Optical power meters have extremely wide power ranges of up to 100 dB
Uncertainties due to power level can be expected when the actual power approaches
the noise level, or when it exceeds the high end of the specified power range
Systematic (and random) uncertainty due to reflections
Commercial power meters are often calibrated with an open beam
In the actual measurement with a fibre, the fibre is held by a connector and connector
adapter
In this case doubly reflected power may strike the detector, causing an increase of the
power reading
Reflections can also cause power stability problems
46
Responsivity Calibration
The most important criterion in conjunction with accurate measurement of absolute power
Generally, all power meters are calibrated through comparison
A test meter and a power measurement standard are exposed to a suitable radiation
source, either sequentially or in parallel
If a calibration in fine-wavelength steps over a wide wavelength range is desired, then
the source should be a halogen white-light source which is spectrally filtered with a
monochromator
A power level of approximately 10 μW and a spectral width of up to 5 nm are desirable
The figure shows a typical monochromator-type calibration setup
47
Responsivity Calibration
Two types of standard sensors
Thermal detector
Photodetector sensors
A monochromator-based calibration setup is expensive and difficult to operate and
maintain
A more affordable setup is shown in the figure
48
Responsivity Calibration
Dual-wavelength calibration
A dual-wavelength source (FP laser) generates precisely known wavelengths around
1300 and 1550 nm
The attenuator is used to isolate the source and to set the appropriate power level
The coupler is used to split the power and to provide power monitoring
A specially calibrated optical head is used as the standard
A blank adapter serves as a spacer, to enlarge the spot diameter on the detector to
approximately 2.4 mm (at the 5% points)
Question
How to perform absolute power calibration over wavelength using the above
configuration?
49
Responsivity Calibration
Switching the two coupler arms between the standard and the test meter (DUT) can be
used to determine both the split ratio and the correction factor
P = the correct power levels from the standard
D = the displayed power of the DUT
50
Responsivity Calibration
Coupling ratio
c=
P1
kD2
=
kD1
P2
Correction factor
k=
P1P2
D1D2
Question
What will happen to the coupling ratio and the correction factor if there is a drift of the
source power?
The correction factor can either be used to correct the test meter or, without correction, as a
test result for the calibration certificate
51
Linearity Calibration
Power meter linearity calibration is necessary because of two reasons
To extend the calibration of absolute power to the whole power range
To prepare the basis for high-accuracy loss and gain measurements
The linearity is expected to be almost wavelength-independent – sufficient to calibrate at
only one or two wavelengths within the detector’s spectral responsivity region
Photodetectors provide excellent linearity from the noise level to approximately 1 mW – often
the specifiable linearity is limited by the performance of the linearity calibration setup
Question
Is the specifiable linearity limited by the linearity of the detector?
Linearity Calibration based on Comparison
Procedure
Measure an arbitrary attenuation with both the test meter and a standard meter
Compare the two attenuation results
52
Linearity Calibration
A possible measurement setup is shown in the figure
The first attenuator is used to set the power level, to generate additional fixed attenuations
and to split the power (a power-splitter is built into this specific attenuator model)
The second attenuator is used to increase the measurement range for very high power
levels - the second attenuator reduces the power level to the usable range for the standard
sensor
For very low power levels, the two sensors can be switched and the second attenuator
produces the low power levels
53
Linearity Calibration
Any difference between the two measured attenuations indicates nonlinearity
The nonlinearity of an optical power meter is internationally defined so that it represents
directly the correspondent error in a loss measurement
N (Dx ) =
Am - A
D / D0
= x
- 1
A
Px / P0
where A is the true power ratio, Am is the measured power ratio, Dx/D0 is the displayed
power ratio (of the test meter), Px/P0 are the true power ratio (of the standard meter)
The calibration procedure is as follows,
Set the desired reference power on the test meter, D0. Record the powers P0 (standard
meter) and D0
Increase (decrease) the attenuation of the first attenuator and record the powers P1
(P2, ..) and D1 (D2, ..)
Calculate the nonlinearity for the power D1 (D2, ..) using the above equation. In these
calculations, the reference level is changing from step to step, which is why these
nonlinearities are termed “partial”
Question
What is the value of nonlinearity at D0?
54
Linearity Calibration
The calibration procedure is as follows,
Increase the attenuation further by repeating the first two steps, until the low (high) end
of the power range is reached. It is advisable to measure the nonlinearity due to range
discontinuities by simply changing the power range and recording the measurement
results in both ranges
Decrease the attenuation to obtain the power levels above P0 and to obtain the
correspondent nonlinearity results
55
Linearity Calibration
Linearity Calibration based on Superposition
This is a self-calibrating method which does not need a standard meter
A possible measurement setup is shown in the figure below
Procedure
In the beginning, the two attenuators are both set to high attenuation and so that each
beam separately gives rise to the same powers at the DUT, Da ≈ Db
56
Linearity Calibration
Linearity Calibration based on Superposition
Procedure
Each attenuator is equipped with a shutter. The shutter of the respective other
attenuator remains closed
Then the beams are combined by opening both shutters at the same time. This
reading should now be the sum of the two preceding individual readings:
Dc = Da + Db (@ 2Da )
Any deviation indicates nonlinearity. Accordingly, the nonlinearity for the first power Dc
is:
Dc
N1 =
- 1
Da + Db
The next cycle starts by generating the combined power separately with each of the
attenuators, before combining them again
At the end of the measurement, the partial nonlinearities for all steps will be determined
57
Linearity Calibration
Linearity Calibration based on Superposition
The figure shows the power superposition used in linearity calibration
58
Linearity Calibration
Linearity Calibration based on Superposition
Finally, the total nonlinearity can be calculated, in other words, the nonlinearity with respect
to a fixed reference level
Start by choosing a reference level, at which the total nonlinearity is zero by definition
Then use the following equation for power levels lower than the reference level:
n
N total (Dn ) = -
å
Ni
i= - 1
where n = -1, -2, etc. indicates the power level number below the reference point and N is
the partial nonlinearity for the i-th step (i = 0 for the step between the reference power and
the next-higher power).
For power levels higher than the reference level, the total nonlinearity is:
n- 1
N total (Dn ) = -
å
Ni
i= 0
where n = 1, 2, etc. The final result is a list of total linearities for the whole power range in 3
dB steps (because the power is doubled in each step)
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