1 Chapter Two – Optical Power Measurement Contents 1. Power Meters with Thermal Detectors 2. Power...

1

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

2

IntroductionTwo 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?

3

IntroductionComparison of thermal power meters and photodetector power meters

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.

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

4

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

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

Questions

What is the parameter to be controlled to achieve time-independent temperature?

What provides the basis for the accuracy of this method?

5


The figure shows the thermal detector with electrical substitution

Question

What is the series of apertures for?

6


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

7


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.

8


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?

9

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

10


The figure shows a cross-section through a commercial large-area optical sensor head based on a photodetector

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

Question

Why is the photodetector angled positioned?

11


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

12


PIN diode

Operation

Each incident photon is absorbed in the intrinsic (i-) layer

An electron-hole pair is created – the photon energy ≥ bandgap energy (material-dependent

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?

13


PIN diode

From the definition, the responsivity r is given by,

Each photon represents the energy Eph,

where h = Planck’s constant, ν = optical frequency, and c = speed of light in vacuum

The optical power which corresponds to one photon is,

The correspondent electrical current is one electron charge q per time span Δt,

The linear spectral responsivity of an ideal photodetector with η = 1,

Ir

P=

ph

hcE hu

l= =

phph

E hcP

t tl= =D D

ph

qI

t=D

qr

hcl

=

14


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

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

Question

Pure InGaAs has a refractive index of 3.5. Calculate the reflectivity (or Fresnel reflection) at the detector surface. [Answer = 31%]

15


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

16


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?

17


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

18


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

19


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?

20


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

The nonlinearity is defined as

Where r(P) is the power meter’s responsivity at an arbitrary power level, and r(P0) is the responsivity at the reference level (usually 10 μm)

Question

What causes nonlinearity in the analogue amplifier at high power levels?

( )( ) ( )

( )0

0

r P r PN P

r P

-=

21



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,2 22 2n n di qB I Aé ù= ´ ë û

22



Total short noise

where r = responsivity and Popt = received optical power

Noise equivalent power (NEP)

Signal-to-noise ratio (SNR)

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?

( )2 2 2n n d opti qB I rP= +

( )21 1 W2 2

Hzn n d optNEP i qB I rPr r

é ù= = + ê ú

ê úë û

optPSNR

NEP=

23



The figure shows the power dependence of the SNR

Question

Why is the SNR linear for low Popt?

24



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

25


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

26


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

27


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

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

Question

Why is the pattern shifted to different wavelength when the thickness changes?

28


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

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

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

( )( )

2

0 2

2exp

rH z H

w z

æ ö÷ç= - ÷ç ÷÷çè ø

det 21

NAr z zNA

NA= @

-

29



Compatibility with Single-mode Fibres

The coupling efficiency is given by

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,

Then the coupling efficiency can be expressed on the basis of the numerical aperture

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%]

2det2

21 exp

rw

hæ ö÷ç= - - ÷ç ÷÷çè ø

5%0.817 0.817w r zNA= = ´

2det1.71

1 expr

zNAh

é ùæ ö÷ê úç= - - ÷ç ÷ê úè øë û

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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

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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,

The effective numerical aperture for the angled case is

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

Question

What is the effective numerical aperture for the straight case?

( )( ) ( )arcsin sin 1n nb a a= @ -

( )sineffNA g b= +

32



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?

33




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

The figure shows the power meter with a lens inserted into the beam path

Question

Suggest one improvement to this solution?

34




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

35



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

36

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

37


The correct LED power is

The uncorrected measurement result is

A correction factor can be calculated to be

Question

What if the LED spectrum is symmetrical and the detector’s responsivity is linearly changing with respect to wavelength?

( )0P p f dl l= ò

( ) ( )0m relP p f r dl l l= ò

( )

( ) ( )m rel

f dPK

P f r d

l l

l l l= =

òò

38


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.

39

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

40


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)

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

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]

41


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

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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

43


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

44

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

45


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

46


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

47

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

48


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

49


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?

50


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

51


Coupling ratio

Correction factor

The correction factor can either be used to correct the test meter or, without correction, as a test result for the calibration certificate

Question

What will happen to the coupling ratio and the correction factor if there is a drift of the source power?

1 2

1 2

P Pk

DD=

1 2

1 2

P kDc

kD P= =

52

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

Linearity Calibration based on Comparison

Procedure

Measure an arbitrary attenuation with both the test meter and a standard meter

Compare the two attenuation results

Question

Is the specifiable linearity limited by the linearity of the detector?

53


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

54


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

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”

( ) 0

0

/1

/m x

xx

A A D DN D

A P P-

= = -

Question

What is the value of nonlinearity at D0?

55


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

56


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

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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:

Any deviation indicates nonlinearity. Accordingly, the nonlinearity for the first power Dc is:

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

( )2c a b aD D D D= + @

1 1c

a b

DN

D D= -

+

58



The figure shows the power superposition used in linearity calibration

59



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:

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:

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)

( )1

n

total n ii

N D N=-

=- å

( )1

0

n

total n ii

N D N-

=

=- å

1 Chapter Two – Optical Power Measurement Contents 1. Power Meters with Thermal Detectors 2. Power...

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Transcript of 1 Chapter Two – Optical Power Measurement Contents 1. Power Meters with Thermal Detectors 2. Power...