University of Nairobi

A Phase Detector for Phase Perturbation

Demodulation in a LASER Signal

Project Index: PRJ067

by

Brian Wekesa Simiyu

Reg. No: F17/1412/2011

SUPERVISOR: Dr. Ing. Wilfred Mwema

EXAMINER: Prof. Elijah Mwangi

Project Report Submitted in Partial Fulfilment of the Requirement for the Award of the

Degree of Bachelor of Science in Electrical and Electronic Engineering of the University of

Nairobi

May 16th, 2016

Department of Electrical and Information Engineering

i

Declaration of Originality

College: Architecture and Engineering

Faculty/ School/ Institute: Engineering

Department: Electrical and Information Engineering

Course: Bachelor of Science in Electrical and Electronic Engineering

Registration Number: F17/1412/2011

Name of Student: Brian Wekesa Simiyu

Title of Work: A phase detector for phase perturbation demodulation in a LASER

signal

1. I understand what plagiarism is and I am aware of the University policy in this regard.

2. I declare that this final year project report is my original work and has not been

submitted elsewhere for examination, award of a degree or publication. Where other

people’s work or my own work has been used, this has properly been acknowledged

and referenced in accordance with the University of Nairobi’s requirements.

3. I have not sought or used the services of any professional agencies to produce this work.

4. I have not allowed, and shall not allow anyone to copy my work with the intention of

passing it off as his/her own work.

5. I understand that any false claim in respect of this work shall result in disciplinary action,

in accordance with University anti-plagiarism policy

Signature Date

ii

Dedicated to

my mum

iii

Acknowledgements This project would not have been possible without the help of many wonderfully helpful

people, to whom I am deeply indebted. It was an honour to work under the supervision of Dr.

Ing. Wilfred Mwema. He introduced me to the project. His refreshing and informed advice

helped me through the project and the writing of this report. Thank you.

I would also like to thank the Electrical Engineering Department at the University of Nairobi for

facilitating my project, especially Mr. Rotich of the Telecommunications Laboratory for ensuring

I had most of what I needed for the project. To the Electronics Laboratory team, I am more than

grateful for providing space and equipment for my project implementation and testing.

Words cannot how grateful I am to my family. Because of their love and encouragement I made

it this far. Heartfelt thanks to my mother, brothers and sister for their constant encouragement

and motivation over time that has made me who I am.

iv

Contents

Declaration of Originality .............................................................................................................................. i

Dedication...................................................................................................... Error! Bookmark not defined.

Acknowledgements ..................................................................................................................................... iii

Contents ....................................................................................................................................................... iv

List of Figures ............................................................................................................................................... vi

List of Tables ............................................................................................................................................... vii

List of Symbols ........................................................................................................................................... viii

List of Abbreviations ................................................................................................................................... ix

ABSTRACT ..................................................................................................................................................... x

1.0 INTRODUCTION ................................................................................................................................ 1

2.0 BACKROUND AND THEORY .............................................................................................................. 2

2.1 Interference .................................................................................................................................. 2

2.2 Doppler Effect ............................................................................................................................... 2

2.3 Interferometry .............................................................................................................................. 3

2.3.1 External Interferometry: The Michelson Interferometer ................................................... 4

2.3.2 Self-Mixing Interferometer .................................................................................................. 4

2.4 LASER Diodes ................................................................................................................................ 8

2.5 Photodiodes .................................................................................................................................. 9

3.0 METHODOLOGY .............................................................................................................................. 11

3.1 Choice of Implementation method ........................................................................................... 11

3.2 Choice of the LASER diode ......................................................................................................... 13

3.3 Design of the LASER Diode Driver .............................................................................................. 13

3.4 Design of the Trans Impedance Amplifier ................................................................................. 16

3.5 Design of the Low Pass Filter ..................................................................................................... 18

4.0 IMPLEMENTATION AND TESTING .................................................................................................. 24

4.1. Testing of the Complete Detector ............................................................................................. 25

4.2. Testing of the LASER driver ........................................................................................................ 27

4.3. Testing of the Transimpedance Amplifier ................................................................................. 29

4.4. Testing of the Lowpass Filter ..................................................................................................... 30

v

5.0 DISCUSSION .................................................................................................................................... 32

6.0 CONCLUSION .................................................................................................................................. 33

7.0 RECOMMENDATIONS ..................................................................................................................... 34

8.0 REFERENCES .................................................................................................................................... 35

vi

List of Figures Figure 1: Illustration of Doppler Shifting by Back Scattering………………………………………………..……3

Figure 1: Set up of the Michelson Interferometer……………………………………………………….………………4

Figure 2: Basic Scheme of a Self-Mixing Interferometer………………………………………….………………….5

Figure 3: Self-mixing output for different feedback regimes with respect to the target

vibration……………………………………………………………………………………………………………………………..….….8

Figure 4: Photodiode Equivalent Circuit…………………………………………………………………………….……..9

Figure 5: Block Diagram of the Phase Detector…………………………………………………………………..……12

Figure 6: Circuit of the Laser Diode Current Source (Driver)… …………………………………………..….….14

Figure 7: Circuit of the Transimpedance Amplifier………………….…………………………………………….….16

Figure 8: Spectral Response of Various Silicon Photodiodes…………….……………………………………....19

Figure 9: Second order Sallen-Key topology………………………………….………………………………………….20

Figure 10: Circuit of the Low Pass Filter……………………………………………………………………………………22

Figure 11: Simulated filter response………………………………………….…………………………………………….23

Figure 12: Schematic capture of the complete detector……………………………………………………………24

Figure 13: Board Layout of the Phase detector…………………………………………………………………………25

Figure 14: Illustration of the fringe counting method………………………………………………………………25

Figure 15: Phase detector testing set up………………………………………..…………………………………………27

Figure 16: Testing circuit of the LASER driver……………………………………………………………………………28

Figure 17: Input Voltage and Output Current Waveforms……………..…………………………………………29

Figure 18: Multisim simulation set up for the transimpedance amplifier…..……………………………..30

Figure 19: Transimpedance amplifier output waveform……………………………………………………………30

Figure 20: Frequency Response of the lowpass filter…………………………………………………………………31

vii

List of Tables Table 1: Self-mixing optical feedback regimes ……………………………………………………………………………………….7

Table 2: Some LASER diodes suitable for self-mixing interferometer…………….……………………………13

Table 3: Fourth order Bessel Filter Table…………………………………….…………………………………………………………21

Table 4: Frequency response data for the lowpass filter…………………………………………………………..31

viii

List of Symbols Ω Ohms

μ micro or 10-6 (as a prefix)

𝜆 Wavelength

oC degree Celsius (unit of temperature)

Ω Ohms (unit of resistance)

ix

List of Abbreviations n nano or 10-9 (as a prefix)

p pico or 10-12 (as a prefix)

m milli or 10-3 (as a prefix)

k kilo or 103 (as a prefix); Boltzmann constant

M mega or 106 (as a prefix)

m meter (as a suffix)

A Amperes (unit of current)

Hz Hertz (unit of frequency)

V Volts (unit of voltage)

F Farads (unit of capacitance)

K Kelvins (unit of temperature)

Op Amp Operational amplifier

dB decibels

LASER Light Amplification through Stimulated Emission of Radiation

x

ABSTRACT Laser interferometry is a powerful tool for vibration measurement. It makes it possible to

measure vibrations without the need for contact with the vibrating object. This makes it

especially suited for measurement of small vibrations which would otherwise be interfered with

by contact-based methods.

This is a report of the design and implementation of a phase detector for LASER phase

perturbation demodulation. Based on self-mixing interferometry, the detector achieves

vibrations measurements using the fringe counting method. The report covers design of a

LASER driver, a transimpedance amplifier and an output filter. With a bandwidth of over 200

kHz, the detector is designed to measure vibrations larger than half a wavelength of the lasing

frequency. This translates to small vibrations as small as a few micrometers for a red LASER

diode for example.

In the later part of the report, the detector sub circuits are tested and analysed. The complete

detector is however not tested for vibration measurements having failed to acquire the

appropriate LASER diode in time. Nevertheless, the vibration testing procedure is presented

and ways on automating and improving the sensitivity of the detector discussed.

1

1.0 INTRODUCTION Light reflecting off a vibrating surface experiences a change in its phase proportional to the

vibrational changes. To recover the vibrations, the reflected signal is usually demodulated by

interferometric means. Interferometry started with the first observation of interference by

Thomas Young and invention of the first interferometer by Albert Michelson, both in the 19th

century. Invention of the laser in the mid 20th century revolutionized interferometry with laser

interferometers. Laser interferometers have been applied in vibrometry (vibration

measurement), velocimetry (velocity measurement), mechanical metrology, space telemetry,

optical fibre sensors among others [1].

The aim of this project was to develop a phase detector for vibrometry or vibration

measurement. The main advantage of LASER vibrometry is that it does not require contact with

the vibrating body which makes it suitable for measurement of very small vibrations as well as

vibrations in inaccessible areas.

Section 2 discusses the necessary theoretical background followed by design of a self-mixing

interferometer in section 3. Testing of the phase detector for vibration measurements is

outlined in section 4 using the fringe counting technique. Section 5 discusses the resulting

findings concluding that the project objectives were met in section 6. The project is however

not a finished product and important improvements are discussed in section 7.

2

2.0 BACKROUND AND THEORY Given a phase-perturbed LASER signal a detector was to be built with the intention of

recovering the phase information and subsequently observing the small target vibrations. The

goal of the project was to generate the appropriate LASER signal, have it reflect off a vibrating

surface, then detect the signal and lastly reconstruct the target vibrations from the phase of the

back-scattered signal. In this section the theoretical background required is discussed. Concepts

examined include interference, interferometry, and Doppler Effect. Also discussed are the basic

principles behind devices that would be used as emitters (LASER diodes) and sensors

(photodiodes) of the LASER signal.

2.1 Interference

Phase demodulation in a LASER signal is made possible by the phenomenon of wave

interference. Interference is observed when two monochromatic waves from coherent sources

interact. Coherence means that the two sources have a constant phase difference between

them. A light wave is monochromatic when it is composed of a single wavelength.

Wave interference is a simple case of wave superposition. When two or more coherent light

waves interact, their amplitudes add or subtract depending on the phase difference between

them. Wherever the waves are in phase their amplitudes add leading to constructive

interference while the amplitudes cancel out at the points where they are out of phase leading

to destructive interference [2]. For any intermediate points, partial addition or subtraction

takes occurs.

2.2 Doppler Effect

The Doppler Effect refers to the apparent change in the frequency of the received wave as

perceived by the receiver when there is relative motion between the transmitter and the

receiver. The observed frequency of the wave appears higher than the source frequency when

the source and receiver are moving towards each other than when they are moving away from

each.

In phase measurements involving a stationary LASER source and a stationary vibrating target,

consideration is only given to Doppler frequency shift due to back scattering as derived by Drain

3

in 1980 [3]. The beam in figure 3 is incident on a mirror with velocity 𝑢 at an angle 𝜃 and

reflected along the same path. The original position of the mirror (at time 𝑡) after a time

interval 𝛿𝑡 are as shown.

Figure 21: Illustration of Doppler Shifting by Back Scattering

The optical path difference 𝜕𝑙 between the incident and reflected wave fronts during time the

interval 𝛿𝑡 is:

𝛿𝑙 = 2𝑢 𝛿𝑡 𝑐𝑜𝑠𝜃 (1)

From 𝑐 = 𝑓𝜆, the Doppler shift in frequency is given by:

Δ𝑓 = 1

𝜆

𝛿𝑙

𝛿𝑡=

2𝑢 𝑐𝑜𝑠𝜃

𝜆 (2)

The phase change perceived in the backscattered LASER signal due to this shift can be

demodulated by interferometric means [4].

2.3 Interferometry

An interferometer is an instrument that allows interference to be observed. LASER

interferometers work by splitting a LASER beam into two. One beam is directed to a target and

another is directed to a stationary mirror. The two beams then recombine causing interference.

A light intensity sensor is positioned at the point of interference to observe the interference

pattern. Variations in the interference pattern are used to reconstruct the motion of the target.

4

Generally, interferometers can be classified based on the configuration used into two types:

external interferometry and self-mixing interferometry [5].

2.3.1 External Interferometry: The Michelson Interferometer

For external interferometers, interference occurs outside the LASER diode cavity. They are

based on a single beam being split into two beams as shown in figure 2. One beam is directed

to the target mirror 2 and the other to the stationary mirror 1. The two beams interact at the

detector after reflection from the respective mirrors. The resulting interference is then picked up by the

detector for observation. The Twyman-Green and the Mach-Zehnder interferometers are other types of

external interferometers.

Figure 22: Set up of the Michelson Interferometer

2.3.2 Self-Mixing Interferometer

A self-mixing interferometer works by allowing a fraction of the light backscattered by a remote

target into the laser cavity to interfere with the standing wave inside the LASER cavity. This

causes an amplitude and frequency modulation of the output LASER beam. Because the LASER

beam carries with it the interference signal, it can be detected by placing a monitor photodiode

anywhere along the LASER beam [6]. This is however often accomplished by having a monitor

diode within the same package as the LASER diode.

5

Figure 23: Basic Scheme of a Self-Mixing Interferometer

2.3.2.1 Basic Theory of Self-Mixing

As shown in figure 3, the LASER source (and monitor photodiode) acts as a sensitive detector

for the path length travelled by the beam to the target and back. A self-mixing LASER diode

configuration can be modeled as a three-mirror cavity made up of the two walls of the LASER

cavity and the remote target as the third mirror, with [5]:

𝑃𝑟 = 𝑃𝑜

𝐴 (3)

Where 𝑃𝑟 is the power backscattered by the remote target, 𝑃𝑜the emitted power and A the

power attenuation of the external cavity. The backscattered field phasor 𝑬𝒓 has a phase of

2ks(t) (where k is the wave number and s is the target distance) with respect to the lasing field

phasor 𝑬𝒇. 𝑬𝒓 is allowed back into the LASER cavity and adds to 𝑬𝒇. As a result, the lasing field

amplitude and frequency are modulated such that the amplitude modulation term is a cosine

function of 2ks while the frequency modulation term is a sine function. The resultant output

field phasor 𝑬𝒐is given by:

𝑬𝒐 = 𝛼𝑬𝒇 + 𝑬𝒓(4)

where 𝛼 is the transmittance of the LASER cavity. The optical intensity of the combined field is

then:

𝑠 = |𝑬𝒐|2 = |𝛼𝑬𝒇|2

+ |𝑬𝒓|2 + 𝛼𝑬𝒇𝑬𝒓∗ + 𝛼𝑬𝒇

∗𝑬𝒓(5)

The terms 𝛼𝑬𝒇𝑬𝒓∗ + 𝛼𝑬𝒇

∗𝑬𝒓 represent the interference signal and can be reduced to:

6

𝛼𝑬𝒇𝑬𝒓∗ + 𝜶𝑬𝒇

∗𝑬𝒓 = 2𝛼|𝑬𝒇||𝑬𝒓|𝑐𝑜𝑠 𝜔𝑚𝑡 (6)

Where 𝜔𝑚 is the angular beat frequency between the two fields.

Setting 𝑆𝑜 = |𝛼𝑬𝒇|2and for weak feedback (

𝐸𝑟𝐸𝑓

⁄ ≪ 1)

𝑠 = 𝑆𝑜(1 + 𝑚 𝑐𝑜𝑠 𝜔𝑚𝑡) (7)

Where 𝑚 = 2 |𝐸𝑟

𝛼𝐸𝑓⁄ | and |

𝐸𝑟𝐸𝑓

⁄ | is the field amplitude feedback ratio.

Equivalently, the output power density which is the signal detected by the monitor photodiode

is given by

𝑃(∅) = 𝑃𝑜[1 + 𝑚 𝑐𝑜𝑠 𝜔𝑚𝑡] (8)

2.3.2.2 Self-Mixing in a LASER Diode

Any single-mode longitudinal Fabry-Perot (FP) LASER diode can be used for self-mixing as long

as the diode has a side mode suppression larger than 7 to 8 dB [7]. Self-mixing in LASER diodes

differs from the simple three mirror model because of the non-linear nature of the

semiconductor medium that relates both refractive index and optical gain to the injected

carrier density. This means the amplitude modulation term differs from the three mirror cosine

function [8].Lang and Kobayashi developed equations for a complete analysis of the LASER

diode with optical feedback. For sensing applications, steady-state solution for the power

emitted by the LASER diode as given by the equations is [8]:

𝑃(∅) = 𝑃𝑜[1 + 𝑚𝐹(∅)] (9)

Where 𝑃𝑜is the power emitted by the LASER diode without optical feedback,𝐹(∅) is a periodic

function of the phase ∅ = 2𝑘𝑠 and 𝑚 is the modulation index. The modulation index and the

function 𝐹(∅) depend on the feedback regime defined by a parameter known as the feedback

parameter C, which depends on both the amount of feedback and the target distance. The

different feedback regimes are discriminated by the value of the C parameter as shown in table

1 and figure 4:

7

Table 1: Self-mixing optical feedback regimes [8]

C parameter

(Feedback Regime)

Modulation index,

m

𝑭(∅) / Self-Mixing Signal

𝑪 ≪ 𝟏

Very weak feedback

Varies as 1√𝐴

⁄ 𝐹(∅) and the self-mixing signal are cosine shaped

𝟎. 𝟏 < 𝑪 < 𝟏

Weak feedback

Varies as 1√𝐴

⁄ 𝐹(∅) and the self-mixing signal are slightly Distorted

𝟏 < 𝑪 < 𝟒. 𝟔

Moderate feedback

Varies inversely but

not proportionally

with√𝐴

𝐹(∅) is three valued for some range of phase ∅.

Self-mixing signal is sawtooth-like and exhibits

hysteresis

𝑪 > 𝟒. 𝟔

Strong feedback

𝐹(∅)is five-valued. Diode goes into mode-hopping

regime and measurements are not possible

Integrating equation 2 and assuming 𝜃 = 0 (target vibrates along the path of the LASER beam),

the phase change ∅(𝑡)in the self-mixing LASER signal is found to be:

∅(𝑡) = 2𝜋 ∫ Δ𝑓 𝑑𝑡 = 2𝜋2

𝜆∫ u 𝑑𝑡 = 4𝜋

𝑚(𝑡)

𝜆 (10)

∅(𝑡)|𝑚𝑎𝑥 = 2𝜋𝑀

𝜆2⁄

(11)

Where (𝑚(𝑡) = 𝑀 cos 2𝜋𝑓𝑚𝑡) is the target vibration assumed sinusoidal and along the path of

the laser beam. Consequently, the self-mixing signal undergoes a complete cycle (phase change

of 2𝜋 radians) for every half a wavelength change in target position due to vibration. As a

result, the amplitude of target vibrations can be found by counting the self-mixing cycles (or

fringes) in half a cycle of target displacement.

8

Figure 24: Self-mixing output for different feedback regimes with respect to the target vibration: (a) Target vibration driving signal; (b) Very weak feedback; (c) Weak feedback (d) Moderate feedback. [5].

2.4 LASER Diodes

LASER is the acronym for “Light Amplification through Stimulated Emission of Radiation”.

LASERs emit near monochromatic light by stimulated emission where electrons are energized

to high energy states before being stimulated to fall back to lower energy levels by a

forthcoming photon of energy. The relaxing electrons release energy at the same frequency as

9

the photon causing light amplification. A LASER device consists of an optical amplifier that

carries out stimulated emission and a frequency selective resonator that confines and feeds

emitted light back to the amplifier.

The amplifying element in semiconductor LASER diodes is a forward biased P-N junction. A

LASER diode is a current sensitive device, and careful operation is required to prevent damage

to the diode due to large transient as well as sustained currents. Also the frequency output of

the diode is current-dependent, and a stable current is required to ensure stability of the

output frequency [9].

2.5 Photodiodes

Photodiodes are light sensors that generate an electrical signal on illumination with light. The

various types of photodiodes include silicon and germanium P-N photodiodes, P-I-N

photodiodes, avalanche photodiodes (APD) and hetero-junction photodiodes. A photodiode

typically has the equivalent circuit shown in figure 5 [10]:

Figure 25: Photodiode Equivalent Circuit

Where 𝐼𝑃 is the photo-generated current, 𝑉𝐷the diode voltage, 𝐼𝐷 the diode current and 𝐼′ the

current through shunt resistance. Capacitance 𝐶𝑗 is the junction capacitance which depends on

the amount of reverse bias. An increase in the reverse bias decreases the capacitance.

Resistance 𝑅𝑆𝐻 is the diode shunt resistance with typical ranges of 10’s to 1000’s MΩ.

Resistance 𝑅𝑆 is the diode series resistance with typical ranges of 10Ω to a few kΩ’s. The output

diode voltage and current are denoted by 𝑉𝑂 and 𝐼𝑜 respectively.

10

Photodiodes can operate in either the photoconductive mode or the photovoltaic mode. In the

photovoltaic mode, the diode is operated with zero voltage bias. This mode eliminates dark

current and is preferred for low noise operation. A large junction capacitance is involved due to

zero bias, which leads to large time constants and it is therefore applicable to slow speed

operation. The photoconductive mode involves reverse biasing the photodiode. This is a fast

mode of operation due to reduced junction capacitances. It however involves large dark

currents.

There are two major noise considerations in photodiode detectors namely shot noise and

Johnson noise. Shot noise depends on the statistical distribution of both the photocurrent and

the dark current. It is the dominating noise when the photodiode is operated in the

photocurrent mode. The magnitude of shot noise is given by:

𝐼𝑠𝑛 = √2𝑞(𝐼𝑃 + 𝐼𝐷)∆𝑓 (12)

Where 𝐼𝑃 is the photocurrent, 𝐼𝐷 the dark current, and ∆𝑓 is the measurement bandwidth.

Johnson noise on the other hand is thermal noise associated with all resistive components. The

photodiode Johnson noise is given by:

𝐼𝑗𝑛 = √4𝑘𝑇∆𝑓

𝑅𝑆𝐻 (13)

Where k is the Boltzmann constant, T absolute temperature in Kelvins and 𝑅𝑆𝐻 is the

photodiode shunt resistance. Johnson noise is the dominant noise in the photovoltaic mode of

a photodiode operation. The total photodiode noise is then given by:

𝐼𝑇 = √𝐼𝑠𝑛2 + 𝐼𝑗𝑛

2 (14)

Equations 12 and 13 show that limiting the bandwidth of measurement, can help minimize the

total photodiode noise.

11

3.0 METHODOLOGY

3.1 Choice of Implementation method

As the project requirements were clear on demodulation of the phase of the LASER signal,

rather than of other LASER parameters such as amplitude, only interferometric methods were

considered. Different types of interferometry were studied and evaluated according to two

categories: external interferometry and the self-mixing interferometry. External

interferometers (such as the Michelson, Twyman-Green and the Mach-Zehnder interferometers)

were found to require a large optical equipment part count including beam splitters and Bragg

cells, on top of separate LASER and photodiodes which made them bulky and part-count

expensive. Moreover, they involve alignment in more than one direction, and hence more

cumbersome to set up. On the other hand, a self-mixing interferometer has the following

advantages:

i. No beam splitters, mirrors and Bragg cells are required, leading to a setup that is

compact, simple and part-count-saving;

ii. No extra photo detector is required as detection is done by a monitor photodiode within

the LASER package

iii. High sensitivity as it can measure vibrations to the order of half a wavelength of the

beam (sub-nanometer lengths). Closed loop techniques can however be employed to

increase sensitivity beyond half a wavelength [11].

iv. It can successfully operate on rough diffusive surfaces

The biggest limitation of the self-mixing set up is the limited target distance as the LASER

regime directly depends on the target distance. To maintain stability, the diode needs to be

operated in moderate feedback regime. As a result, the ratio of the maximum to the minimum

target distance becomes 4.6 in the absence of any light. However, varying the amount of light

fed back (by use of a variable density filter for example), can increase the measurement range

further.

The interferometer was thus chosen to be of the self-mixing architecture. To detect vibrations,

the simple fringe counting method was adopted. This way, the self-mixing concept could be

12

tested and with the resulting insight help in the design of an automated measurement of the

target vibrations. The detector was designed as per the block diagram of figure 6.

Figure 26: Block Diagram of the Phase Detector

Starting with the Fabry-Perot LASER diode package (with a monitor photodiode), a LASER diode

driver was designed to provide a stable current to the LASER diode. The work of the variable

neutral density filter was to vary the amount of light fed back into the diode to maintain the

diode in the moderate feedback regime. The transimpedance amplifier was designed to convert

the photodiode current into an amplified voltage with high voltage-to-current ratio and fast

response time. A low pass filter was also added to limit the bandwidth of the observed self-

mixing signal and in turn limit the system statistical noise.

This section describes the design procedure for the LASER phase detector. The design was split

into modules as shown by the block diagram of the figure 9. For every module, description is

made of the design considerations and how each consideration was met.

13

As shown in the block diagram, the overall design involved:

i. Choice of the LASER Diode

ii. Design of the LASER diode driver

iii. Design of the Trans Impedance Amplifier

iv. Design of the output filter

3.2 Choice of the LASER diode

Any single longitudinal mode Fabry-Perot LASER diode with an inbuilt monitor photodiode can

be used for self-mixing [7]. Low power was desired to reduce the dangers that come with high

power LASERs. Table 2 shows some of the LASER diodes that can be used for self-mixing

interferometry. Design of the LASER driver in the next section was based on the Hitachi

HL6724MG red LASER diode. However, being that the maximum drive current of the LASER

driver is 50 mA, most of the other diodes can still be reliably driven as well.

Table 2: Some LASER diodes suitable for self-mixing interferometer

Laser Diode Typical Wavelength Output Power Typical operating current

HL6724MG 670 nm 5 mW 35 mA

HL6314MG 635 nm 3 mW 30 mA

DL3149-057 670 nm 7 mW 40 mA

HL6722G 670 nm 5mW 32 mA

3.3 Design of the LASER Diode Driver

A LASER diode is basically a current controlled device that emits highly coherent and

monochromatic light. However, the diode is very sensitive to current disturbances and can

easily get damaged. The LASER driver was thus meant to ensure that:

i. The diode was protected from damage due to excessive transient and sustained

currents

ii. The LASER current was stable to reduce the noise frequency in the diode output

14

Different configurations were tested including the Howland current source and simple

transistor based current sources. The set up shown in figure 9 was selected for its simple design

and ease of control as a voltage controlled current source should feedback control for the

LASER diode frequency be implemented. It has an equally stable output current as was

determined through the square wave test. The set-up also has a low part count which keeps the

cost of implementation low. The schematic of the current source was as shown in figure 7:

Figure 27: Circuit of the Laser Diode Current Source (Driver)

Resistor R3 acts as the limit resistor for the maximum current through the diode. To ensure this

driver could work with all of the aforementioned diodes, a maximum drive current of 50 mA

was chosen. A trimmer pot resistor P1 was added so that the current could be varied to suit the

requirements of the particular diode. Together, potentiometer P1 and resistor R3 act as output

current sensors. Capacitor C1 was to stabilize the output current by shunting out high frequency

components and therefore eliminate ringing in the LASER diode current. The Zener diode D1

15

was used as a voltage reference while resistors R1 through R3 determined the output current

per unit of reference voltage.

Using an Op Amp with a high open loop gain Ad, the voltage Vo at the output of the Op Amp

with respect to the differential input voltage Vd is:

𝑉𝑜 = 𝐴𝑑𝑉𝑑 (14)

But 𝑉𝑑 = −(𝑉𝑅2 + 𝑉𝑍𝐷) where 𝑉𝑅2 is the voltage across R2 and 𝑉𝑍𝐷 the Zener diode terminal

voltage:

𝑉𝑅2 = 𝐼𝑅2𝑅2 (15)

Because the current through R1, 𝐼𝑅1 = 𝐼𝑅2 (current through R2), the voltage 𝑉𝐸 at the emitter

of transistor Q1 is given by:

𝑉𝐸 = 𝐼𝑅2𝑅1 (16)

𝑉𝑜 = 𝑉𝐸 + 𝑉𝐵𝐸 (17)

Thus the Op Amp input differential voltage becomes:

𝑉𝑑 = 𝑉𝑜

𝐴𝑑=

𝑉𝐸 + 𝑉𝐵𝐸

𝐴𝑑≅ 0 (18)

for large 𝐴𝑑. Thus 𝑉𝑅2 = −𝑉𝑍𝐷 and current through the LASER diode 𝐼𝑜 becomes

𝐼𝑜 = 𝑉𝐸

𝑅3 + 𝑃1=

𝐼𝑅2𝑅1

𝑅3 + 𝑃1=

−𝑉𝑍𝐷

𝑅2𝑅1

𝑅3 + 𝑃1= −𝑉𝑍𝐷

𝑅1

𝑅2(𝑅3 + 𝑃1) (19)

For the current source to work 𝑉𝑍𝐷 was chosen to be negative so that the forward current 𝐼𝑜

through the LASER diode is positive. Small values were chosen for 𝑅3 and 𝑃1 so that they

dropped only a small voltage leaving as much voltage as possible available for the LASER diode.

With a 2.2V Zener diode together with R2 of 5.5 kΩ, R1 of 1 kΩ and R3 of 8 Ω, the LASER diode

driver current limit was thus made:

16

𝐼𝑜 = −𝑉𝑍𝐷

𝑅1

𝑅2(𝑅3 + 𝑃1)= 2.2 𝑉

1 𝑘Ω

(8 Ω)5.5 𝑘Ω= 50 𝑚𝐴

The trimmer potentiometer P1 of value 50 Ω meant that the output current could be varied

down to 5.5 mA.

3.4 Design of the Trans Impedance Amplifier

The work of the trans-impedance amplifier was to convert the small photocurrent from the

photodiode into an amplified voltage with minimal noise addition. The trans-impedance

amplifier was thus designed with the following considerations:

i. Stability with regard to temperature and drift noise

ii. Large volts/ampere conversion ratio

iii. Fast speed of response.

The transimpedance amplifier set up was as shown in figure 8:

Figure 28: Circuit of the Transimpedance Amplifier

A fast speed of response was ensured by operating the photodiode in photoconductive mode

achieved through reverse biasing the photodiode by 5 V. This bias condition was also chosen to

17

simplify the design so that the common mode voltage appearing at the input of the

transimpedance Op Amp was zero. Current from the photodiode sees a large impedance on the

non-inverting input of the Op Amp, and is thus forced through resistor RF. Because the non-

inverting input is at virtual ground, a negative voltage proportional to the current is registered

at the Op Amp output. The voltage gain of the amplifier per unit of photodiode current is given

by:

𝐺𝑎𝑖𝑛 (𝑉 𝐴⁄ ) = 𝑅𝐹 (20)

A large resistor RF was needed to provide enough gain for the small photodiode current.

However, this had the effect of increasing thermal noise in the circuit due to the resistor, and

𝑅𝐹 was thus implemented as a trimmer. Resistor 𝑅𝐹 together with stray capacitance in the

circuit creates an oscillatory behavior that causes gain peaking in the circuit and a small

feedback capacitor CF was added to stabilize the transimpedance amplifier. The 3dB

bandwidth𝑓3𝑑𝐵 of the amplifier is then given by [12]:

𝑓3𝑑𝐵(𝐻𝑧) = √𝐺𝐵𝑃

2𝜋𝑅𝐹(𝐶𝐽 + 𝐶𝐹 + 𝐶𝐴) (21)

Where GBP is the Op Amp gain-bandwidth product, 𝐶𝐽 is the junction capacitance of the

photodiode and 𝐶𝐴 is the Op Amp input capacitance.

To realize gains of 106 V/A, RF was selected to be a 1 MΩ trimmer together with 𝐶𝐹 of 2pF. With

this gain, a 10 nA input current would provide a voltage of 10 mV. Most photodiode datasheets

including datasheets for the monitor photodiodes in LASER diodes do not carry information

about the photodiode capacitance. A typical photodiode capacitance of 50pF was used in

determination of the transimpedance bandwidth. However, the actual capacitance was

expected to be lower as the 5V reverse bias on the photodiode lowers this capacitance.

The opa2381 transimpedance amplifier was chosen for the design because it has excellent

desired features, and it was readily available from within the university. The Op Amp has a high

unity-gain bandwidth of 18 MHz, a low input offset current less of than 100 pA but typically of 6

18

pA. The Op Amp also has a low input offset voltage of less than 25 μV and a low drift of 0.1 μV/

oC.

The OPA2381 has a typical input capacitance of 3 pF and a gain bandwidth of 18 MHz. Based on

equation 27, the transimpedance 3 dB bandwidth was found to be:

𝑓3𝑑𝐵(𝐻𝑧) = √18𝑥106

2𝜋𝑥106(50 + 2 + 3)𝑥10−12= 228 𝑘𝐻𝑧

At this bandwidth, and at room temperature 𝑇 of 300 Kelvins, the thermal voltage of the 1 MΩ

resistor was as given by equation28; 𝑘 is the Boltzmann constant.

𝑉𝑟𝑚𝑠 = √4𝑘𝑇𝑅𝐹𝑓3𝑑𝐵 (22)

= √4 ∗ (1.381 ∗ 10−23) ∗ 106 ∗ 228 ∗ 103 ≅ 3.5𝜇V

With such small thermal voltage, the main trade off for a larger resistance was thus the

transimpedance amplifier bandwidth. The offset current of the Op Amp creates a maximum

voltage of 0.1 mV across 𝑅𝐹. The sum of the feedback resistor thermal noise, the Op Amp offset

current and offset voltage noise gives a maximum noise voltage for the transimpedance

amplifier of less than 0.15 mV.

The LASER driver and transimpedance amplifier were tested through simulation as discussed in

the testing section.

3.5 Design of the Low Pass Filter

Typical spectral responses of some silicon photodiodes are as shown in figure 9. Sensitivity of a

photodiode is significant in the visible light range with peak response in the infrared region

(about 900 nm to 1000 nm). In figure 12, QE is the photodiode quantum efficiency, which is the

number of electrons or holes that can contribute to the photodiode current as a fraction of the

number of incident photons.

19

Figure 29: Spectral Response of Various Silicon Photodiodes

As a result, it is anticipated that there would be noise especially from the ambient light from

the sun (which is essentially DC), and from the electrical lighting (50 Hz). The DC noise is easy to

eliminate with a coupling capacitor. However, a high pass filter to limit the electrical lighting

frequencies was not designed as significant vibrations occur at these low frequencies to have

them filtered out. Instead, noise at such frequencies could be minimized by modulating the

LASER diode current by closed loop (feedback) means, which would be appropriately designed

once the detector was tested and its behavior characterized.

A fourth order low pass filter was designed to limit the bandwidth of measurement. This was

necessary so as to limit the system statistical noise such as shot and Johnson noise in the

output of the detector. A fourth order filter was chosen because of its better attenuation in the

stopband (-80 dB per decade) as compared to lower order filters. The filter was designed as

20

Bessel type filter to ensure a maximally flat response in the passband. Moreover, the Sallen-Key

topology was selected for its simplicity. A 3 dB cut-off frequency for the low pass filter was set

at 250 kHz to just cater for the bandwidth of the transimpedance of the amplifier. The filter was

designed as a cascade of two second order Sallen-Key filters as shown in figure 10.

A second order lowpass filter is described by the following transfer function in the frequency

domain.

𝐻(𝑓) = 𝐾

(𝑓

𝐹𝑆𝐹 × 𝑓𝑐)

2

+1

𝑄

𝑗𝑓

(𝐹𝑆𝐹 × 𝑓𝑐)+ 1

(23)

Where f is the frequency variable, K is the zero frequency gain, 𝑓𝑐 is the cut-off frequency, 𝑄 is

the filter quality factor and 𝐹𝑆𝐹 is the frequency scaling factor. The passband of the filter is the

frequency range below 𝑓𝑐.

For the Sallen-Key second order low pass filter shown in figure 13, the zero-frequency gain,

scaled cut-off frequency and quality factor are given by equations 30, 31, and 32.

Figure 30: Second order Sallen-Key topology

𝐾 = 1 (24)

21

𝐹𝑆𝐹 × 𝑓𝑐 = 1

2𝜋√𝑅1𝑅2𝐶1𝐶2

(25)

𝑄 =√𝑅1𝑅2𝐶1𝐶2

𝑅1𝐶1 + 𝑅2𝐶1=

1

2𝜋 × 𝐹𝑆𝐹 × 𝑓𝑐(𝑅1𝐶1 + 𝑅2𝐶1) (26)

For a fourth order filter, the FSF and Q for each of the two stages were read off from the Bessel

filter tables as shown in the table below:

Table 3: Fourth order Bessel Filter Table

First stage Second stage

FSF Q FSF Q

1.4192 0.5219 1.5912 0.8055

For the first stage 𝑅1 was taken equal to 𝑅2. 𝐶1 was fixed at 0.47 nF and using equation 26,

𝑅1 = 𝑅2 =1

4𝜋 × 𝐹𝑆𝐹 × 𝑓𝑐𝐶1𝑄=

1

4𝜋 × 1.4192 × 250 × 103 × 0.47 × 10−9 × 0.5219

= 914 Ω

A standard resistance, nearest to the calculated was selected. Thus 𝑅1 and 𝑅2 were chosen to

be 1 kΩ. Using equation 25, capacitor 𝐶2 was found by:

𝐶2 = 1

(2𝜋 × 𝐹𝑆𝐹 × 𝑓𝑐 × 𝑅1)2𝐶1=

1

(2𝜋 × 1.4192 × 250 × 103 × 914)2 × 0.47 × 10−9

= 0.51 𝑛𝐹

Capacitance 𝐶2 was also set to the nearest standard capacitance of 0.47 𝑛𝐹. In a similar

manner, and using the FSF and Q for the second stage, the values of 𝑅3, 𝑅4, 𝐶3, 𝐶4 as shown in

figure 11,

22

Figure 31: Circuit of the Low Pass Filter

From the frequency response of the lowpass filter in figure 12, the filter bandwidth was found

to be about 200 kHz. This response was obtained using Multisim 2013, the National

Instrument’s simulation software.

23

Figure 32: Simulated filter response

24

4.0 IMPLEMENTATION AND TESTING The complete designed circuit was built on a printed circuit board of dimensions 8.5 cm × 6.7

cm using the Eagle PCB software. The schematic and board layout of the complete detector

were as shown in figures 13 and 14 respectively.

Figure 33: Schematic capture of the complete detector

Unfortunately, the complete detector could not be tested. This was because an appropriate

LASER diode could not be found from within the country and the importation process was to

take longer than the outlined duration of this project. The testing procedure for the detector is

outlined in section 4.1. Moreover, tests carried out on the individual LASER driver,

transimpedance amplifier and output filter are outlined in the remaining parts of this section. It

is my desire to finally see the designed LASER detector tested.

25

Figure 34: Board Layout of the Phase detector

4.1. Testing of the Complete Detector

Figure 35: Illustration of the fringe counting method

26

To measure vibrations using the fringe counting technique, the frequency transitions defined by

reduced frequency as shown in figure 15 are marked. These points denote change of direction

of the vibrations. Time difference 𝑇𝑓 between such two points is equal to half the period of the

target vibrations. Let the number of complete oscillations counted between two such points be

n. Then n wavelengths of the laser signal correspond to the peak-to-peak target vibration, and:

Vibration Amplitude = (n

2) (λ)

𝑉𝑖𝑏𝑟𝑎𝑡𝑖𝑖𝑜𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =1

𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛=

1

2𝑇𝑓

Where λ is the lasing wavelength. By determining n and 𝑇𝑓, and knowing the lasing wavelength,

vibration amplitude and frequency can be read off of the self-mixing interferometric signal.

Measurement by fringe counting has the drawback that such detector features as linearity and

sensitivity cannot be accurately determined. To effectively measure such features, the detector

can be modified so that the interferometric signal tracks the vibrational signal rather than

producing a complete oscillation for every half a wavelength vibrational movement.

Nevertheless, the fringe counting method can be tested to:

i. Determine how well the interferometric signal obeys the theoretical self-mixing model

ii. Determine target distance from the LASER diode within which stable self-mixing is

possible.

iii. Determine the rough accuracy and linearity of this detector against some standard

phase detector such as a commercial LASER vibrometer or a piezo-electric sensor.

In the event of testing, the following procedure will be followed. The set up for testing of the

detector is shown in figure 16. The sound speaker is driven by a function generator as shown. A

resistance of 8.2 Ω is incorporated to match the output impedance of the generator and that of

an 8 Ω speaker, eliminating reflections in the speaker sub circuit. The vibrating speaker causes

vibrations on the target surface which are picked up by the detector. The detector’s output is

then observed on the oscilloscope. The target distance from the LASER diode is varied to

27

determine the range within which the diode interferometric signal is stable. A variable neutral

density filter is then placed between the target and the LASER diode and varied to determine

the increase in the stable target range.

Figure 36: Phase detector testing set up

4.2. Testing of the LASER driver

The LASER driver was tested through simulation and by building its circuit on the Breadboard.

The testing was set up as shown in figure 16. With the signal generator V1 set to 0 V, the

emitter voltage of transistor Q1 was read on a multimeter as the 50 Ω trimmer was varied from

maximum to minimum. The emitter voltage remained constant at 0.39 V even as the trimmer

resistance was varied. The maximum current of the detector Imax was thus:

𝐼𝑚𝑎𝑥 = 0.39 𝑉

8 Ω= 49 𝑚𝑉

A square wave test was then performed on the LASER driver. The signal generator was set to a

square wave amplitude of 65 mV. The driver current output was observed on the oscilloscope

28

as the voltage drop across the 8Ω resistor R3 and the trimmer RF1. The input voltage and output

current waveforms are shown in figure 18.

Figure 37: Testing circuit of the LASER driver

The output current waveform in figure 18 shows no ringing or oscillations. Instead, the

smoothing at the voltage transitions shows that very high frequency components are filtered

out. Again, the rise time of the output current waveform is less than a microsecond, showing

that the LASER driver can handle feedback signals of over 1 MHz. Being that the bandwidth of

the system is 250 kHz, the LASER driver has enough bandwidth for the design of a feedback

controller based on the detector output.

29

Figure 38: Input Voltage and Output Current Waveforms

4.3. Testing of the Transimpedance Amplifier

The testing of the transimpedance amplifier requires a small current comparable to the small

current expected from the LASER package monitor diode. Testing of the amplifier was

accomplished through simulation. A hardware testing could not be accomplished without the

LASER diode. The simulation set up was as shown in figure 19.

A sinusoidal signal of 5 mV amplitude was input on the non-inverting input of the LASER driver

op amp through the signal generator XFG1. The MOC8101 optocoupler was used to simulate

the LASER and photodiode package system. A voltage waveform output of 23 mV amplitude

was observed on the oscilloscope at the output of the transimpedance amplifier. The output as

shown in figure 20 confirmed that the transimpedance amplifier was stable.

30

Figure 39: Multisim simulation set up for the transimpedance amplifier

Figure 40: Transimpedance amplifier output waveform

4.4. Testing of the Lowpass Filter

The fourth order Sallen-Key Bessel filter was implemented and tested by building it on the

Breadboard and its frequency response determined. Frequency response of the filter was

determined by feeding 40 mV at its input and the output voltage was recorded for frequencies

from 100 Hz to 600 kHz as shown in table 7. The frequency response was plotted as shown in

figure 20. The filter has a bandwidth of about 200 kHz.

31

Table 4: Frequency response data for the lowpass filter

Frequency (kHz) 0.1 0.5 1 2 30 65 96

Output Voltage (mV) 40 40 40 40 40 39 38

Frequency (kHz) 156 206 225 300 400 617

Output Voltage (mV) 36 30 26 22 16 8

Figure 41: Frequency Response of the lowpass filter

32

5.0 DISCUSSION A 200 kHz bandwidth LASER phase perturbation demodulator was designed and built. The

detector was based on self-mixing interferometry and achieved phase demodulation by the

fringe counting method. Its component circuits namely the LASER driver, the transimpedance

amplifier and the output lowpass filter were tested and verified to meet their design

specifications. Although a single longitudinal mode LASER diode appropriate for self-mixing

could not be acquired in time to test the detector for its phase demodulation characteristics,

the testing procedure was presented. The detector is still far from automated, requiring manual

counting to convert fringes into the equivalent vibration amplitude and frequency. Moreover,

its sensitivity is based on the lasing wavelength and can only be used for measurement of

vibration amplitudes greater than half the lasing wavelength.

33

6.0 CONCLUSION The main objective of the project was to build a phase detector for demodulation of the LASER

signal phase perturbations and use the phase detector to observe small vibrations on a glass

window. Theoretical background was developed and the detector designed and implemented.

The detector is however not a finished product. Instead, it forms the basis upon which more

control and automation of the phase demodulation mechanism can be built. The use of a self-

mixing interferometer which is suited for closed loop feedback control further adds to the

reasons to not only fully test this detector but also improve upon it.

34

7.0 RECOMMENDATIONS The developed detector can be improved in a few areas. It can be improved upon to track the

vibration signal instead of outputting a full oscillation for every half a wavelength target

vibration. This can be achieved through open loop techniques as well as phase locking through

a phase locked loop (PLL). Having made the LASER driver a voltage controlled current source,

interfacing with the PLL is made simpler. The same feedback phase locked loop can be used to

modulate the lasing current and eliminate dependence of the detector sensitivity and range on

the lasing wavelength. This would serve to increase the target range and improve stability of

the LASER diode current, hence its linewidth thereby improving the sensitivity of the diode

beyond half a wavelength of the lasing signal.

35

8.0 REFERENCES [1] A. L. Kachelmyer and K.I.Schultz, “LASER Vibration Sensing”, the Lincoln Laboratory

Journal, Vol. 8, No. 1, 1995

[2] P.R. Kaczmarek et.al, “LASER Doppler Vibrometry with Acoustooptic Frequency

shift”, Optica Applicata, Vol. XXXIV, No. 3, 2004

[3] L. E. Drain, The LASER Doppler Technique, 1980, New York: J. Wiley

[4] A. Y. Karasik, B. S. Rinkevichius and V. A. Zubov, Laser interferometry principles,

Advances in science and technology, 1995, Boca Raton: Mir Publishers, CRC Press

[5] T. Bosch, N. Servagent and S. Donati, “Optical feedback interferometry for sensing

application”, Optical Engineering 40(1) 207, 2001.

[6] S. Donati, Electro-optical instrumentation : sensing and measuring with lasers, 2004

Upper Saddle River, NJ: Prentice Hall

[7] Pawan Kumar Shrestha, “Self Mixing Laser Interferometry: A thesis submitted to the

University of Waikato for the degree of Masters of Engineering”, The University

of Waikato, Hamilton, New Zealand, 2010

[8] R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor

injection laser properties”, IEEE Journal of Quantum Electronics QE-16(3), 1980,

pp. 347-55.

[9] R. Wolfson and J. M. Pasachoff, Physics: extended with modern physics, 1990,

Glenview, III: Scott, Foresman/Little, Brown HigherEducation

[10] S. Donati, Photodetectors, Devices, Circuits and Applications, 2000, Englewood

Cliffs NJ, Prentice-Hall

[11] G. Giuliani, M. Norgia, S. Donati and T. Bosch, “Laser diode self-mixing technique for

sensing applications”, Journal of Optics A; Pure and Applied Optics 4(2002), 2002

pp. 283-294

[12] S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed.

McGraw-Hill, 2002