Wednesday 10th May 2017
9:30 – 11:00
EXAMINATION FOR THE DEGREE OF MSC
Integrated PhD in Intelligent Sensing and Measurement,
MSc in Sensors and Imaging Systems
[ PHYS5044 ]
Fundamentals of Sensing and Measurement
Candidates should answer Question 1 (16 marks)
and either Question 2A or Question 2B (24 marks each)
Answer each question in a separate booklet
Candidates are reminded that devices able to store or display text or images
may not be used in examinations without prior arrangement.
Approximate marks are indicated in brackets as a guide for candidates.
Fundamentals of Sensing and Measurement/114-701
Fundamental constants
name symbol value
speed of light c 2.998× 108 m s−1
permeability of free space µ0 4pi × 10−7 H m−1
permittivity of free space 0 8.854× 10−12 F m−1
electronic charge e 1.602× 10−19 C
Avogadro’s number N0 6.022× 1023 mol−1
electron rest mass me 9.110× 10−31 kg
proton rest mass mp 1.673× 10−27 kg
neutron rest mass mn 1.675× 10−27 kg
Faraday’s constant F 9.649× 10−4 C mol−1
Planck’s constant h 6.626× 10−34 J s
fine structure constant α 7.297× 10−3
electron charge to mass ratio e/me 1.759× 1011 C kg−1
quantum/charge ratio h/e 4.136× 10−15 J s C−1
electron Compton wavelength λe 2.426× 10−12 m
proton Compton wavelength λp 1.321× 10−15 m
Rydberg constant R 1.097× 107 m−1
Bohr radius a0 5.292× 10−11 m
Bohr magneton µB 9.274× 10−24 J T−1
nuclear magneton µN 5.051× 10−27 J T−1
proton magnetic moment µp 1.411× 10−26 J T−1
universal gas constant R 8.314 J K−1 mol−1
normal volume of ideal gas – 2.241× 10−2 m3 mol−1
Boltzmann constant kB 1.381× 10−23 J K−1
First radiation constant 2pihc2 c1 3.742× 10−16 W m2
Second Radiation constant hc/kB c2 1.439× 10−2 m K
Wien displacement constant b 2.898× 10−3 m K
Stefan-Boltzmann constant σ 5.670× 10−8 W m−2 K−4
gravitational constant G 6.673× 10−11 m3 kg−1 s−2
impedance of free space Z0 3.767× 102 Ω
Derived units
quantity dimensions∗ derived unit
energy ML2T−2 J
force MLT−2 N
frequency T−1 Hz
gravitational field strength LT−2 N kg−1
gravitational potential L2T−2 J kg−1
power ML2T−3 W
entropy ML2T−2 J K−1
heat ML2T−2 J
capacitance M−1L−2T 4I2 F
charge IT C
current I A
electric dipole moment LTI C m
electric displacement L−2TI C m−2
electric polarisation L−2TI C m−2
electric field strength MLT−3I−1 V m−1
electric (displacement) flux TI C
electric potential ML2T−3I−1 V
inductance ML2T−2I−2 H
magnetic dipole moment L2I A m2
magnetic field strength L−1I A m−1
magnetic flux ML2T−2I−1 Wb
magnetic induction MT−2I−1 T
magnetisation L−1I A m−1
permeability MLT−2I−2 H m−1
permittivity M−1L−3T 4I2 F m−1
resistance ML2T−3I−2 Ω
resistivity ML3T−3I−2 Ω m
∗ M = mass, L = length, T = time, I = current
1 (a) A 16-bit analogue-to-digital converter is used to digitise a ±10 V input
signal with a quantisation voltage of ∆. Show that the standard deviation of
the quantisation noise is ∆/
√
12 or 88 µV in this case. [5]
(b) Assuming that the full scale of the device is used, estimate the Signal-
Quantisation Noise Ratio (SQNR) in decibels. [4]
(c) The traditional Wheatsone bridge is an example of a measurement tech-
nique that uses both a ratiometric measurement and nulling to determine the
resistance of a component. Explain the advantages of
i. ratiometric measurement
ii. nulling in measurement
In each case, illustrate your answer with one or more practical examples using
such a technique.
[7]
[Total: 16]
Fundamentals of Sensing and Measurement/114-701 3/6 Paper continued over. . .
2A An optical sensor operated at room temperature utilises an LED and a pho-
todiode. The average power falling on the photodiode is measured as 10 µW,
with the detection circuit comprising a current-voltage converter as shown in
the figure below.
(100k)
(a) If the responsivity of the photodiode is 0.5 A/W, determine the total volt-
age noise spectral density at the output of the amplifier. You should consider
the three dominant noise sources only: thermal noise in the feedback resistor
(RF ), amplifier voltage noise (vn) and shot noise in the photodiode current
(iPD).
You may assume that the mean square shot noise and current thermal
noise are
I2shot = 2qI∆f,
I2thermal =
4kT∆f
R
,
where q is the electron charge, I is the mean detected current, ∆f is the
bandwidth, k is the Boltzmann constant, T is the temperature and R is the
resistance. [6]
(b) Assuming the RC network of the amplifier acts like a low pass filter,
estimate the roll-off frequency of the amplifier and the rms noise at the output. [2]
Fundamentals of Sensing and Measurement/114-701 4/6 Q2A continued over. . .
Q2A continued
(c) The LED is now modulated such that the output voltage of the circuit
can be measured with a lock-in amplifier. The voltage reference which is used
for the lock-in is given by
VREF = 0.5 cos (ωRt+ φ) ,
and this voltage is fed into a suitable current source to drive the LED. The
measured power at the photodiode is
Pin = 10× 10−6 (1 + 0.05 cosωSt) ,
where ωR and ωS are the reference and output angular frequencies respectively
and φ is the phase.
By multiplying the reference voltage by the measured output voltage of
the circuit, show that when ωR = ωS the DC output of the lock-in amplifier
can be written
Vlock−in = 0.00625 cosφ,
stating what assumptions you have made. You might find the following trigono-
metric formulae useful:
sinωRt cosωRt =
1
2
sin 2ωRt
cos2 ωRt =
1
2
(1 + cos 2ωRt)
[8]
(d) Sketch the output of the lock-in amplifier (Vlock−in) over 1 complete cycle
of ωR for the case of ωR = ωS and φ = 0. On your sketch you should also
include the reference voltage (VREF ) and the output voltage of the circuit
(Voutput). [4]
(e) Why is the lock-in particularly useful for low noise measurements? [2]
(f) The lock-in amplifier is set to a time constant of 1s and connected to the
optical sensor shown above. Estimate the rms noise that is now measured. [2]
You might find the cosine formula useful:
cos(a± b) = cos a cos b∓ sin a sin b.
[Total: 24]
Fundamentals of Sensing and Measurement/114-701 5/6 Paper continued over. . .
2B Measurement of shape using optical techniques can be relative or absolute.
(a) Using diagrams as appropriate suggest, with reasoning, an optical tech-
nique for measurement of:
i. the absolute thickness of human tissue, such as the skin or the retina.
ii. the relative vibrational motion of a room window excited by acoustic
vibrations so as to provide covert eavesdropping at a large standoff range.
In each case state the characteristics of the light source (wavelength, bandwidth
or coherence length, pulsed or continuous wave) and how this, or another
factor, relates to the precision of the range measurement. Suggest approximate
values for the attainable precision in each case. [8]
It is required to measure the absolute range of a satellite moving in a
low-Earth orbit at an approximate altitude of 800km.
(b) briefly describe a technique, using diagrams as necessary, to measure the
satellite range using a pulsed laser and a telescope [4]
The system will employ an Earth-based telescope with an aperture of
diameter 0.3m and a pulsed laser with an output wavelength of 532nm, a pulse
length of 0.1ns and pulse energy of 10mJ. The satellite has a cross-sectional
area of 10m2 and can be considered to approximate a Lambertian scatterer of
light (that is, backscatters light with equal intensity into a hemisphere) with
an albedo (reflectivity) of 0.1.
(c) Assuming the most favourable conditions and a perfect instrument, esti-
mate very approximately the number of photons in each received pulse and
comment on whether this could be sufficient to reliably measure range. [7]
(d) Suggest briefly for what reasons the number of photons may, in practice,
be fewer than the number you have calculated. [3]
(e) What measures might be taken to improve the overall accuracy and reli-
ability of the measurement of range using this equipment? [2]
[Total: 24]
End of Paper
Fundamentals of Sensing and Measurement/114-701 6/6 END





















































































































































































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