OPTICAL MEASUREMENTSWednesdayJuly 1st2015
Prof. Cesare Svelto3thExamYR 2014/2015
Time available2 hrroom T.2.1at hr8.15
SURNAME: ______ Name: ______(block capital)
MS Degreeand year: ______
POLIMI-ID number and readable Signature ______
POINTS (per exercise)(8+8+8+8=32p)
YOU MUST cross all subpointsyou gave, even partly, an answer[e.g. 1a), 1c), 1d) 2a), 2c), 3b) etc.].
YOU MUST be able solving all problems in order to conclude and deliver the test (no blank exercises).
SOLUTIONS
(30 min)Exercise 1
(answer using this sheet front and back)
1)A red HeNe is based on a planespherical resonator with length L=100cm (reflectivities of the mirrors R1=100% andR2=99%) and emits 10mW output power. The output mirror has a radius of curvature ROC=1.2m. The laser line shows a Doppler broadening GAIN=2pm and,as a simplifying hypothesis, all the longitudinal modes beneath the gain curve are oscillating simultaneously with equal power.
1a)Evaluate the laser central frequency and the number of oscillating longitudinal modes.
1b)Evaluate the Finesse of this laser resonator.
Evaluate the optical power circulating in the laser cavity.
1c)Evaluate the dimension of the beam waist and its position along the laser propagation axis.
Evaluate the divergence (halfangle) of the output beam.
1d)Evaluate the spot size at 100m distance from the output mirror.
1e)Design an extracavity FabryPerot filter, based on a solid glass etalon, for the selection of a single longitudinal mode to be transmitted toward an external photodiode.
If the collecting and focusing optics toward the silicon photodiode have a global transmission Topt=90%, evaluate the generated photocurrent IPD.
1f)For the DC photocurrent calculated at point 1e), evaluate the corresponding shotnoise level observed within a 1kHz bandwidth.
Evaluate the rms voltage noise, only due to shot noise previously calculated, after transimpedance amplification with gain R=10k.
(30 min)Exercise2
(answer using this sheet front and back)
2)Using a pulsed laser telemeter we measure the L=4.321km with an atmospheric attenuation of 0.5km1. The optical source is a diffractionlimited Qswitched Nd:YAG laser, with pulse duration =10ns and repetition rate of 10kHz. The laser works with an electrooptical overall efficiency eo=5% being powered with Pele=300W from the electrical plug.
The telemeter output beam has divergence s=4mrad (full angle), the cooperative target has diameter Dcc=6cm, and the receiver lens diameter is Dr=20cm. The receiver optics have an overall transmission Topt=0.7, from the optical power impinging on the lens to the one delivered to the InGaAs photodiode (responsivity curve shown in the figure), and a transimpedance gain R=1k.
2a)Evaluate the nonambiguity range of the telemeter.
Evaluate the atmospheric attenuation at the limit distance of the nonambiguity range.
2b)After writing the power budget equation for the considered telemeter, calculate the value of optical power of the pulses impinging on the receiver photodiode.
2c)Evaluate the peak voltage at photoreceiver output.
What is the bandwidth required for this detector?
2d)Considering that the noise of electronic circuits allows for detection of arrival times of optical pulses with resolution 1/10 of the pulse duration, evaluate the absolute and relative resolution of distance measurement (yet for L=4.321km).
(30 min)Exercise3
(answer using this sheet front and back)
3)We want to use a Michelson Interferometer (MI) to measure the displacement of a mechanical sledge. The optical source is a HeNe laser emitting 1mW of optical power (P0). Power reflectivity of the Reference Mirror (Rm) is 100%. The beam-splitter has 50%-50% power reflectiontransmission. The photodiode used has a spectral responsivity A/W.
3a)What is the reflectivity of the Moving Mirror (Mm) if the fringe visibility is ?
3b)If we a use a trans-impedance amplifier to read the photo-detected current from the photodiode, what is the minimum value of the feedback resistance to achieve a minimum voltage signal mV?
3c)Assuming that we are dealing with a Double-Beam MI, what is the resolution of the measurement?
If the mechanical sledge moves with a linear velocity mm/s, what is the minimum bandwidth (B) needed to perform the measurement?
3d)If the total displacement of the sledge is mm, how many counts are given by the DoubleBeam MI read-out circuit?
What is the value of the total interferometric phase variation?
How many fringes of interference will be seen in the photo-detected current?
(30 min)Exercise4
(answer using this sheet front and back)
4a)After drawing the experimental configuration, describe the working principle and setup of a Laser Doppler Velocimeter.
4b)With reference to an expanded and detailed drawing of the interference region, derive the expression of the distance between interferometric fringes.
Derive the formula of the observed signal frequency when measuring a velocity v.
An LDV measurement system id used to detect the exhaust gas speed at the output of a jet engine. As a laser we use a red HeNe and the divided laser beam is incident on the focusing/collimating lens (f=800mm) at distance 3cm from the optical axis. In the focus/interaction zone, the two laser spots have the same radius equal to w0=4mm.
4c)When the velocityv ranges from 50m/s to 1400m/s, evaluate the detectable frequencies at the photodetector output.
4d)When measuring the photodetected signal with an FFT spectral analysis, state the required sampling speed.Which type of A/D converter should we use? What resolution shall we require for the A/D converter? Explain/motivate the answers and numbers provided.
4e)Which measurement instrument could be suitably used to perform the measurement of point 4d)?
Describe the instrumental setup that we should use for the measurements.
Exercise ___ (continued)
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