ork Istitute of Techology Bachelor of Sciece (Hoours) i Applied Physics ad Istrumetatio-Award - (NFQ Level 8) Istructios Aswer Four questios, at least TWO questios from each Sectio. Use separate aswer books for each Sectio. All questios carry equal marks. Physical costats: e =.60 x 0-9 k =.38 x 0-3 J K - c =.998 x 0 8 m s - h = 6.63 x 0-34 J s m e = 9. x 0-3 kg Sprig 005 Optical Istrumetatio (Time: 3 Hours) Examiers: Professor B. Macraith Dr. N. McMilla Mr J. A. O Doherty Dr. N. Smith Sectio A- OPTIS Q. (a) Explai i detail the physical factors which limit the data trasmissio capacity of optical fibres. Prove that the modal dispersio i a step-idex multimode fibre is give by the equatio; modal dispersio per uit legth = sigificace. ( - ). The symbols have the usual c (c) A model optical fibre commuicatios lik has the followig specificatios for dispersio; modal dispersio = 6 s km - material dispersio = 6 s (m-km) - waveguide dispersio = - s (m-km) - legth of the lik = 8 km spectral badwidth of the light source =. m alculate the badwidth ad the maximum data-rate of the lik. (9 marks) (8 marks
Q. (a) Explai the differece betwee Mach-Zehder ad Michelso iterferometers. Support your aswer with diagrams. What advatages are associated with the former cofiguratio? (c) Prove that the output curret (i) from the detector i the Michelso iterferometer is give by the equatio; i = E ( + cos φ(t)), where (E o ) ad (ϕ(t)) represet the o amplitude of the electric field i the light wave ad the phase differece betwee the arms of the iterferometer respectively. Hece prove that the phase differece (ϕ) betwee the arms of a Mach-Zehder i - i iterferometer is give by the equatio; cos φ =, where i ad i represet the i + i output currets from the detectors i the iterferometer. (9 marks) A Fabry-Perot iterferometer operates at a wavelegth of 633 m. It has mirror separatio of 5 mm ad mirror reflectivity of 0.95. alculate values for Reflectace fiesse, free spectral rage ad resolutio (or miimum resolvable wavelegth) of the istrumet. Is this performace likely to be achieved i practice? Explai the reasos for your aswer. 3. (a) Explai the priciple of operatio of (i) a acousto-optic modulator ad (ii) a electrooptic modulator. What is the approximate highest modulatio frequecy each of these devices is capable of? Iclude diagrams with your aswer. ( marks) The half-wave voltage for a Pockels cell modulator is 3.40 kv. The liear electro-optic coefficiet ad refractive idex of the electro-optic material are 45.45 pm V - ad.5 respectively. alculate a value the operatig wavelegth of the modulator. (6 marks) (c) alculate the miimum differece i legth betwee the two arms of a fibre-optic iterferometer i order to esure the operatig poit of the istrumet is set at maximum sesitivity. Data: refractive idex of the core of the optical fibre =.460 operatig wavelegth, λ o = 633 m (7 marks)
Sectio B- OPTIAL INSTRUMENT DESIGN 4. (a) A small object faces the covex spherical glass widow of a small water tak. The radius of curvature of the widow is 5cm. The ier back side of the tak is a plae mirror, 5cm from the widow. If the object is 30cm outside the widow, determie the ature of its fial image, eglectig ay refractio due to the thi glass widow itself. ( marks) A parallel beam of light is icidet o a plao-covex les that is 4 cm thick. The radius of curvature of the spherical side is also 4 cm. The les has a refractive idex of.50 ad is used i air. Determie where the light is focussed for light icidet o each side. (3 marks) 5. (a) Explai the differeces i the architecture of frot-illumiated ad back-illumiated Ds. Why do back-illumiated devices achieve higher quatum efficiecies? (5 marks) Explai the readout sequece of a frame-trasfer D. Hece, explai the terms (i) sigle track readout, (ii) multi-track readout ad (iii) biig. What are the advatages of hardware biig a D? (5 marks) (c) Describe the priciple of operatio of a Low-Light-Level D. Hece, explai why the readoise is essetially zero. (7 marks) (d) Two leses with focal legths of cm ad 0cm are used to form a image o a D. The D is 0mm behid the secod les. alculate the separatio of the two leses whe formig a image o the D of a object at ifiity. 3
6. (a) A spherical glass ball has a refractive idex of.50 ad a diameter of 8 cm. (i) By the matrix approach, determie the locatio of its pricipal poits. (ii) Where will sulight be focussed by the glass ball? Draw a simple ray-trace diagram of a object placed a distace of 6 cm to the left of the crystal ball. (4 marks) (c) Discuss what is meat by the f-umber of a les ad how it iflueces the depth of field. (4 marks) (d) What is a afocal system? Give a example of oe applicatio. (4 marks) (e) Describe the formatio of chromatic aberratios i a les, usig diagrams to support your aswer. How may it be miimised? (5 marks) 4
Equatio for a plae wave, ψ = e Useful Equatios for Sectio A ψo i(k z - ω t) Numerical Aperture, N A = - π ( diameter) ( N A) V umber for a fibre, V = λo For sigle mode operatio, V.405 τ ( - ) Modal dispersio, = L c t Normalized impulse respose i a fibre, h(t) = e σ out, σ π ω σ Fourier trasform of h(t) out = H( ω) = e 0.3 Fibre badwidth = τ Poweri Atteuatio i a fibre = 0 log Power out Output curret from the detector i a Michelso iterferometer = A ( + cos φ) 4π Phase differece betwee successive reflectios i a optical cavity, = d cosθ λo T 4 R Trasmitted itesity i a optical cavity, I = I, where F = - R + F si ( / ) ( - R) Airy Fuctio, = A + F si ( / ) π R Reflec ta ce Fiesse, FR = - R hage i refractive idex due to a applied field i electro optics, = E + E r R λo Half wave voltage i a Pockels cell = 3 r o Bragg equatio; d si θ = m λ Joes vectors; LP =, RP =, i i o ± Joes matrices: Liear polarizer with axes at ± 45 = ± 0 Quarter wave plate with fast axis horizotal (+) or vertical (-) = 0 i ± 0 Half wave plate = 0 T o 5
Useful Equatios for Sectio B 0 Thi Les: M = / f 0 Refractio (sigle surface): M = ' R ' ' Traslatio: M = L 0 where f = ' R R Refractio (sigle surface): s + s = R Magificatio: s m = s Lesmakers Formula: f = ' R R Equivalet focal legth: f eq = f + f d f f ardial Poit Locatios i terms of System matrix Elemets p = D ; q = A (back focal legth, F ) s = A v = D w = o f A r = D o f f = p r = o f f = q s = 6