THE DETERMINATION OF THE EFFICIENCY OF OPTICAL FIBRE SENSORS

Transcription

1 Jounal of Optoelectonics and Advanced Mateials Vol. 3, No. 1, Mach 001, p THE DETERMINATION OF THE EFFICIENCY OF OPTICAL FIBRE SENSORS M. A. Chita, S. Anghel a, I. Ioga-Siman a, I. Vlad b Electonics Depatment, Faculty of Electonic and Electomechanical, Univesity of Pitesti, Steet Tagul din Vale, No. 1, Pitesti, Ages, 0300, Romania. a Physics Depatment, Faculty of Sciences, Univesity of Pitesti, Steet Tagul din Vale, No. 1, Pitesti, Ages, 0300, Romania b Geneal Manage of S.N.Tc. Romtelecom S.A. Ages, Steet B-dul Republicii, No.90, Pitesti, Ages, 0300, Romania The pape pesents a calculation method fo the detemination of the efficiency of tempeatue pobes with optical fibe and fluoescent cystal. An equivalent model is fistly defined, stating fom the pobe effective stuctue, based on geometical optics ules and applying the supeposition pinciple. The computation elations fo the value of the fluoescence optical flux collected by the eceiving fibe wee developed as pat of the equivalent model. Fom the value of the fluoescence optical flux elated to the excitation optical flux of the emitting fibe, the optical efficiency of the pobe can be obtained. The computation of the effective optical efficiency was made numeically, using a computation pogam elaboated in MATLAB language. The analysis of the values fo the efficiency fo a pobe with cube shaped cystal allowed to find impotant conclusions egading the optimum dimensions of the cystal and the maximum value of the efficiency. These conclusions ae useful fo getting an optimal tempeatue senso. (Received Decembe 5, 000; accepted Mach 5, 001) Keywods: Optical fibe pobe, Sensing head, Efficiency, Computation method, Fluoescent cystal 1. Intoduction The divesity of optical phenomena and the unlimited possibilities of coupling these ones with mechanical, electical and magnetic phenomena lead to the spectacula evolution of optical fibe sensos. These sensos epesent nowadays a field in full expansion, moe and moe solutions being tansfeed fom laboatoy to industy. Optical fibe sensos ae no longe a subject of laboatoy eseach only [1], but a vey attactive solution fo diffeent industial applications, because of thei advantages: small size, immunity to intefeence with electical and magnetic fields, total safety in explosive envionments, chemical inetness, intinsic galvanic isolation. The geneal stuctue of an optical fibe senso is pesented in Fig. 1.

2 66 M. A. Chita, S. Anghel, I. Ioga-Siman, I. Vlad Fig. 1. The geneal stuctue of an optical fibe senso. Two sections can be delimited: optical section, whee the measuement poduces the vaiation o the modulation of one of the light paametes and the electonic section, whee the optical modulated signal is conveted to an electical signal which may be futhe electonically pocessed. This delimitation is achieved by two intefaces: electo-optical and opto-electonic intefaces, which ensue the coupling of optical tansmitte to optical fibe, espectively, the coupling of optical fibe to optical eceive. Thee is an active zone in the optical section on which the size of measuing will act, ceating changes on the popagation of the light adiation. The active zone may be a section of the optical fibe o othe optical medium outside the fibe. That is why is pefeed the name of optical fibe sensos to othe vaiants as optical sensos o senso of optical fibes.. Computation method of the efficiency of the sensing head by modelling the pobe with optical fibe and fluoescent cystal The active pat of the optical fibe and fluoescent cystal pobe is the sensing head, which epesents the senso active zone, being in contact with the measued facto (the tempeatue). The sensing head consists of a fluoescence cystal volume and one o two optical fibes stickled of this. The optical fibes have the ole to pefom the excitation optical pumping and to collect the fluoescence adiation emitted in the cystal volume. Until now it was poposed seveal constuctive solutions fo the sensing head egading the positioning of the optical fibes on the cystal. The sensing head has a majo contibution to the global enegetic balance of the senso. In Fig. ae illustated the solutions pesented in the liteatue on this subject [], [3], [4]. The fibes used ae made fom glass, with gadual vaiation of the efactive index, and of vaious diametes, fom 100 µm to 1 mm.

3 The detemination of the efficiency of optical fibe sensos 67 Fig.. Sensing head stuctues: a) with the fibes of the some pat of the cystal; b) with the fibes on opposite sides of the cystal; c) with a fibe and couple Y; d) with optical filte in the sensing head; e) with cystal powde immobilised in optical adhesive. In the optical section of the sensos using fluoescence, the sensing head has the lowest efficiency. The design of the senso is, theefoe, stongly influenced by the efficiency of the sensing head. Using the method pesented in this pape, it is possible to compute accuately the sensing head efficiency, and following this, the optical powe of the souce equied fo a safe opeation of the senso. An optimised design of the sensing head and senso can be done. The computation pocess includes two steps: the geneation of an equivalent model fo the sensing head and the computation of the efficiency using the equivalent model. The equivalent model is built stating fom eal stuctue of the sensing head. In the eal stuctue (Fig. 3) the emissive fibe illuminates a volume of the fluoescent cystal, of the fustum of cone shape, defined by the numeical apetue of the fibe and the cystal efactive index. As a esult of the absoption, each point of the illuminated cystal volume emits fluoescence adiation. The emission by fluoescence is isotopic (unde a solid angle of 4π). A pat of this adiation can be collected by eceiving fibe, eithe diectly, (λ f ) d, o as a eflection poduced on the cystal walls, (λ f ). Fig. 3. The fluoescence emission in the sensing head eal stuctue. In ode to be collected and guided to the detecto, the fluoescence adiation must be diected on the fibe coe, unde an incidence angle θ i (θ i θ imax, whee θ imax is the maximal incidence angle defined by the numeical apetue of the eceiving fibe). The emegent ays fom a point which fulfils

4 68 M. A. Chita, S. Anghel, I. Ioga-Siman, I. Vlad the mentioned conditions fills a solid angle, named acceptation solid angle of the fluoescence elementay souce, θ sa. In ode to calculate the collected fluoescence optical flux, it must be evaluated the acceptation solid angle value of each point fom illuminated cystal volume. A fist stage in the analysis elief is the sepaation of the phenomena of diectly collected adiation eception (λ f ) d, fom the collected adiation as a esult of eflection on the cystal walls (λ f ). This can be obtained using the effects of the supeposition pinciple and the geometical optical popeties. The fluoescence cystal, whose faces ae mios of eflectivity R fo the adiation within the cystal, is eplaced by a homogeneous tanspaent medium, with the same efactive coefficient as the cystal, in which ae placed the fibes. The adiation loss by efaction at the cystal faces is modulated with absobent sceens without thickness and total tansmittance T, numeically equal to the eflectivity R. In this medium the emission fibe and eceiving fibes ae placed in the position established accoding to the cystal geomety. Each eceiving fibe collects the fluoescence adiation fo which the combined optical outes of the excitation light and fluoescence light suffe the same numbe of eflections. The numbe of the eceiving fibes inceases as moe eflections occu. The equivalent model of a tempeatue pobe, built and used in expeiments is pesented in Fig. 4. Fig. 4. The tempeatue pobe equivalent model with paallelepiped fluoescent cystal. The model of tempeatue pobe has two eceiving fibes. The fibe 1, placed in the same position as the eal eceiving fibe, collects the fluoescence light fo which the combined path of excitation light and fluoescence light has no eflection on cystal faces. The fibe, placed in mio configuation with espects to sceen T, collects the fluoescence light fo which the combined path of excitation light and fluoescence light has one eflection on cystals faces. Using the equivalent model the fluoescence optical flux collected by eceiving fibe can be calculated and consequently, the cystal dimensions that ensue the equied value of the sensing head efficiency can be deteminated. The optical efficiency of the sensing head η cp, is defined as: Φ f η cp = (1) Φ whee: 0 Φ f is the flux of fluoescence light coupled by eceiving fibe; Φ is the optical excitation flux launched in the cystal. Between the emitted fluoescence adiation and absobed adiation exists the elation: φ = η( λ) () fe φ a whee: φ fe, φ a ae the total fluoescent and absobed fluxes of adiation, espectively, and η(λ) is the fluoescence efficiency, defined as the atio between the numbe of photons emitted by fluoescence and the numbe of photons absobed which poduce excitations followed by adiation emission by fluoescence [3].

5 The detemination of the efficiency of optical fibe sensos 69 The absobed adiant flux φ a can be detemined on the base of adiation absoption ules in substance. Thus, consideing a substance laye of thickness dz on which falls a adiation beam of wavelength λ and flux φ 0 fom which come out an emegent beam of flux φ, the absobed flux dφ a, is equal with the flux decease due to absoption that veifies the elation: Using in the Lambet law (3): d a φ = k( λ) φ dz (3) k (λ ) z 0 e φ = φ (4) it esults that the absobed flux into a laye of dz thickness, at the distance z in substance, dφ a ( is: k ( λ ) z dφ ( = k( λ) φ e dz (5) a whee k (λ) is the substance absoption coefficient of the laye, fo the adiation of wavelength λ. If S( is the suface of the incident flux at the distance z in the substance laye, then the elementay flux absobed by a suface element ds, dφ 0a ( is: 0 d ds k d φa ( λ) k ( ) z φa( = = φ0 e λ dzds (6) S( S( Replacing in elation () the expession fo the elementay absobed flux fom (6) the value of the fluoescence elementay flux, dφ 0f ( is obtained: d η( λ) k( λ) k( ) z ( = φ0 e dzds (7) S( φ λ 0 f In this way each volume element dv=dz ds can be consideed as a adiation souce. The fluoescence flux is emitted isotopically and only a faction coesponding of the acceptance solid angle of the elementay souce, θ sa, is collected. Consequently, the collected fluoescence elementay flux, dφ 0f, can be defined as: d d φ0 f φ ( ) 0 fc = θsa (8) 4 π whee is the position vecto of the volume element, having as oigin the eceiving fibe cente. The difficulty consists in detemination of the value of θ sa () fo each volume element of emission cone. Consideing of the definition the elementay souce acceptation solid angle, peviously shown, it is defined a calculation elementay souce, which emits a conical beam in the pependicula diection on the end plane of the eceiving fibe, of solid angle θ c, equal with the acceptation solid angle of the eceiving fibe fo a given medium. Fo a fibe with numeical apetue NA, the maximum incidence angle sinus value of the guided ays, ϕ, (Fig. 4) is: whee NA is the numeical apetue of the fibe: n1 n1 NA NA sin ϕ = sinϕ = = (9) n n n n 1

6 %$# # "! 70 M. A. Chita, S. Anghel, I. Ioga-Siman, I. Vlad NA = n 1 n (10) Fig. 5. The acceptance angle of the fibe in a medium with efactive index n. Fo the defined cone of angle ϕ coesponds the solid angle θ c : Scal NA θ c = = π 1 1 (11) n whee: S cal is the undestetched spheical calotte suface of the cone; R is the sphee adius with the cente in the cone top, which includes the calotte S cal. Computation elementay souce illuminates a cicula suface S i in the plane of the eceiving fibe. If the supeposition suface of illuminated suface S i and fibe coe suface S c, is S s, then the acceptation solid angle of the elementay calculation souce is: Ss θ sa ( ) = θ c = θ c F (1) S Based on the elation (7), (8), (11), (1) and on fluoescence elementay flux emitted fom an element of volume and collected by the eceiving fibe, it esults that the collected elementay fluoescence flux is given by the elation: i k k z NA d fc = e η( λ) ( λ) ( ) φ0 ( ) φ λ F dzds (13) S( n whee n is the efaction index of the exteio medium and F is a atio that can be detemined by geometical analysis. Because the sensing head models take in consideation the optical outes with successive eflections, with the inclusion of some sceens with tansmissivity T, the expession of the collected elementay fluoescence flux must be coected, becoms: k k z NA n d fc = e η( λ) ( λ) ( ) φ 0 (& ) φ λ F T dzds (14) S( n whee n is the eflection numbe of the consideed oute.

7 The detemination of the efficiency of optical fibe sensos 71 The total fluoescence flux collected of eceiving fibe i of a equivalent model, (φ 0fc ) I is obtained by integation of expession (14) on the volume fom the equivalent model of the consideed fibe: Φ 0 fc i = V i dφ 0 fc Fo a sensing head whose equivalent model contains p eceiving fibes, the fluoescence collected flux of the eal eceiving fibe, φ f is: ( ) = p f Φ 0 fc i i= 1 If in elation (4) the excitation flux, φ 0 is taken as: (15) Φ (16) φ 0 = 1 (17) then elation (17) epesents the sensing head efficiency, accoding to the elation (1): p ( Φ0 fc ) 1 η = (18) cp i= 1 Φ i 0 = 3. Results The detemination of the value of the optical pobe efficiency, which uses fluoescence phenomena, can be done only by numeical calculation. In ode to pefom the calculation pogam it can be used divese pogam media, as FORTRAN, PASCAL, C, C ++ languages o specialised pogammes fo scientific calculations, developed in the last peiod. In this case it was used MATLAB language, which allow the eduction of the equied time fo witing the pogams, using the specialised existent functions and gaphic facilities. The method developed was applied fo the computation of the efficiency of pobes with paallelepipedic shaped cystal, a geomety fequently used in applications. The numeical calculation of the efficiency supposes the cummulation of collected fluoescence elementay fluxes emitted by all elementay volumes in the illumination cone of the emission fibe. Fo each elementay volume can be decided if this is included o not in the emission fibe illumination cone and fo the cone inside can be detemined the geometical coodinates at the cente of the eceiving fibe, needed fo the computation of the collected fluoescence flux. A system of othogonal axes, with the oigin in the plane of emission fibe end and axes x=0, y=0, tangent to the emission cone in the plane of eceiving fibe (Fig. 6) is used fo discetisation. The active volume is divided in a numbe of layes of height dz, paallel with the emission fibe end. The suface of each laye illuminated by the excitation light is divided in N s squae elements, each of them of ds aea.

8 7 M. A. Chita, S. Anghel, I. Ioga-Siman, I. Vlad Due to the discetisation pocedue descibed above all layes have the same numbe of illuminated (and, theefoe, active) elements. Fig. 6. The discetisation of the equivalent model. The effect of the incease of the volume elements is compensated by the decease of excitation flux, due to absoption. The analysis of the influence of the dimensions of the volume element upon the computed value of the efficiency, independently pefomed fo dz and ds, shows a stabilisation tend both dz and ds decease. Fo simulation it was used the following input data wee used: the fibe numeical apetue NA = 0.47; the fibe coe efaction index n 1 = 1.49; the uby fluoescence efficiency η = 0.8 fo λ = 550 nm; the uby absoption coefficient k = 14 mm 1 fo λ = 550 nm; the uby efaction index n = 1.76 fo λ = 550 nm. In ode to study the influence of the cystal dimensions on with the efficiency value, the pogamme was un fo the thickness values of it between 0.5 and 3 mm. The esults obtained fo the cystal suface eflectivity R = 0.9, ae pesented in Table 1, whee it is distinctly emphasised the contibution of the outes without eflection and with one eflection on the efficiency total value. Table 1. Calculated values of the sensing head efficiency as a function of the cystal thickness. The cystal thickness (mm) The contibution of the outes without eflection The contibution of the outes with one eflection, R = 0.9 The total efficiency In Fig. 7 is pesented the dependence of the sensing head efficiency as a function of the cystal thickness, fo a eflectivity value of R = 0.9.

9 The detemination of the efficiency of optical fibe sensos 73 Fig. 7. The sensing head efficiency vesus the cystal thickness. 4. Discussion One obseves that the optical head efficiency has educed values, situated in the ange 10 4 and The dependence of the efficiency on the cystal thickness is moe ponounced up to mm thickness. Then a tendency to limitation is obseved. Fig. 6 shows that this effect is due to the contibution of the outes with one eflection and appeas fo a cystal thickness fo which the eceiving fibe is completely included in the emission fibe cone. It can be seen the impotant contibution of one eflection outes that epesent appoximately 70% of the total efficiency value, this value depending on the eflectivity of cystal faces. The efficiency stongly depends on the eflectivity value of the cystal faces too. But the eflectivity is a paamete that can be impoved by simple pocedues, as e.g. the polishing of the cystal faces and the placement of the cystal into a eflective cove o even by a mio fomation when films ae deposited on the cystal faces. 5. Conclusions The computation method of the sensing head efficiency, can be successfully applied to vaious categoies of fluoescence optical fibe sensos, as e.g. chemical and biological sensos. Using this method, it is possible to get the value of the efficiency of the citical component fo the optical section of the senso and indicates ways fo its impovement, the sensing head being the element of the optical section of sensos using fluoescence, with the lowest efficiency. The computation method plays an impotant ole in the senso design pocess. It is possible to calculate the global efficiency of the optical section, thus offeing the possibility of an entie ensemble of optimised design that contains the optical souce, the fibes, the active zone and the photodetecto. The geneal esult is obviously a minimum pice of the senso, unde equied pefomance. The method can be used fo evey geomety of the sensing head, if the coesponding equivalent model is geneated.

10 74 M. A. Chita, S. Anghel, I. Ioga-Siman, I. Vlad Refeences [1] J. Dakin, B. Culshaws, Optical Fibe Sensos: Pinciples and Components, 1, Atech House, ISBN , Boston and London, [] K. T. V. Gattan, The use of the fibe optic techniques fo tempeatue measuement, Measuement & Contol 0, 3, (1987). [3] Z. Zhang, K. T. V. Gattan, A. W. Palme, SPIE, Measuement Technology and Intelligent Instuments 11, 476, [4] Z. Zhang, K. T. V. Gattan, A. W. Palme, Rev. Sci. Instum. 63 (8), 3869 (199).