CHARACTERISATION OF REDIRECTING DAYLIGHTINGSYSTEMS BY GONIOPHOTOMETRIC MEASUREMENTSMassimo SarottoPolitecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy, Tel. n. (+39) 0113919228, email@example.comGiuseppe RossiIEN Galileo Ferraris, Strada delle Cacce 91, 10135 Torino, Italy, Tel. n. (+39) 0113919226, Fax n. (+39) 011346384,firstname.lastname@example.orgAbstract – The goniophotometric characterisation of materials plays an important role in photometrywith different applications in metrology, daylighting system design, etc.. At IEN this characterisation iscarried out through a special goniophotometer that allows obtaining material characterisations (inreflection or transmission) for practically any orientation of the lighting and observing directions. Themeasurement procedure is here applied to characterise redirecting and diffusing daylighting products,which are utilised to improve illuminance and internal comfort in non-residential buildings. Thegoniophotometric characterisation is often necessary to simulate the illuminance distribution in officerooms equipped with these glazing units. After a short presentation of the IEN goniophotometer, thispaper describes the measurement procedure. The system utilises a CCD (Charge Coupled Device) matrix:the availability on a single chip of a high number of independent and closely spaced small detectorspermits the analysis of surface uniformity of materials and/or to resolve the angular behaviour in smallsteps. The matrix of pixels permits to apply a sophisticate geometrical model that considers the effectsdue to deformation and defocusing, typical in directional measurements. Furthermore the 2D (twodimensional)Fourier transformation can be utilised to evaluate the effects of the inevitable not alignmentbetween source, sample, detector and optical system lenses.1. INTRODUCTIONAt IEN the goniophotometric characterisation ofmaterials in transmission and reflection is carried outthrough a special goniophotometer (Rossi and Soardo,1991). The detector utilised is a CCD matrix: theavailability of a high number of closely spaced smallindependent sensitive elements on a single chip permitsthe analysis of the surface uniformity of materials, afeature which is almost impossible to obtain withtraditional detectors. So the utilisation of a digitaldetector can improve the metrological realisation of somephotometric quantities (Rossi et al., 1997).In the last years we have conduct our investigationstowards diffusing glazing systems utilised to improveinternal comfort in non residential buildings. Thediffusing glazing units can avoid discomfort phenomenaand permit to obtain a more uniform illuminance insidethe room in spite of the solar direct radiation thatgenerally causes many problems like uncomfortablevisual conditions, photo-degradation, etc.. Generally theoptical characterisation of such samples presents somedifficulties as a consequence of their large anglescattering properties. As example, in measurementscarried out with integrating sphere, the transmitted orreflected beams striking the sample should not be entirelycollected inside the sphere (Maccari et al., 1998). On theother side, integrating spheres with large sample portscannot be always achieved for economical and technicalreasons. The goniophotometric characterisationrepresents a solution for these problems. Furthermore itbecomes necessary for redirecting systems: the maininteresting properties request directional measurements inorder to investigate the specimen behaviour for anyorientation of the lighting and observing directions.This paper describes an accurate procedure to measurethe luminance coefficient (CIE publication N. 17.4,1987), in transmission or reflection, for practically anygeometrical configurations. The measurement techniqueutilises a sophisticate geometrical approach since itconsiders a matrix detector that can be turned accordingto the sample orientation.The measure analysis, now under test, considers:• deformation and defocusing of the CCD image of theluminous spot that lights the sample;• the theory of 2D Fourier transformation to overcomea possible not perfect alignment between thedifferent parts of the measurement system during therotation of the goniometer.This measurement procedure is particularly important forredirecting glazing unit characterisation, when thetransmitted light distribution strongly changes withsample orientation.2. MATERIAL CHARACTERISATION BY IENGONIOPHOTOMETER2.1 The instrumentsThe IEN gonioreflectometer (Rossi and Soardo, 1991)consists essentially of a fixed source, a 4 m long opticalbench supporting at one end a detector and rotating at itscentre around the vertical axis of the instrument (figure
1). On this same axis a set up is mounted, consisting of acradle, on which the specimen is placed through a threeaxes positing system and a rotator. It is easy to verify thatthe specimen can be lighted and observed from anydirection in the space, for reflection measurements (somedead angles due to the sample dimension exist intransmission directions). The cradle can also be loweredfor permitting the measurement of the luminance of thelighting beam directly through the detector.Figure 1 – IEN goniophotometer.The source utilised is a tungsten halogen lamp realisingthe CIE illuminant A (colour temperature of 2856 K -CIE publication N. 17.4, 1987). To stabilise the sourcethere are two quantities continuously under test: its colourtemperature and luminance. Moreover there is thepossibility to automatically control the power supplycircuit of the lamp by the output signal of a silicondetector head, illuminated by the source light linked witha fiber optic. Between the fiber output and the silicondetector, a turret can rotate four different filters:• one black that obstructs the signal to avoid detectorfatiguing;• one reproduces the V(λ) colour matching function ofCIE, to measure the source luminance;• one blue, centred on 430 nm and one red, centred on990 nm (for both the full width half maximum is 10nm), to control the source colour temperature.The red to blue ratio evaluation is a traditional methodfor fast measurement of colour temperature ofincandescent sources: with only two measures it ispossible to control the colour temperature, in our casewith an accuracy of 4 K. Using the V(λ) filter, the sourceluminance is stabilised better than 0,2%. (Rossi andSarotto, 2000).The detector utilised is a CCD matrix composed by 512x 512 square pixels, with a side of 27 µm: the size of thewhole matrix being 13,8x13,8 mm 2 . Like any other lightdetectors, a CCD can measure luminance when used witha lens or illuminance if alone (Rossi et al. 1997). In thefirst case the availability of a great number of pixels on asingle chip permits a great directional resolution of theincoming light and it could be employed in the analysisof surface of materials. Furthermore there are othermetrological characteristics (i.e. linearity) that make theCCD preferable if compared with the traditional detectorsused in photometry and permit to improve the measuringuncertainties.2.2 The measured physical quantityA full photometric characterisation of materials requiresthe measurement of the spatial distribution of reflected ortransmitted light when the specimen is lighted from anydirections. For this reason a complete set of spatialmeasures is required in the CIE publications: a fourdimensionalmatrix depending on the illumination andobservation angles shall be defined. The characterisationis usually carried out through the measurement of theluminance coefficient, which is definite as:2( ε2, ϕ2) dL2( ε2, ϕ2)BRDF, BTDF( ε1,ϕ1;ε2, ϕ2) ==dE ( ε , ϕ ) L ( ε , ϕ ) ⋅ cos ε ⋅ dωdL (1)1where:• BRDF (Bi-directional Reflectance DistributionFunction), BTDF (Bi-directional TransmittanceDistribution Function) are the luminance coefficientsmeasured in reflection or transmission conditions;• E 1 is the incident beam illuminance on the sample;• L 1 is the incident luminance;• dω 1 is the incident beam solid angle;• L 2 is the reflected or transmitted luminance;• the angles (ε 1 ,ϕ 1 ;ε 2 ,ϕ 2 ) are self evident in figure 2where the reflection geometry is represented;• (xsn, ysn, zsn) are the axes for the sample referencesystem with zsn axis along the sample normal.dωSampleplane1zsnε11ϕε221111ϕ1ysn11xsnFigure 2 - Reference angular system for incident andreflected light.As equation (1) suggests, the luminance coefficientmeasuring procedure is of relative type when theluminances L 2 and L 1 are measured through the samedetector. Therefore its measurement uncertainty is inprinciple low because no detector calibration is required.At the same time, the linearity requirements of thedetector can be greater then four orders of magnitude: thetypical ratio of the two luminances in equation (1). Thisrequirement can be reduced using different exposure
times: of course a very good and stable shutter isnecessary (Rossi et al., 1996). The solution adopted hereconsists in utilising a calibrated filter that reduce thesignal level in L 1 measurement, even if it produces alimited uncertainty grown of the luminance coefficientvalues.2.3 The image optical systemIn photometric measurements of materials thepossibilities to light a sample are generally two: with acollimated beam or with an image optical system thatproduces on the sample the source image. We havechosen the second possibility projecting the image of aPTFE (polytetrafluoroethylene) sheet on the sample. Fornormal incidence, the projected spot is circular and has anominal diameter of 13 mm. The focused spot on theCCD matrix has theoretically the same dimension sincethe magnification ratio of the second part of the opticalsystem is 1.The diffusing behaviour of the PTFE in transmissionguarantees good uniformity of the luminous spotprojected on the sample. However the use of CCD systempermits to control the uniformity of the incident lightingbeam and to get a correspondence between the arraypixels and different zones of the measured sample.In L 1 measurement (upper part of figure 3), the samplecradle rotator is lowered but the CCD is anyway focusedon an imaginary sample plane. This plane is normal toincidence direction, parallel to PTFE sheet and it passesthrough the sample central point (centre of thegoniophotometer cradle rotator that remains fixed foreach geometrical configuration (ε 1 , ϕ 1 ; ε 2 , ϕ 2 )). So we canimagine the source and the imaginary sample plane alsodivided in pixels (figure 3): in L 1 measurement eachsource pixel has a single pixel as image on the imaginarysample plane and consequently on the CCD matrix.measurement, the direct correspondence between sourceand sample pixels is generally not satisfied because theimage is deformed and defocused (lower part of figure 3:L 2 measurement). However the geometry of the problemcan be analysed (as shown in §3) in order to restore thecorrespondence between lighting areas of the source andtheir projection on sample plane.2.4 The full oriented CCD matrixAs shown in figure 3, in the L 2 measurement the imageof an ideal source single pixel generally keeps differentideal pixels on sample plane. In other words, if theincidence is not normal, the source image on the sampleis deformed and defocused.For simplicity only the first part of the optical system isrepresented in figure 3, avoiding to represent the otherpart (sample plane, CCD lens, CCD matrix) thatcomposes the entire system. But in the deformation anddefocusing analysis, we can consider only the first part ofthe optical system, since images on the CCD matrixshould be on focus for any angular position of the samplewith reference to the observation axis. In principle (Bornand Wolf, 1964), this can be obtained if the planescontaining the sample and the CCD matrix aremaintained symmetrical with reference to the plane of thelens throughout the whole measurement procedure, asshown schematically in figure 4 (Scheimpflug condition).A full orientation system for the CCD matrixsynchronised with the cradle-rotator set-up for the sampleis required. Mechanical constraints do not permit tosatisfy this requirement for all the measuring conditions.L1 measurement:detector calibration.P1nOpticalaxisPTFEsheetL2 measurement:samplecharacterisation.Lens f1ImaginarysampleplaneFigure 4 - Measurement set-up without deformation anddefocused effects.PTFEsheetP1nOpticalaxisRealsampleplaneFigure 3 - Geometrical consideration on image opticalsystem in the two measurement conditions.Otherwise, in the reflected or transmitted luminance3. ANALYSIS OF DEFORMATION ANDDEFOCUSING EFFECTSIn the case of ideal lenses, perfect alignment andsatisfying the Scheimpflug condition, the deformationand defocusing for the spots on sample plane and onCCD the matrix are the same. Reducing the deformationand defocusing analysis to the first part of the opticalsystem, it is however necessary to evaluate:
• the CCD matrix orientation for each measurementgeometry in order to obtain images always focused(Rossi and Sarotto, 2000);• the deformation and defocusing of the PTFE sheetimage projected on the sample plane.To evaluate the deformation we have to consider onlyrays passing through the nodal point P1n of lens f 1(figures 3 and 5). So the image of an ideal source pixel isa quadrilateral formed by the intersections of linesstarting from the ideal pixel edge, passing through thenodal point P1n, and the sample plane. In figure 5 theseintersections are represented by points PsA,B,C,D,images on the sample of the four object pointsPoA,B,C,D (vertices of PTFE sheet pixel). Furthermorethere are indicated the ideal vertex images PidA,B,C,Dobtained by the intersection of rays starting from sourcepixel edges PoA,B,C,D passing through nodal point P1nand rays passing trough the focal point Pf1. The focusedimage of the PTFE is on the plane ys-zs that correspondsto a normal incident geometrical configuration (figure 5).xPTFEsheetPoA(B,C,D)Lens f1yzP1nPf1ε1yszsPsA(B,C,D)PcsSampleplanePidA(B,C,D)vertex co-ordinates have been calculated (Rossi andSarotto, 2000) as function of the pixel position on PTFEsheet and of the angles set up on sample cradle rotator.In figure 6 it is also schematised the defocusing of asingle point PoA: an ellipse passing through 4 points(PssupA, PsinfA, PsdxA, PssxA) that surround the imagepoint PsA. These four points are obtained consideringrays starting from PoA and passing through the verticaland horizontal lens extremes.Considering ideal lenses and the system (source, lenses,sample and CCD) perfectly aligned, we can argue whichCCD and sample pixels are lighted by a single PTFEsheet pixel during L 1 or L 2 measurement. An example ofcalculation is reported in figure 7: deformation (dsABn:continuous lines) and defocusing (dssupinfAn: dash lines)are represented in number of pixels as a function of:• the polar angle α imposed by the sample cradle-rotator;• a fixed position for the PTFE point PoA(yoA,zoA);• a fixed azimuth direction β= 0 imposed by the samplecradle-rotator.In this particular case β= 0, therefore α = ε 1 i.e. the polarincident angle.Figure 5 - Pixel source deformation and its ideal image.PoDPoCPTFEsheetplanePoAPoAPoBFigure 7 - Deformation (dsABn: continuous lines) anddefocusing (dssupinfAn: dash lines) versus polar angle α,for a fixed geometrical configuration with: azimuth planeβ = 0, pixel position on the PTFE sheet PoA(0, 0,3 mm).Out of focusPssxAPssupAPsAPsinfAPsdxAPsDPsAPsCPsBDeformationSampleplaneFigure 6 - Ideal source pixel deformation and defocusingof a single point PoA.As shown in figure 6 the source pixel image on sampleplane (obtained by rays passing through P1n) is generallya quadrilateral of vertices PsA, PsB, PsC, PsD. TheOne of the investigated samples measured intransmission is a clear diffusing laminated-glazed madeby two glass sheets of the same thickness (3 mm) and adiffusing PVB (PolyVinylButyral) material, 0.38 mmthick. The goniophotometric measurements demonstratedthat the transmittance and reflectance properties of thispane were the same on both sides and independent of theorientation of the pane.An example of acquisition, done in the normal directionof transmission with a polar incidence of 10°, is reportedin figure 8. To highlight the form of the luminous spotprojected on the sample (lightly elliptic), the area lighteddirectly by the incident beam is represented as white infigure 8. The luminance values outside this area aredifferent from zero and are due to the multiple reflectionsbetween the layers that compose the laminated pane. The
form of this luminous area is approximately a ring. Inother words observing the lighted sample, a luminousarea greater than the zone intercepted by the beam isclearly visible. In this case a CCD lens of focal 50 mmand a magnification ratio lower than 1 was utilisedotherwise, using the optical system previously described,only the region lighted by the beam will be detected. Thedeformation and defocusing analysis permit us todistinguish between:• an area interested by the incident beam calculatedapplying the deformation analysis;• an area interested by the defocusing;• a lighted area due to multiple reflections inside thepane.Pixel row1008060402020 40 60 80 100Pixel columnFigure 8 – Image of a lighted laminated-glazed pane.It is to be outlined that integrating sphere measurementsconsider the flux transmitted by the ring surrounding thearea of the sample hit by the incident beam only if theport sphere is sufficiently greater than beam diameter: afeature that is not always possible to realise (Maccari etal., 2000). Furthermore usual luminancementers used fordirectional measurements refer to sample areas lowerthan the zone hit by incident beam: so also in this case theluminous ring is not detected. Otherwise this effect isclearly shown by the CCD acquisition.4. ILLUMINANCE EVALUATION ON SAMPLEPLANE AND CCD MATRIXTo correlate the light emitted by a single PTFE sheetpixel to the light measured by several CCD pixels, theillumination level on the sample shall be evaluate.The radiation emitted by a single PTFE sheet pixel andcollected by lens f 1 (figures 3 and 5) lights the sample(and then the CCD) over an area determined bydeformation and defocusing. The CCD measures theilluminance distribution on its matrix plane. Thedistribution form depends on sample plane orientation; itsvalue depends on the light flux collected by the imageoptical system (solid angles taken by incident beam andsubtended by the detector).Nevertheless our measure analysis is limited to CCDpixels, in a preliminary evaluation step we need todeterminate the hypothetical (because can exceed sampleor CCD dimension) area lighted by the flux generated byeach source pixel. The illuminance level on deformedzones is surely greater than that on defocusing zones: sothe two regions shall be distinguished. The optical systemaberrations shall be considered too.To simplify the problem and to reduce the computationtime, we strongly approximate the illuminancedistribution generated by each single source pixelconsidering only two signal levels respectively for thedefocusing and deformed lighted areas (Rossi andSarotto, 2000).The signal level of each CCD matrix pixel is thenobtained by:• starting from the luminance of each pixel source(measured in source calibration);• determining the deformed and defocused pixel imageand its two signal levels;• applying equation (1) to represent sample behaviourin reflection or transmission.5. THE 2D FOURIER TRANSFORM FOR IMAGEANALYSIS5.1 The two dimensional discrete Fourier TransformThe Fourier transform theory for one-dimensional signalprocessing can be extended to two dimensions for theanalysis, manipulation and enhancement of images of alltypes. An image is represented by a two-dimensionalarray of numbers. In visible light images, the array ofnumbers corresponds to object luminance levels or imageilluminance levels.The 2D discrete Fourier transform (DFT) is written as:M∑∑− 1 N−11⎡ ⎛ u ⋅mv⋅n⎞⎤F(u, v) =f(m, n) ⋅exp⎢−j2ð ⎜ + ⎟(2.a)M⋅N⎥m=0 n=0 ⎣ ⎝ M N ⎠⎦while the inverse DFT is:f(m,n) =M − 1N−1∑∑⎡ ⎛ u ⋅ m v ⋅ n ⎞⎤F(u,v) ⋅ exp⎢j2ð⎜ + ⎟⎥⎣ ⎝ ⎠⎦u=0 v=0 M N(2.b)In equations (2.a) and (2.b) the integers m, n determinethe pixel position on CCD, while u, v represent the spatialfrequencies. Both equations can be easily calculated by acomputer program: to speed up the calculation time theFFT algorithm is utilised (Rossi and Sarotto, 2000).On the contrary of deformation and defocusing analysis,the Fourier transform theory is applied on the wholeimage of the source and not on a single pixel. It is utilisedto check the alignment between source, sample, detector
and the optical system lenses. This control is different inthe case of L 1 or L 2 measurement since image on theCCD in L 1 measurement is a circle always focused, whilein L 2 measurement the luminous spot projected on sampleplane becomes a defocused ellipse. In both cases thePTFE sheet image projected on the material is sampledby the discrete grid of CCD pixels and is quantized by 14bit for each pixel.5.2 Modelling imaging systemOur imaging systems can be considered as a twodimensionallinear system. If x(m, n) represents the pixelluminance distribution of PTFE sheet, and y(m, n)represents the pixel illuminance distribution on CCDmatrix, we can write:y(m, n) = H [ x(m, n) ] (3)where “H” is the function that represents the imagingsystem. When the input is the two-dimensionalKronecker delta function at location (m’, n’), the outputat location (m, n) is defined as:h(m, n; m’, n’) = H [ δ(m-m’, n-n’) ] (4)and it is called the impulse response of the system orpoint spread function (PSF). In our case, it represents theimage of a single source pixel of the PTFE sheet (m’, n’)projected on sample and then on CCD plane.The output of any linear system can be obtained from itsimpulse response and the input by applying thesuperposition rule:y(m, n) = H [ x(m, n) ] = ∑∑ x(m', n') ⋅ h(m,n;m', n' ) (5)since:∑∑m'n'x(m, n) = x(m',n') ⋅δ (m - m';n - n') (6)m'n'Generally a system is called “spatially invariant” or“shift invariant” if a translation of the input causes only atranslation of the output. Defining the impulse responsein the origin:H [δ(m, n)] = h(m, n; 0, 0) = h(m, n) (7)it must be true for shift invariant systems that:h(m,n;m’,n’) = H[δ(m-m’,n-n’)] = h(m-m’,n-n’;0,0) (8)that means the shape of impulse response does not changeas the impulse moves on the input plane. For shiftinvariant systems, the output becomes:=x(m', n' )y(m, n) = x(m, n) ⊗ h(m, n) =⋅h(m - m', n - n' )=h(m', n' )⋅ x(m - m', n - n' )∑∑m' n'∑∑m' n'which is called convolution of the input with the impulseresponse. The last equation means that impulse response(9)is a function of the two displacement variables only.Goniophotometric system is:• Spatially invariant in L 1 measurement: the shape anddimension of source pixel image on CCD does notchange varying the input pixel position.• Spatially varying in L 2 measurement in the first part ofthe optical system (PTFE sheet – lens f 1 – sample)since a translation of the input pixel does not cause asimply translation of the output: the shape of PSFchanges as the impulse moves on the input plane.• Spatially invariant in L 2 measurement in the secondpart of the optical system: the Scheimpflug condition(imposed on sample, CCD and its lens planes)guarantees that the shape and dimension of samplepixel image on CCD does not change varying thesample pixel position.The image detected by the CCD is a reconstruction ofreal image (in L 1 or L 2 measurements) by sampling (on adiscrete grid of pixels) and quantization (using 14 bits).The reconstructed image is given by the interpolationformula:⎛ ⎛ y ⎞ ⎞⎜⎟⎛ ⎛ z ⎞sin⎞⎜ ⎜ − ⎟ ⎟⎜⎜ − m⎟πsin n π⎝ Äy ⎠ ⎟ ⎜ ⎝ Äz ⎠ ⎟f(m⋅∆y,n ⋅ ∆z)⋅⎜⎟ ⋅⎜⎛ ⎞⎟⎜ ⎛ y ⎞ ⎟ z⎜ ⎜ − ⎟⎟⎜⎜ − m⎟πn⎟⎝ ⎝ Äy ⎠ ⎠ ⎝ ⎝ Äz ⎠ ⎠∑ ∞m',n' = −∞π(10)The CCD pixel dimensions fix the bandwidth (spatialfrequency) or Nyquist rate of the measurement system:u 0 = v 0 = 1 / (2⋅∆y) = 1 / (2⋅∆z) = 1 / 54 µm -1 (11)The measured sampled image is obtained by a flat topsampling on the CCD pixels: the system does not registerilluminance variations over a distance less than 27 µm.The cost of attenuate higher spatial frequencies ishowever inevitable since the finite aperture of opticalsystem causes resolution decrease too (Jain, 1989).5.3 Application of Fourier theory in L 1 measurementIn L 1 measurement the Fourier theory is utilised to findthe best alignment between source, detector and theirlenses. As representative of ideal image on the sample weconsider a circle of diameter Φ S = 13 mm with a unitaryluminance value, projected on the ideal sample plane yszs(figure 5) normal to incident direction and centred in(ycs’, zcs'):g(ys, zs)⎪⎧1= ⎨⎪⎩ 0(ys - ycs')2otherwise+ (zs − zsc' )2≤ ( Φ /2)S2(12)The circle is generally centred in (ycs’, zcs’) instead oforigin (0,0) to consider eventual not perfect alignments.The ideal signal (equation 12) varies over an infinitesimaldistance. The CCD output (ideal sampled signal - f IS )obtained by simulated the flat top sampling on finitedimension pixels can never exactly reproduce it.Figure 9 shows the measured profile of a CCD matrix
column interested by the incident beam: the L 1 luminanceis almost uniform in the zone interested by the beam.100008000Source luminanceIn order to maximise equation (13), some problems canarise. If the dimension of measured signal is differentfrom the ideal image dimension, there are several coordinates(ycs’, zcs’) that maximise the spatialcorrelation. This problem can be solved choosingbetween co-ordinates (ycs’, zcs’) which make thedifferences between bounds of measured and ideal signalsas close as possible in each direction (figure 11).Arbitrary luminance units600040002000Ideal imageReal imageIdeal image00 20 40 60 80 100Pixel column(ycs’, zcs’)Figure 9 – Signal levels on a CCD pixel column by L 1measurement.To determinate the real centre co-ordinates (ycs’, zcs’)of the PTFE image, we have to maximise the spatialcorrelation between the ideal sampled signal (f IS ) and themeasured sampled signal (f MS ):⎡⎤MS (m, n) ⊕ f IS (m, n) = ⎢∑∑f MS (m',n' ) ⋅fIS (m + m' , n + n' ) ⎥⎢⎣m' n'⎥⎦f(13)Using the properties of Fourier transform the spatialcorrelation is reduced to a product of Fourier transforms:F[fMS(m, n) ⊕ f (m, n)] = F ( −m,−n)⋅ F (m, n) (14)ISMSImposing co-ordinate (ycs’, zcs’) to change discretelyon centre of adjacent pixels, the centre of measured signalcoincides with co-ordinates that maximise the correlationproduct (equation 13).As example the one-dimensional Fourier transform ofCCD pixel column signal of figure 9 is reported in figure10. In this case, we can approximately neglect spatialfrequencies greater than 0,010 µm -1 : this valuecorresponds to a spatial variation of 3-4 pixels.Amplitude in arbitrary units400030002000100000,000 0,005 0,010 0,015 0,020Spatial frequency (µm -1 )Figure 10 – FFT of a CCD pixel column.ISFigure 11 - Determination of centre if ideal and realimage dimensions are different.5.4 Procedure utilised for L 2 measurementFor L 2 measurement configuration, using the samplereference system (xsn, ysn, zsn) of figure 2, the equationedge of the deformed image is theoretically an ellipsecentred in the origin (0,0):⎪⎧A ⋅ xsn⎨⎪⎩ zsn = 02+ B⋅xsn ⋅ ysn + C⋅ysn2+ F⋅xsn + G ⋅ ysn + H = 0 (15)Its parameter values are generally functions of anglesset up on sample cradle rotator and of the geometricaldistances involved (Rossi and Sarotto, 2000).As in L 1 measurement, to take in account eventual notperfect alignments, we consider as ideal image an ellipsenot centred in (0,0) but shifted in (xsn’, ysn’). Then thealignment between sample and CCD cradle rotators ischecked looking for the maximum of the spatialcorrelation of ideal and measured signals. Again someproblems can arise if the dimension of ideal andmeasured images are different: these problems can besolved in similar way as done for L 1 measurement, takinginto account that measured signal is deformed anddefocused, while ideal signal is only deformed. Howeverthis aspect should not generate problems because thesignal level in the defocused zone (on the edge of theimage) is lower than signal level in the central zone,where there are both contributes (deformed anddefocused).To conclude we observe that the alignment check in L 2measurement can be done only for angle values lowerthan 20°: for greater values the projection of luminousspot on the CCD exceeds the matrix dimension.However, if the system is aligned for angles lower than20°, we can reasonably retain that it maintains withacceptable accuracy this property for the othergeometrical configurations.
6 SOME APPLICATIONS OFGONIOPHOTOMETRIC CHARACTERISATIONThe reflection and transmission properties of materialscan be utilised in different application fields. Twogoniophotometric characterisations and their applicationsare here analysed:1. Diffusing daylighting system to improve internalcomfort in non residential buildings;2. Redirecting daylighting system to exploit the solarradiation in different seasons.6.1 Characterisation of diffusing daylighting systemsDiffusing glazing systems, able to diffuse daylight in alldirections, permit to obtain a more uniform illuminanceinside the room, in spite of the variability of the directand diffuse components of the solar radiation. On theother side, the optical characterisation of such samplespresents some difficulties as a consequence of their largeangle scattering properties. As a matter of fact, to performaccurate transmittance (reflectance) measurements withintegrating spheres is necessary that all the transmitted(reflected) beams, striking the sample, are collectedinside the sphere. Consequently, large integrating sphereswith large sample ports must be used. Nevertheless, forlambertian and/or remarkably thick samples, some of thetransmitted (reflected) radiation is lost, introducing asystematic error: the higher is the port diameter, the lowerwill be the error (Maccari et al., 2000).For design purposes the detailed knowledge of thespatial scattering light distribution of a specimen is oftennecessary, but generally too complex to manage: in thiscase a reduced set of parameters is preferred. We haveidentified a suitable model of the glazing unit to find outthe more appropriate analytical function for thegoniophotometer result point fitting. In the case of normalincidence, the luminance coefficient of equation (1) canbe expressed as a sum of two or more cosine terms withdifferent n j scattering indexes (not necessarily integer)and k j scaling factors:M∑n j( ) = k ⋅cos( ε )BTDF, BRDF ε (16)2j=1where:• ε 2 is the reflection / transmission polar angle;• the values of k j and n j depend on the prevailingdiffusing (lambertian: n j = 0) or regular (n j → ∞)behaviour of the glazing unit;• each one of the M terms in the above sum representsa different scattering comportment.As example, in figure 12 the luminance coefficient intransmission and its fit are reported for a typical diffusingglazing. With only four parameters, equation (16) fits themeasured function with accuracy sufficient for nowadaysrequirements and simulation algorithms.j2BTDF [sr -1 ]2,01,51,00,50,0BTDF measuredBTDF fit-80 -60 -40 -20 0 20 40 60 80 100ε 2[°]Figure 12 - Goniophotometric characterisation of adiffusing glazing in transmission: measured and fittedvalues.6.1 Characterisation of redirecting daylighting systemsTransparent glazing systems are used in architecturewhen a perfect view through is need. In order to preventglare effects, a reduced level of natural light intake isobtained by using tinted or coated glass or, alternatively,redirecting glazing systems. These systems are usuallyimplemented to exploit the solar radiation in differentseasons in order:• to collect the maximum of light in winter;• to reduce the light in summer to avoid effects likeoverheating, photo-degradation, etc...If compared with diffusing glazing units, the opticalcharacterisation of such samples presents some moredifficulties. The utilisation of a digital detector becomesvery useful to stabilise how the transmitted light isscattered. In figures 13 and 14 two images of one of suchsamples obtained by the CCD detector are reported.Pixel row1008060402020 40 60 80 100Pixel columnFigure 13 - Redirecting glazing systems measured for ε 1= ε 2 = 45°, ϕ 2 = ϕ 1 ± π.
Pixel row100806040• source luminance stability and colour temperatureabsolute values controlled by the fiber optic feedbackwith an accuracy of 0,2% and 4 K respectively(described in §2);• angular alignment precision during movements:guaranteed lower than 0,1°;• deformation and defocusing of the luminous spot onthe sample and on the CCD: influence considered asdescribed in §3 starting from the geometry of theproblem;• alignment between source, detector and sample:checked and corrected by the 2D Fourier analysisshown in §5.20REFERENCES20 40 60 80 100Pixel columnFigure 14 - Redirecting glazing systems measured for ε 1= ε 2 = 5°, ϕ 2 = ϕ 1 ± π.Both acquisitions refer to a regular transmittancemeasurement. In the first case (figure 13) themeasurement geometry is: ε 1 = ε 2 = 45°; in the second(figure 14): ε 1 = ε 2 = 5°. In both cases the incident beamdiameter is the same and ϕ 2 = ϕ 1 ± π, so ϕ 2 is the azimuthplane containing the regular transmittance component. Tohighlight the different behaviour of the specimen theluminance scale of the two graphs is different. The twodigital acquisitions (particularly the first) show theinternal structure composes by glass deflecting prismssupported by a plastic grid. These deflecting prismsobstruct the light incoming when the incident polardirection is near the normal (figure 14) and increase thetransmitted flux if the polar incident angle increases. Ifglazing systems like this one are mounted on a mansardroof window, the solar radiation will exploit in order tomaximise daylight in winter and avoid overheating insummer.7. CONCLUSIONSGoniophotometric measurements are important tocorrectly characterise unconventional glazing units whenthe main application parameter is their redistribution ofincident daylight in the internal environment.From the metrological point of view the measurement ofthe transmitted or reflected light is a difficult taskparticularly when redirecting daylighting systems areconsidered. The use of CCD digital detectors andsophisticated measurement algorithms and proceduresgreatly simplify this problem.For the characterisation of diffusing and redirectingglazing units, the IEN goniophotometer main featuresare:G. Rossi, P. Soardo, (1991) A new gonioreflectometer,CIE Proceeding 22nd Session, pp. 59-60, Melbourne.G. Rossi, Paola Iacomussi, M. Sarotto, P. Soardo (1997),CCD matrix detector for photometry, VIII InternationalMetrology Congress, Besançon France, 20-23 October1997.Maccari, P. Polato, G. Rossi, M. Sarotto, M. Zinzi(1998), Asymptotic technique in integrating spheretransmittance measurements on diffusing transparentmaterials, Proceeding Eurosun 1998, Slovenia.CIE (Commission Internationale de l’Eclairage)Publication N. 17.4 (1987), International LightingVocabulary, Genève.G. Rossi, M. Sarotto (2000), A system to measurephotometric behaviour of materials: analysis of the fulloriented CCD multiluminancemeter, IEN TechnicalReport n. 606, May 2000.G. Rossi, G. Fusco, P. Soardo (1996), The calibration ofCCD matrix detectors for the measurements onphotometric materials and lighting installations,Proceedings of the XXIII CIE Session, Vol. I, pp. 132-133, New Delhi (India), November 1996.Born and Wolf (1964), Principles of Optics, Pergamonpress.Maccari, P. Polato, G. Rossi, M. Sarotto, M. Zinzi(2000), Characterisation of scattering properties andevaluation of a scattering glazing unit for daylightingapplications, Proceeding Eurosun 2000, Denmark.A. K. Jain (1989), Fundamental of Digital ImageProcessing, Prentice Hall, 1989.