Three different techniques were used to determine the

Modulation Transfer Function (MTF) of a 35mm film

scanner. The first involved scanning sine wave charts

comprising a number of patches with different frequencies

of known modulation. The second method involved the

scanning and Fourier transform of a photographic grain

noise pattern to simulate low modulation white noise.

Finally, the ISO 12233 Slanted-edge Spatial Frequency

Response (SFR) plug-in was used to determine the average

MTF of the device. This creates a super-sampled edge

profile from sequential scan-lines of the sampled image of

an edge.

Procedures for creating test targets, where appropriate,

are described. Advantages and limitations encountered in

applying each methodology are discussed, as well as the

precision of each method for deriving the MTF.

Conclusions are drawn concerning the comparability of

MTFs determined by the three methods

Fagard-Jenkin, R.

Jacobson, R.E.

Triantaphillidou, S.

WestminsterResearch

An Evaluation of MTF Determination Methodsfor 35mm  Film ScannersS. Triantaphillidou, R. E. Jacobson, R. Fagard-JenkinImaging Technology Research Group, University of WestminsterWatford Road, Harrow, HA1 3TP,  UK.AbstractThree different techniques were used to determine theModulation Transfer Function (MTF) of a 35mm filmscanner.  The first involved  scanning  sine wave chartscomprising a  number of patches with different frequenciesof known modulation.  The second method involved  thescanning and Fourier transform of a photographic grainnoise pattern to simulate low modulation white noise.Finally, the  ISO 12233 Slanted-edge Spatial FrequencyResponse (SFR) plug-in was used to determine the averageMTF of the device. This creates  a super-sampled edgeprofile  from sequential  scan-lines of the sampled  image ofan edge.Procedures for creating test targets, where appropriate,are described. Advantages and limitations encountered inapplying  each methodology are discussed,  as well as theprecision of each method for deriving the MTF.Conclusions are drawn concerning the comparability ofMTFs determined by the three methods.IntroductionIn analogue imaging systems the determination of theMTF  depends critically on the method of measurement dueto non-linearities.   Digital imaging devices suffer fromadditional non-linearities, because they are non-stationary,anisotropic systems and often incorporate non-linear imageenhancement [1].  These result in additional problems forevaluating the system MTF and different techniques oftenyield large discrepancies.The Spatial Frequency Response plug-in [2] has beenproposed as a standard method for the determination ofaveraged digital MTFs.  However, other measurementmethods are being used and a need for comparison wasconsidered essential.Experimental Methods and ResultsA 35 mm film scanner was used for which the overallsystem MTF is a combination of the MTF of the CCD array,the lens and the electronic components.  It acquires imagesat 12 bits per channel and saves files down-sampled to 8 bitsper channel. Down-sampling is achieved via look-up tables(LUT), located in the firmware of the scanner.The size of the monochrome linear image sensor is2592 pixels, resulting in a maximum image size of 2592 x3888 square pixels, of  9.4 x 9.4 µm size [3]. These pixeldimensions were confirmed by scanning in a target ofknown physical size. The Nyquist frequency (1 / (2∆x)where ∆x is the sampling pitch) for both fast and slowscanning directions was calculated as 53.2 cycles/mm.Only the scanner’s monochrome MTF responses wereevaluated because the same principles can be applied to thedetermination of multi-channel MTFs. The device’s tonalcharacteristics were optimised to give a linear relationshipbetween target transmittance and pixel values, unless statedotherwise. This was achieved by adjusting the scannergamma settings [4], keeping all other parameters constant. MTFs were evaluated for the optical resolution of thescanner (2700 dpi). Scanning exposures were optimised bythe scanner while the overall integral density of the testtargets were kept similar to avoid large exposure variations.MTF measurements were carried out in the centre of theframe.Sine Wave MethodThis method involves a one-dimensional exposuredistribution, E(x), of the form:  )2sin()( xbaxE piω+=  (1)where x is the distance, a is the average signal  level, bis the amplitude and  ω the spatial frequency.  The recordedexposure is expressed as the transmittance distribution, T, ofthe sine target, with modulation, Min(ω),  given by:abTTTTM in =+−=ωminminminmax)( (2)The  modulation recorded by the scanner, Mout(ω), iscalculated by:minmaxminmax)(PVPVPVPVM out +−=ω (3)Provided that film transmittance is linearly related to theoutput pixel values, PV, the MTF of the scanning system,M(ω), is given by the ratio of the output to the inputmodulation, with respect to the spatial frequency.The test targets [5] comprised patches of sinusoidallyvarying transmittance (0.75 to 128 cycles/mm), on 35 mmfilm. The targets also included twelve uniform transmittancesteps.  Two targets, A and B were used, with averagemodulations of 0.35 and 0.60 respectively. Target B  wascemented in glass.Scanning was performed by placing the targets in twoorientations, at right angles to each other,  to evaluate MTFresponses for the fast and slow scanning directions. After thetargets were scanned, the transfer characteristics wereevaluated for each image.  This was achieved by plottingtransmittance against normalised pixel values, measured foreach uniform grey step. The scanner’s transfer functionswere determined by power curve fitting procedures whichgave correlation coefficients in excess of  0.999.  Pixelvalues were converted to linear transmittance units, byapplying the inverse power functions to normalised pixelvalues.Figure 1.  MTF curves derived from sine wave targets A and B  forthe fast and slow scanning directions.Multiple one-dimensional sinusoidal traces wereextracted for each spatial frequency patch.  Individual cycleswere identified by examining the traces. Maximum andminimum pixel values corresponding to each cycle werethen extracted and averaged.   These averages were used tocalculate Mout(ω) according to Equation (3).  The amount ofdata necessary to determine the output modulation increasedwith respect to spatial frequency. This is because themodulation becomes highly dependent on the phase of thesine patterns relative to the sampling array as spatialfrequency increases [6]. Therefore, the number of cyclesfrom which the output modulation was determined rangedfrom 30 to 300.  According to Granger [7], when at least 20samples are dedicated over a cycle,  a good estimate of theMTF in digital systems is achieved.   At a sampling rate of106 samples/mm,  20 samples correspond to 10% of theNyquist frequency.  In this work, the MTF was calculatedfor up to 40 cycles/mm, or 75% of the Nyquist  frequency.Figure 1 shows MTF curves corresponding to the fastand slow scanning directions, for  targets A and B. Thefrequency response of the fast and slow scans are verysimilar, up to 25 cycles/mm. The two test targets, however,gave different MTF responses, with target B resulting inlower scanner performance.  Although the input modulationof the two targets was not the same, such a largedisagreement in the MTFs should not occur.  Possibleexplanations include:  exposure flare  caused  the glass coveron target B lowering  the response of the scanner, orsignificant difference in the scanning exposures of the twotargets.Figure 2 shows the slow scan MTFs, after scanningchart A when using three different scanner transfer functionsand correcting the scanner responses for  transfer non-linearities. It is apparent that, using this method, themeasurement of the system MTF is highly repeatable.Results in Figure 2 indicate also that quantization andtransfer correction does not affect the final calculated MTFcurve.Figure 2. MTF curves resulting from three different scans oftarget A, using  different gamma settings and then correcting  thescanner responses  for the transfer non-linearities.Noise MethodFor a linear system, the output noise power spectrum,NPSout(ω),   is related to that of the input, NPSin(ω), and theMTF, M(ω), by [8]:2)()()( ω×ω=ω MNPSNPS inout (4)If the NPSin(ω) is constant over the required spatialfrequency range (i.e. white noise), then the NPSout(ω)  issimply the square of the system MTF.Photographic grain was used to simulate white noise.Test targets were generated by photographing a  grey cardand a Kodak Q-13 greyscale, at different de-focused levels0.00.10.20.30.40.50.60.70.80.91.01.10 5 10 15 20 25 30 35 40 45 50 55Cycles/mmMTFSine A SlowSine A FastSine B Slow Sine B Fast0.00.10.20.30.40.50.60.70.80.91.01.10 5 10 15 20 25 30 35 40 45 50 55Cycles/mmMTFCorrected forgamma=0.57Corrected forgamma=0.95Corrected  forgamma=1.04[9], using Kodak T-Max P3200 film. The film may beconsidered as having a constant noise power spectrum up to40-50 cycles/mm [10]. Therefore, there is little need forcompensation until frequencies approach the Nyquist limitof the scanner. A  35 mm frame was scanned and an array of 512 by512 pixels which corresponded to the centre of the scanningframe was selected.  The mean was subtracted from everypixel value of the image array to remove the DC componentand slight scanning non-uniformities. The modulus of theFast Fourier transform [11] of the data gave the two-dimensional scanner response. This was then normalized anddecimated [12] by 20 points  in both frequency directions, tosmooth the MTF (see figure 3).Figure 3.  Section of the rotational  MTF of the scanner afterdecimating by 20 points in both frequency directions.Figure 4.  MTF curves corresponding to the fast and slow scanningdirection, deduced  by cross sectioning the rotational MTF and  bysimulation of scanning with a thin long slit.Fast and slow scan MTFs were determined by takingthe appropriate cross sections. Similar one dimensionalresults were obtained by averaging separately rows andcolumns of the digital image array to simulate scanning witha thin long slit. The mean was subtracted from the resultingdata and the modulus of the one dimensional Fouriertransform was calculated to obtain the fast and slow scanMTF responses.Figure 4 shows one dimensional MTF curves for bothscanning directions. The results  indicate that the slow scanMTF is significantly lower than that of the fast scan.Asymmetry in the two dimensional MTF of the system wasexpected, but not in the MTF curves at 90o orientation. Thelower slow scan MTF might be due to the electro-mechanical components of the scanner, necessary in thisscanning direction.Separate scans were performed with varying scanningtransfer characteristics (image contrast), resulting in  imagesof different modulations, ranging from 0.46 to 0.85. MTFresponses where found identical after the normalization ofthe data.Slanted Edge SFR Plug-In MethodThe ISO 12233 slanted-edge Spatial FrequencyResponse plug-in can be used for the creation of one-dimensional uniformly super-sampled edge profiles and thecalculation of the frequency response of a digital system.Details on the method which is based on the traditional edgetechnique have been published [13,14].   An account of thecomputational steps performed by the SFR plug-in is givenby Williams [15], as well as a detailed evaluation of itsprecision.When an edge exposure is reproduced on film, scannedand processed using the SFR plug-in, the resulting spatialfrequency response, SFR(ω), is a combination of thefrequency content of the edge-target, MTFfilm(ω),  and theresponse of the scanner M(ω):)()()( ω×ω=ω MMTFSFR film (5)A stepped edge  was printed on a high quality laserprinter, as a binary digital image file, at 600 dpi. A numberof density measurements were taken from the print, toensure that the edge maintained uniform densities all alongits length. The laser print was then  photographed at amagnification of 0.19, using 35mm Ilford Pan-F black-and-white film, together with a Kodak Q-13 greyscale. The edgewas recorded at an angle of approximately 15o from thevertical on the film and  had a density difference of  0.9. Thefrequency content of the edge-target was evaluated using thetraditional edge technique [16].The edge-target was scanned, in positive scanningmode, with the edge falling horizontally with respect to thescanning array and positioned in the centre of the scanningframe.  Pixel values corresponding to individual steps of thegreyscale were averaged and plotted against respective filmtransmittances.  A third degree polynomial successfullyfitted the measured data to develop a 256 step LUT, whichserved as the Opto-Electronic Conversion Function [17]. Arectangular region-of-interest [18] covering 200 by 1200pixels was selected, over which the calculations of the SFRplug-in (version 7.1) were performed. The vertical tohorizontal aspect ratio of the region-of-interest  was kept as5536180 55361800.00.10.20.30.40.50.60.70.80.91.0MTFCycles/mm Cycles/mm0.00.10.20.30.40.50.60.70.80.91.01.10 5 10 15 20 25 30 35 40 45 50 55Cycles/mmMTFNoise Slow(x-section)Noise Fast(x-section)Noise Slow(columns)Noise Fast(row s)high as possible to increase the signal-to-noise ratio of theSFR estimates [15].Multiple scans, with slight horizontal translation of theedge with respect to the scanning frame were performed.They were  processed  in the above way  and then averagedto determine the average SFR of the centre of the scanningframe, for the fast scanning direction. To evaluate the slowscan SFR, a number of scans were produced and calculatedin the above way, by rotating the edge-target 90o. Theresulting SFRs were corrected for the frequency content ofthe edge-target. MTF curves are illustrated in Figure 5.Figure 5. MTF curves of  fast and slow scans, calculated with theSFR technique.  ‘Edge 2 Fast’ is an MTF curve produced from asecond edge- target, with density difference of 0.75.Figure 5 shows that the fast and slow scan MTFs aresimilar. The use of  edge-targets with little difference incontrast gave agreeing results. While experimenting withthis method it was noticed that the SFR curvescorresponding to individual displaced scans of the edge-target were almost identical. This is an indication of theconsistency of the response of the scanner within thescanning frame.Comparison of the Three MethodsMTF curves for the fast and slow scanning directions,evaluated by the three methods, are shown in Figures 6 and7 respectively. The results indicate that each method gavedifferent frequency responses. The variation in the MTFs isshown to be less in the slow than in the fast scanningdirection. Figure 8 illustrates mean MTFs for the fast andslow scans, up to 40 cycles/mm. The mean MTFcorresponding to the fast scan was higher than that of theslow scan, beyond 10-15 cycles/mm.An interesting result is the particularly high fast scanMTF, determined by the noise method,  in comparison withall the other MTFs (Figure 6). Apart from this, MTFsevaluated using sine waves were higher than those evaluatedwith the other methods (Figures 6,7). The reason may bethat the maximum and minimum responses extracted fromindividual cycles included noise effects, resulting in higheroutput amplitudes.Figure 6. MTF curves of the fast scan, determined with the threemethods.Figure 7. MTF curves of the slow scan, determined with thethree methods.Although all methods gave highly repeatable resultswithin ± 6%, further work on the experimental accuracyfor each method is being carried out. Before this work iscompleted, a rigorous conclusion cannot be reached on thecomparability of  the MTFs.The advantage of the sine wave method for measuringdigital MTFs is that calibrated targets are used, for which themodulation is provided. This method, however, is very timeconsuming.  Also, for the precise evaluation of thefrequency response of different parts for the scanning frame,frequency patches need to be scanned and evaluatedindividually. The MTF is not measurable after 70-80% of0.00.10.20.30.40.50.60.70.80.91.01.10 5 10 15 20 25 30 35 40 45 50 55Cycles/mmMTFEdge 1 Fast Edge 1 Slow Edge 2 Fast0.00.10.20.30.40.50.60.70.80.91.01.10 5 10 15 20 25 30 35 40 45 50 55Cycles/mmMTFSine A SlowSine B Slow Edge  Slow Noise Slow0.00.10.20.30.40.50.60.70.80.91.01.10 5 10 15 20 25 30 35 40 45 50 55Cycles/mmMTFSine A FastSine B FastEdge 1 Fast Noise Fastthe Nyquist limit of the system, due to phase and noiseeffects.   Different sine wave targets may give differentresults.Figure 8. Mean MTFs corresponding to the fast and slow scans.Advantages of the noise method include: Test targetsare simple to make and the device’s MTF is easilycalculated with appropriate software. Also, as a two-dimensional frequency response is obtained,  the MTF canbe extracted for every scanning angle.  By selectingindividual parts of the scanned image, the MTF of differentparts of the scanning frame can be evaluated.  Finally, thereis no need for device transfer correction, as long as theresulting MTFs are normalized. On the other hand, filmgrain is used only as an approximation of white noise andthus compensation for the frequency content of the targetmay be needed at high spatial frequencies.The SFR plug-in gives an average spatial frequencyresponse of the device.  It is very  easy to apply and returnsreliable SFRs of the area of the CCD where the edge falls.Repeated scanning by translating the edge is needed for thedetermination of the  frequency response of various areas ofthe scanning frame. The plug-in is largely insensitive to edgeangle [15] and theoretically estimates SFRs to four times theNyquist limit of the system. Precise estimation of the Opto-electronic Conversion Function is essential for the correctSFR computations. Compensation for the  frequency contentof the edge-target is needed to cascade the system MTF.ConclusionFor this work, sine waves, photographic noise and theSFR plug-in were used for the determination of the spatialfrequency response of a 35 mm scanner.  The three methodsgave different MTFs  for both fast and slow scanningdirections. MTFs determined using sine waves weregenerally highest. The mean spatial frequency response ofthe fast scan was found slightly better than that of the slowscan. This is mostly due to the surprisingly high MTF curvecalculated with the noise method. Comparison of the resultswas found difficult. Further work is needed to calculateexperimental errors for each method.AcknowledgementsThe authors are thankful to N.R.Axford, member of theImaging Technology Research Group, for usefuldiscussions. Sophie Triantaphillidou gratefullyacknowledges the Leverhulme Trust for supporting thiswork.References1. Y.Okano, Proc. 51st IS&T’s 1998 PICS Conference, 74-78,(1998).2. ISO Committee Draft 12233, Photography – Electronic StillPicture Camera – Resolution measurements, (1997).3. Nikon Scan Macintosh User's Manual, Nikon Corporation,Electronic Imaging Division, 1995.4. S.Triantaphillidou, R.E.Jacobson and A.M.Ford, Proc. ICPS’98Vol.2, 204-209, (1998).5. R.L.Lamberts, Sine Patterns, 236 Henderson Drive, Penfield.New York 14526, USA.6. G.C.Holst, CCD Arrays, Cameras, and Displays, SPIE Press,Bellingham, USA, 1996, 213.7. E.M.Granger, Image Quality of Digital Cameras, Proc. 51stIS&T’s 1988 PICS Conference, 188-191, (1998).8. J.C.Dainty  and R. Shaw, Image Science, Academic Press,London, UK, 1974, 249.9. M.Gouch and M.Roe, Image MTF Analysis Using Grain  Noise,Proc. SPIE, 1987, 96-102, (1993).10. F.H.Perrin, The Theory of the Photographic Process, ThirdEdition, The Macmillan Company, New York, USA, 1966,535.11. W.H.Press, B.P.Flannery, S. A. Teukolsky and  W.T.Vetterling, Numerical Recipes in C: The Art of ScientificComputing, Second Edition, Cambridge University Press,Cambridge, UK, 1988, 496-536 .12. MatLab Signal Processing Toolbox, User’s Guide V.4, TheMath Works Inc, (1996).13. S.E.Reichenbach, S.P.Park and R.Narayanswamy, OpticalEngineering, 30, 170-177, (1991).14. H.S.Wong, Opt. Eng., 30, 1394-1398, (1991).15. D.Williams, Benchmrking of the ISO 12233 Slanted-edgeSpatial Frequency  Response Plug-in, Proc. 51st IS&T’s PICSConference, 133-136, (1998).16. R.A.Jones, Photgr. Sci. Eng., 11, 102-106, (1967).17. ISO Committee Draft 14524, Photography – Electronic StillPicture Camera – Methods for measuring Opto-electronicConversion Function, (1996).18. Image Analyser SFR Plug-in User Guide,http://www.pima.net/it10a.htm, (1998).0.00.10.20.30.40.50.60.70.80.91.01.10 5 10 15 20 25 30 35 40 45 50 55Cycles/mmMTFMean MTFFastMean MTFSlow

An evaluation of MTF determination methods for 35mm scanners

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An evaluation of MTF determination methods for 35mm scanners

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