Radiographic screen-film noise power spectrum: calibrationand intercomparison

John M. Sandrik, Robert F. Wagner, and Kenneth M. Hanson

The magnitude of a measurement of the noise power spectrum (NPS) of a radiographic screen-film systemis affected by the light-scattering properties of the film studied and the optical characteristics of the micro-densitometer used to sample the image. To facilitate absolute NPS intercomparisons among laboratories,NPS in terms of instrument density must be converted to diffuse density. Conversion in terms of a Callier

Q factor was found to be inadequate due to nonlinearity of the density response of the microdensitometer.By establishing instrument-to-diffuse density characteristic curves for the microdensitometers at two labo-ratories and correcting the NPS by the square of the slopes of these curves at the density of the image, goodagreement was achieved for independent NPS measurements of a given film sample.

1. Introduction

The determination of the noise power spectrum(NPS) of a radiographic screen-film image is generallyaccomplished by the microdensitometric measurementof fluctuations of transmission optical density. Thesquared moduli of Fourier transforms of these densityfluctuations are used to calculate the NPS according tothe definition 1

W(uV) = lim (X S f (Xy)

X exp[-27ri(ux + vy)]dxdy) (1)

where x and y are the coordinate space axes, u and v arethe corresponding frequency space axes, AD is thedensity fluctuation, and ( ) denotes an ensemble av-erage.

The actual density quantity whose fluctuations arebeing measured depends on the optical instrument usedand its optical coupling to the emulsion being evaluated.Densitometers that illuminate the sample with a narrowbeam of light and collect transmitted light from 27r sr

When this work was performed, both J. M. Sandrik and R. F.Wagner were with U.S. Food & Drug Administration, Bureau of Ra-diological Health, Division of Electronic Products, Rockville, Mary-land 20857; J. M. Sandrik is now with General Electric Company,Medical Systems Operations, Applied Sciences Laboratory, Mil-waukee, Wisconsin 53201. K. M. Hanson is with University of Cali-fornia, Los Alamos National Laboratory, Los Alamos, New Mexico

87545.Received 18 June 1982.0003-6935/82/193597-05$01.00/0.© 1982 Optical Society of America.

measure diffuse transmission density.2 Densitometersthat both illuminate with and collect very narrow beamsmeasure specular density, which depends on the scat-tering properties of the emulsion as well as the collectingproperties of the instrument optics. The ratio ofspecular to diffuse density of a sample is called theCallier coefficient Q of the sample.3 Most microden-sitometers both illuminate and collect light over smallangles (the sine of the half-angle ranges from 0.05 to0.25), hence their measurements approximate speculardensities. But the illumination and collection anglesare finite in practical microdensitometers and varybetween instruments. Therefore, the density DI of asample measured with a particular instrument will bepeculiar to the instrument used. If the density fluc-tuations in Eq. (1) are expressed in terms of DI, the re-sulting NPS will have a magnitude peculiar to the mi-crodensitometer used to perform the measurement. Itis desirable to convert the AD measured by the micro-densitometer to fluctuations of diffuse density DD SOthat the magnitude of the NPS is intercomparable be-tween laboratories.

II. Theory

The similar problem of converting measurements ofrms granularity, r(D), from instrument to diffusedensity was addressed by Schmitt and Altman.4 Theirsolution was to measure net (above base but includingfog) instrument density and net diffuse density of aparticular film type exposed to a given density and tocorrect granularity measurements by dividing thosemade in instrument density by the ratio of the instru-ment-to-diffuse density. This procedure would work

1 October 1982 / Vol. 21, No. 19 / APPLIED OPTICS 3597

D vs DD

Doa~- DD /

DII

/ D~ iD I

Do

Diffuse Density (DD)

Fig. 1. Hypothetical microdensitometer calibration curve illustratingthe difference between Q1 and Q1.

in general if the density ratio were constant for all dif-fuse densities or, equivalently, if the microdensitometerresponded linearly for all diffuse densities. The authorsstate that neither requirement is achieved exactly, al-though, in practice, the ratio may be sufficiently con-stant to obtain useful results.

Linear microdensitometers have been designed thatmeasure diffuse transmission density directly.5 ,6 Themain purpose in designing such microdensitometers isto eliminate problems of partial coherence in the opticalsystem and achieve a system that is linear in the sensethat the microdensitometer output is the convolutionof the intensity transmittance of the sample with theprojected source aperture. However, such a densi-tometer was not available to the authors or to any of thelaboratories with which they have intercompared re-sults, and the need to correct the measured NPS re-mains.

The nature of the error in an NPS corrected by a ratioof densities is illustrated in Fig. 1, which shows a hy-pothetical microdensitometer characteristic curve. Acorrection factor Q analogous to that described aboveis defined in terms of gross instrument density, DI, andgross diffuse density DD, as

Q = D/DD. (2)

QI is the slope of a linear operating characteristic de-fined over the range of -DD gross diffuse density.However, the slope of the microdensitometer charac-teristic may differ from that given by Q when mea-suring small fluctuations of density about DD. Sinceit is these fluctuations that must be used in Eq. (1), thecalibration of the microdensitometer must be in termsof the slope of the characteristic at the density of thefilm being analyzed. This slope is defined as

AD, ADD DD (3)

where the dot identifies an instantaneous or point valueof QI.

A relation linking Q and 01 can be derived if one

assumes that Qi does vary with DD and expresses thedifferential of DI as

ADi = QIADD + DDAQ. (4)

Then

AD = Q = Qi + DD A ADD ADD

(5)

or

1Ql = Ql 1t1 + D AQl .(6)

If QI is independent of DD, then QI = QI. However, ingeneral, using Q instead of QI to correct the NPS in-troduces a relative error of -2(DD/Ql)(AQI/ADD) intothe resulting NPS since the correction is applied to thesquared density fluctuations. The magnitude of thiserror will be estimated for a particular case in Sec.IV.

Ill. Methods

Film samples for the measurement of NPS wereprepared at the Kurt Rossmann Laboratories for Ra-diologic Image Research (K. Doi, director), U. Chicago,as part of a general screen-film imaging-characteristicintercomparison project.7 8 Kodak XRP films9 wereexposed with DuPont Hi-Plus and Detail screens9 to agross diffuse density of 0.98 and 0.97, respectively. Forthe intercomparisons described here, NPS measure-ments were performed on the same set of film samplesat the Bureau of Radiological Health, Division ofElectronic Products, Medical Physics Branch (BRH)and at the Los Alamos National Laboratory.

At BRH the film samples were scanned on a Perkin-Elmer PDS microdensitometer 9 equipped with 4X, 0.11N.A. objectives and a slit size of 15 X 588 tIm 2 at the filmplane. The method of NPS determination has beendescribed in detail.8 10,11 Factors of relevance to thepresent discussion are the effective slit length, whichwas extended to 5.88 mm by acquiring ten contiguousscans, and the standard error of the spectral estimates,

3598 APPLIED OPTICS / Vol. 21, No. 19 / 1 October 1982

which was +5%. A section of the 2-D NPS was esti-mated from linear, 1-D microdensitometric scans usingstandard methods.12 -'4 The calibration of the micro-densitometer was accomplished by performing aTchebycheff polynominal fit of the measurements of DIobtained from a scan of a sensitometric image (de-scribed below) vs the diffuse densities on the image;typically a fifth or sixth-order fit was used. The slopeQI of the curve fit at the average gross diffuse densityof the NPS image was used to convert the NPS to ex-press fluctuations of diffuse density by dividing theoriginal NPS by (QI)2 at each spatial frequency.

At Los Alamos the film samples were also scannedwith a Perkin-Elmer PDS microdensitometer usingeither 6X, 0.17 N.A. or 3X, 0.10 N.A. objectives.However, the 2-D NPS was obtained directly by 2-Dsampling of the image and application of a 2-D FFT.The high-frequency portion of the NPS was measuredby sampling with a 25 X 25-,um2 aperture in 12-Mim stepsin both directions. A total film area of 1.84 X 1.84 cm2

was segmented into 256 X 256-pixel 2 regions. Eachregion was windowed with a square Hanning windowand 2-D Fourier transformed. The average NPS fromthese thirty-six regions was corrected for the aperturesize and normalized using the known effect of the win-dowing function and the Qi measured for the micro-densitometer. Finally, the average radial frequencydependence was obtained from the 2-D NPS. The lowfrequencies were measured by sampling with a 100 X100-,um2 aperture in 40-Mm steps. A total film area of7.17 X 7.17 cm2 was segmented into forty-nine regions,each 256 X 256 pixels2 in size. The analysis then fol-lowed that used for the high frequencies. The low- andhigh-frequency NPS were in good agreement between2 and 6 cycles/mm and, arbitrarily, the low-frequencydata were used up to 4.4 cycles/mm and the high-fre-quency data above that. The standard deviation in thespectral densities is -5% at 0.39 cycles/mm and im-proves as the frequency increases since the number ofcontributing 2-D frequency bins increases. The cali-bration of the microdensitometer at Los Alamos wascarried out using the sensitometric image describedbelow.

Values of QI and QI vs DD were determined frommicrodensitometric scans of sensitometric imagesgenerated by inverse square, x-ray sensitometry usingradiographic intensifying screens with Kodak XRP film.The sensitometric image consisted of twenty-one stepsat increments of 0.1 on a logarithmic (base 10) x-rayexposure scale. Diffuse densities were measured on aMacbeth model TD404 densitometer9 calibrated witha National Bureau of Standards photographic steptablet, standard reference material 1008. The stepwedge was scanned with all apertures used for the NPSmeasurements and appropriate corrections applied toeach NPS.

IV. Results

Figure 2 shows plots of QI and QI vs DD for mea-surements made at BRH. The data for QI are typicalof those for the Callier Q factor expressed in terms of

2.0 r

*aa.da

1 -----QI

0 1.0 2.0 3.0

Diffuse Density (DD)4.0

Fig. 2. Q and Q vs diffuse density measured at BRH on KodakXRP film; sampling aperture = 15 X 588,um2, N.A. = 0.11.

2.0 r

<0C 1.0a

01 2

Diffuse Density3

Fig. 3. Q and QI vs diffuse density measured at Los Alamos onKodak XRP film: (a) QJ, 100-pim square aperture, 0.17 N.A.; (b) QJ,100-,um square aperture, 0.17 N.A.; (c) QI, 25-,um square aperture,

0.17 N.A.; (d) Qi, 25-,m square aperture, 0.10 N.A.

gross densities.3 The slope /QI/ADD of the linearportion of the plot between DD = 0.5 and 2.5 is -0.10.At DD = 1.0, the typical density of the noise images wehave examined, QI = 1.57. Hence, in Eq. (6), the term(DD/QI) (AQI/ADD) = -0.064. Correcting the NPS byQ' instead of Q' would underestimate the NPS by-13%. The value of QI used to correct the NPS was1.47.

QI and QI data measured at Los Alamos are plottedvs diffuse density in Fig. 3. These data were acquiredfor both sampling apertures-25 X 25 and 100 X 100Mm2 -and both numerical apertures-0.10 and0.17-used when measuring the NPS. QI has a densitydependence similar to that shown in Fig. 2. Changingthe sampling aperture (Fig. 3, curves b and c) was ob-served to have a greater effect on QI than changing thenumerical aperture (curves c and d). Apparently, in-

1 October 1982 / Vol. 21, No. 19 / APPLIED OPTICS 3599

I I I Iu

10

Ea3

z; O

Zoi

0.1

* Los Alamos- BRH

a) a1. 0

3; a

o E.tx Eo 0

z Da) .

3: I...

0.10.11.0

Spatial Frequency (mm-')10

Fig. 4. Comparison of NPS of Hi-Plus/XRP film sample measuredby BRH () and by Los Alamos (). BRH measurements used5.88-mm slit length; Los Alamos low-frequency measurements used

a square Hanning window with a FWHM of 5.1 mm.

creasing the illuminated areas of the film and the opticsby a factor of 16 by increasing the sampling aperture hasmore effect on reducing the specularity of the trans-mission than does increasing the acceptance area by afactor of -2.9 by increasing the N.A. Although only oneplot of QI vs DD is shown in Fig. 3, Q exceeded Q2I at DD= 1.0 for all sampling and numerical apertures. Thisexcess was 4% for the 100 X 100-m 2 sampling aper-ture and -7% for the 25 X 2 5 -Am2 aperture. Values ofQI used to correct the NPS were 1.46 for the largesampling aperture and 1.62 for the small one.

Figures 2 and 3 demonstrate that both Q and 0? aredensity dependent and, therefore, so is the error in theNPS corrected by Q instead of QI. At a particular lowdensity-DD = 0.5 in Fig. 2 and 0.8 in Fig. 3-QI equalsQI and no error is introduced. However, at lowerdensities the curves deviate rapidly. At higher densitiesthe curves are approximately parallel and slowly varyingover a range of 1.5 density units. At DD = 2.0, Qiexceeds QI by 12% in Fig. 2 and 11% in Fig. 3. NPS atthis density corrected by Q would be underestimatedby more than 20%.

A comparison between the two laboratories of NPSexpressed in diffuse density is shown in Fig. 4 for mea-surements on the Hi-Plus/XRP system and in Fig. 5 forthe Detail/XRP system. The agreement is very good.In the 0.4-5-cycles/mm frequency range the spectraagree to within 10%; at frequencies up to 10 cycles/mmthe agreement is to within 20%. It is expected that, atthe higher frequencies, frequency-dependent effects ofthe microdensitometers may begin to influence thespectra. Nevertheless, in a frequency range of impor-tance to the analysis of radiographic screen-filmimaging, the NPS was measured with very good preci-sion by two laboratories using independent methods ofdata acquisition and analysis.

I * Los Alamos* BRH

..I

1.0

Spatial Frequency (mm-')10

Fig. 5. Comparison of NPS of Detail/XRP film sample measuredby BRH () and by Los Alamos (). Measurement conditions are

as for Fig. 4.

V. Discussion

The need for an improvement in the method of ex-pressing NPS in terms of diffuse density became ap-parent after replacing the photomultiplier tube (PMT)in the BRH microdensitometer. When expressed interms of DI, NPS measured after replacing the PMTagreed, within the estimated statistical uncertainty,with the NPS measured previously on the same filmsample. However, the average DI over the scanned areaof a particular film sample was 1.54 with the old PMTand 1.44 with the new one. Since DD of the sample hadnot changed, this 6.7% shift in Q would produce a shiftof 13% in an NPS converted by division by QI.

During the course of expanding the screen-filmimaging-characteristics intercomparison study, theconcept of using the differential measurement of Q toconvert NPS to fluctuation of diffuse density evolved.Subsequently, measurements of the microdensitometriccharacteristic curve were made routinely, and the con-version of NPS was performed using QI as describedabove.

Measurements of QI made before and after changingthe PMT are shown in Fig. 6. At DD = 1.0, QI was 1.40before the change and 1.42 after-a 1.4% difference.The difference in the correction applied to the NPSwould be <3%. After both NPS were converted todiffuse density, the rms deviation between corre-sponding frequency elements over the range of 0.39-10.16 cycles/mm was 4.5%.

Naturally it is prudent to reexamine the character-istics of an instrument after replacing one of its majorcomponents. Being able to generate and analyze thecharacteristic curves with reasonable facility can pro-vide such information as well as provide additional in-sights about the behavior of the instrument. For ex-

3600 APPLIED OPTICS / Vol. 21, No. 19 / 1 October 1982

'o0

.I

. , I , ,., I . . . . .... .... II , , , , , , ,1I . . . ,

2.0

1 1.0I

Nl PM,,

New PM I

I I l IN

1 2DD

3 4

Fig. 6. ch vs diffuse density for characteristic curves measured be-fore and after changing PMT.

ample, by acquiring DI vs DD data at intervals over a25-h period, we established the warm-up characteristicsof the BRH microdensitometer. We found that theinstrument must remain on for at least 5 h before the DIand QI readings attain a plateau value for DD = 3.8. AtDD = 1.0, the readings were stable after 3 h.

Finally, it is apparent from Fig. 6 that Qi is not con-stant. Therefore, the DI to DD conversion is nonlinear,and ideally it should be performed prior to the Fouriertransformation given in Eq. (1). While this conversionwould be straightforward for digitally processed data,it may be difficult to implement in analog NPS systems.However, for DD in the 1.00 i 0.02 range that is typi-cally achieved, Qi has a range of -0.015 and a typicalmagnitude of 1.50 (for XRP film). Therefore, we con-sider it sufficiently accurate to apply the correction tothe NPS instead of to the density measurements. Thismanner of correction should also be readily adaptableto analog systems.

VI. Conclusion

Since film densities and their fluctuations measuredwith a microdensitometer will vary between instru-ments, it is desirable to convert an NPS expressed interms of instrument density to one expressed in termsof diffuse density for which standard measurementmethods exist. This can be done by establishing aninstrument density-to-diffuse density calibration curveof the microdensitometer and correcting NPS by thesquare of the slope QI of that curve at the diffuse den-sity of the examined image. Qi has been found to be-1.5; hence, the correction is by a factor of -2. NPSmeasured independently and by different methods attwo laboratories were found to be in good agreementwhen corrected to fluctuations of diffuse density by thismethod. We feel that establishment of the NPS mag-nitude with this technique will facilitate the intercom-parison of NPS between laboratories and contribute toa consensus methodology for NPS measurement.

We wish to acknowledge the contributions of Earl W.Denny, who prepared the sensitometric film samples,Penny R. Phillips and Mary M. Ryeom, who assistedwith the microdensitometry and data analysis, Dean F.Elbert, who prepared the illustrations, and Pamela L.Clatterbuck, who typed the manuscript. The workdone at Los Alamos was supported by the U.S. De-partment of Energy under contract W7405-ENG-36.

References1. J. C. Dainty and R. Shaw, Image Science (Academic, London

1974), p. 222.2. American National Standard Conditions for Diffuse and Doubly

Diffuse Transmission Measurements (Transmission Density),ANSI PH 2.19-1976, 8 Dec. 1975.

3. J. H. Altman, "Sensitometry of Black-and-White Materials," inThe Theory of the Photographic Process, T. H. James, Ed.(Macmillan, New York, 1977), p. 487.

4. H. C. Schmitt, Jr., and J. H. Altman, Appl. Opt. 9, 871 (1970).5. Ref. 1, p. 329.6. D. Hoeschen and W. Mirande, Photogr. Sci. Eng. 24, 259

(1980).7. J. M. Sandrik, R. J. Jennings, and R. F. Wagner, "Comparison

of Modulation Transfer Function, Noise Power Spectrum, andSensitometric Measurements of X-ray Screen-Film SystemsMade in Two Different Laboratories," Symposium on BiologicalEffects, Imaging Techniques, and Dosimetry of Ionizing Ra-diations, HHS Publication (FDA) 80-8126 (U.S. GPO, Wash-ington, DC, 1980), p. 181.

8. K. Doi, G. Holje, L. N. Loo, H. P. Chan, J. M. Sandrik, R. J. Jen-nings, and R. F. Wagner, MTFs and Wiener Spectra of Radio-graphic Screen-Film Systems, HHS Publication (FDA) 82-8187(U.S. GPO, Washington, DC, 1982).

9. Mention of commercial products, their sources, or their use inconnection with material reported herein is not to be construedas either an actual or implied endorsement of such products bythe Department of Health and Human Services.

10. R. F. Wagner, Med. Phys. 4, 157 (1977).11. J. M. Sandrik and R. F. Wagner, Appl. Opt. 20, 2795 (1981).12. R. Clark Jones, J. Opt. Soc. Am. 45, 799 (1955).13. K. Doi, Jpn. J. Appl. Phys. 5, 1213 (1966).14. Ref. 1, p. 276.

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