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Linearity and Optimum Working Density of Optical and Nuclear Emulsions
Linearity and Optimum Working Density of Optical and Nuclear Emulsions M. COHEN and E. KAHAN Department of Applied Physics. Imperial Colleye, Uniuergity of London, Englarid
INTRODUCTION I n a previous publication1 a comparison was made between Kodak IIa-0 optical emulsion, a type widely used in astronomy, and the Spectracon in conjunction with various types of electron-sensitive emulsions. This was done a t a density of unity, mainly because a t this sort of density the photographic plate presents an acceptable image t o the eye. However, this density is not the optimum working density in either the optical case or the electronographic case as elementary considerations show. Thus, for the linear portion of the H and 1) curve of the optical C, the symbols having their usual meanings. emulsion D = y log E Let E l and E2 be the maximum and minimum exposures in a given image. Then the signal height
+
If for the same image the exposure is increased by a factor of 2, say, then the new signal height
That is, as long as the exposure is such that the linear portion of the H and D curve is reached, further exposure is pointless, and since for a large class of photographic emulsions the noise is proportional to the square root of the density, further exposure only serves to increase the noise with no further increase in the signal. I n the electronographic case, the situation is different. Here the density is directly proportional to the exposure, and not the logarithm 68
54
M. COHEN AND E. K A H A N
of the exposure as in the optical case. Thus, providing that there is not a disproportionate increase in the noise, the signal-to-noiseratio should improve as the exposure for a given object is increased.
LINEARITY OF NUCLEAR EMULSIONS There has been a considerable difference of opinion in the past amongst workers using nuclear emulsions as to the extent of their linearity. In order to make some attempt t o clear up the situation a controlled experiment was carried out in which a single batch of Ilford G5 emulsion (10-pm emulsion on Melinex) was divided up and sent out to laboratories in different parts of the world. The development and fixing were carried out by all participants in an agreed, identical manner, i.e. development, 5 min in Ilford ID-19 ; stop bath, Kodak SB-5 for 30 sec ; fixing, 5 min in Kodak F-5. All of these processes were done in solutions at 20 “C and made up according to precise instructions. Four participants returned their exposed plates to be measured within a reasonable length of time and these results, as measured on a Joyce Loebl Mark IIICS microdensitometer, are shown in Fig. 1. Other participants did not expose the plates sent to them for a very considerable time and, as in the authors’ experience, there is some evidence for aged plates to be somewhat non-linear, these are not included in the results given here. Where the participants gave details of the conditions of their density measurements, i.e. numerical aperture of lenses used and slit size, these were adhered to as far as possible. The authors’ own measurements coincided very closely with those given by the participants, except in the case of the measurements by Griboval whose own measurements showed a considerable divergence from linearity. It is thought that this difference is almost certainly ascribable to the different microdensitometers used, since in this case in particular, the numerical aperture of the objective lens and the area of the scanning slit were the same in both the authors’ measurements and those of Griboval. It is worth noting in this context that the linearity of response of the Joyce Loebl microdensitometer is very easy to check and, providing that care is taken to remove all traces of stray light, optical densities up to 6 can be measured with ease and measurements up to a density of 8 are possible, but with reduced reliability, if suitable precautions are taken. As can be seen from the diagram, there is a strong tendency for the density/exposure relationship to be linear (in the case of Griboval’s results up to D w 7) even though the conditions of exposure varied from 27 kV to 40 kV. Variation of the type of developer, as was done
LINEARITY OF OPTICAL AND NUCLEAR EMULSIONS
55
by Griboval but for which no results are shown in Fig. 1, showed no appreciable change. A peculiar result was obtained by Duchesne. Although a group of 6 plates in all were exposed and processed together, only 3 of these proved to have a linear response, the most nearly linear and least linear results being reproduced in Fig. 1 .
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Grlbovol (Leveloped offer 2 4 n) C Gnboval (Immediate development) %
+ Kahon
Kron CTY Duchesne iShorles1 llneor range) : Duchesne (Longest Ilneor range) Q
Exposure (arbitrary units)
Fro. 1. I)ensity/exposurerelationship f i r Ilford GK emulsion. Kahan, 40 keV electrons through mica; Griboval, 40 keV electrons direct; Kron, z 3 0 keV electrons direct; Duchesne, 27 keV electrons direct.
56
M. COHEN AND E. KAHAN
From these results it would appear that although on the whole Ilford G5 emulsion can be relied upon t o have a linear response, where accurate quantitative work is contemplated each plate must be individually calibrated. The smallest change in density that can be detected with certainty using the Joyce Loebl microdensitometer is about 0.002 and the highest, approximately 7 or 8 ; the dynamic range of the Spectracon, or, indeed, of any other electronographic device when used in this way, is thus a little more than thre2 orders of magnitude.
SIGNALTRANSFER It has been explained in the introduction that for an emulsion having a linear response the signal, which is in fact D , - D,, should increase linearly as the rccorded density incrcases. This change in Oh
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FIG.2. Signal-transfer function as a function of density for Kodak I I a - 0 emulsion.
signal with density waa measured as a function of spatial frequency using a sine-wave grating and, for lack of a better term, is here called the signal transfer. The results for Kodak I I a - 0 emulsion, the Spectracon and Ilford G5 emulsion (10-pm emulsion on Melinex) and the Spectracon and Ilford
57
LINEARITY OF OPTICAL A N D NUCLEAR EMULSIONS
L4 stripping emulsion (5-pn1cniulsion on 10ym gelatine) are shown in Pigs. 2, 3 and 4, respectively. The nuclear emulsions were processed as described in the section dealing with linearity of G5 emulsion and the IIa-0 emulsion was developed for I U min in Johnson Solufin Developer, placed in SB-5 stop bath for 30 see and fixed in Kodak F-5 fixer for 15 min.
1
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Cycles/mm
Fro. 3. Signal-transfer function as a function of dronity for the (Spectracon combination.
+05)
It can be seen from Fig. 2 that for I l a - 0 emulsion, as higher densities are reached (greater than 0.9 in the diagram since values for average densities between 0.6 and 0.9 were not measured) the corresponding increase in signal is very small, zero in fact for very low spatial frcquencies. For G5 emulsion (Fig. 3), the Mignal-transfer function starts to deteriorate a t densities greater than 2 but this is because the particular batch of emulsion used was not linear up to the density expected. For the L4 emulsion (Fig. 4), the expected linear increase of signal with average density is found, particularly a t the lower spatial frequencies. The fall-off in response a t the higher spatial frequencies is probably due t o the reduced response of the microdensitometer a t high densities.
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M. COHEN AND E. KAHAN
It should be noted that the values of signal transfer given in the diagrams have not been corrected for slit width or projector lens response. As far as these measurements are concerned only comparative values are necessary and the constancy of this was assured by keeping all conditions constant for each of the measurements.
i
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FIG.4. Signal-transferfunction EB a function of density for the (Spectracon combinstion.
+ L4)
NOISEPOWER The zero frequency noise power for the three systems measured is shown in Fig. 5. This parameter is in fact the product of the scanning area and the mean square deviation in density and, providing that the noise-power spectrum of the emulsion is flat over the frequency response of the measuring apparatus,a it is independent of the scanning area. The area used in these measurements was 2000 pm2 so that the mean square deviation for any other area can easily be calculated. Approximately 900 independent measurements were made at each individual density to calculate these results.
LINEARITY O F OPTICAL AND NUCLEAR EMULSIONS
59
It is immediately apparent from the diagram that for both H a - 0 and L4 emulsions the noise power increases linearly with the density as expected. However, in the case of G5 emulsion, the noise-power increases extremely rapidly with density. This has been found to be so for G5 emulsion by Brand3 when exposing this emulsion t o electrons but not for optical exposure, although this type of noise characteristic has also been found for optical emulsion^.^ It is thought that the rapid
/
Density (0)
FIG.5. Zero-frequencynoise power versus density for Kodak 11s-0optical emulsion and the Spectraoon in conjunction with Ilford G5 and L4 emulsions. Plotted values of noise power for IIe-0 and (Spectracon L4) are actual values x10 and x l 0 0 rcspectively.
+
increase in the noise-power of G5 emulsion with density is due t o grain clumping at these densities. This would appear t o be borne out by the low frequency peaking in the noise-power spectrum shown in Fig. 6. It should be noted that noise-power measurements on nuclear emulsions exposed t o an electronographic device in the normal manner are fraught with difficulty because of the non-uniform response of the photocathode. To overcome this, only those parts of the trace in which there appeared to be no photocathode non-uniformities were accepted for noise-power measurements. Although this was A fairly easy task as far as the L4 emulsion was concerned since the emulsion noise and
60
E. KAHAN
M. COHEN AND
photocathode non-uniformities could be distinguished with a fair degree of certainty, with the G5 emulsion both effects were of a similar nature and it was difficult t o separate them, However, when the various measuring parameters have been taken into account, the present measurements agree reasonably well with the authors’ own previous results and those of Brand. However, in the case of the L4 emulsion, the results obtained here are somewhat lower than have been obtained previously by the authors and could possibly be the result of over-careful selection of the pieces of recording taken for measurement. They are, nevertheless, within the bounds of values calculated on elementary grain statistics.
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FIQ.6. Noise power spectrum for the (Spectracon + G 6 ) combination at a mean density of 2-86.
It was thought that photocathode non-uniformity was not an inherent feature of the system because this is a fixed pattern type of noise and in principle it can be measured and eliminated from subsequent measurements. Further, the extent of this non-uniformity varies widely from tube t o tube and figures quoted for one tube would bear little relationship t o values for another. For this reason, noise arising from this source was eliminated as far as possible in this work.
61
LINEARITY OF OPTICAL A N D NITCLEAR EMIX3IOP;S
SIGNAL-TO-NOISE RATIO The values for signal-to-noise rtatio given here are based upon the assumption that the noise-power spectrum of the emulsion used is flat. This is fairly well established at densities of about unity1, and t o verify that it is still so at higher densities, an analysis was made of the noise-power spectrum for G5 ernulsion exposed t o a mean density of 2-85, i.e. =3. This is shown in Fig. 6 where the values given are absolute, corrections for the slit width and length having been made. The graph shown has been smoothed using a method due to Harln, quoted by Blackman and Tukey6 and is the result of 50 separate tracings, each yielding 25 independent sampling points. As can be seen from the diagram, t h r spectrum is not flat, but fBlls fairly sharply in the low spatial-frequc.nc.y region and then tends to flatten off. This would tend to bear out the presence of grab cluniping mentioned previously. However, the fall-off over the spatial frequencies concerned here (up t o 40 cycleB/rnm for G5) is only about 25% and also density 3 is in any case well ahove the optimum working density of G.5. The zero noise-power of L4 increases directly with the density. This indicates that the distribution of grains is still n random process,
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Denstry a b o v e fog l e v e l (f og level 0 14)
b h . 7. Sigxral-to-1..m.,.-nolspratio for Kodalc J l a - 0 rmul.iion as w. funrtion of frequency and clunsity above fog level ( D : 0.14). Valitr-< arc for an arbitrary constant, signal, thr same value being U H for ~ F i p . 7, X ant1 9.
62
M. COHEN AND E. KAHAN
even at fairly high densities so that the assumption of a flat power spectrum would appear to be justified. No attempt was made to measure the noise-power spectrum over a range of densities because of the enormous amount of work involved. The signal-to-noise ratio, plotted as signal/r.m.s. noise, for IIa-0 emulsion and the (Spectracon G5) and (Spectracon L4) combinations for the same arbitrary, constant signal are shown in Figs. 7, 8 and 9, respectively. As can be seen from Fig. 7, the signa1-to-r.m.s.noise ratio peaks in the region of 0435D for I I a - 0 emulsion. This density is a little higher than the usually accepted figure (0.5 to 0.6 D) and is probably due to the slow, ultra-fine-grain developer used. The curve for zero spatial frequency on the right of the peak follows the (signal)-'I2 relationship implied in the introduction to this paper and the dotted extension to the curve is the path it would follow if the H and D curve were linear over its entire length. The (Spectracon G5) combination (Fig. 8) peaks at about 1.9 D. As
+
+
+
Density D
+
Fro. 8. Signal-to-r.m.8.-noiseratio for the (Spectracon G6) Combination. The individual points are Hhown for zero spatial frequency only, for the other values of spatial frequency the experimental points lie on the curves.
LINEARITY OF OPTICAL AND NUCLEAR EMULSIONS
63
was pointed out earlier, this particular batch of emulsion turned out to be linear over a smaller region than usual ; had this not been so, the maximum signal-to-r.m.s.-noise ratio would have occurred a t a density a little higher than 1 a 9 and its value would have been correspondingly a little greater. The signal-to-r,m.s.-noiseratio for the (Spectracon + L4) combination (Fig. 9), which had the most nearly linear densitylexposure relationship of the systems compared, increased for zero spatial frequency over the entire range of densities measured, i.e. up to D w 5. It is suspected that the fall-off a t high densities for the higher spatial frequencies is due t o the inadequacy of the microdensitometer at these densities. CONCLUSIONS
Comparing the three systems, it can be seen that, except at zerofrequency, an optimum recording taken on IIa-0 emulsion would be roughly comparable with that taken by means of the Spectracon +G5 combination. However, because of the vastly superior speed of the latter, a comparable image would be obtained in a fraction of the time necessary for direct recording. As far as the (Spectracon L4) combination is concerned, the signalto-r.m.s.-noise values obtained a t optimum density are about 10 times higher than those of the other two systems over all spatial frequencies. It is thus obvious that when it is desired t o detect extremely weak signals, and this is presumably when an image tube would be used in any case, a fine-grain emulsion such as L4 should be used even though it is much slower. It would in fact appear from the results obtained here that, even when the exposure time is limited t o some fixed period, and even for a speed ratio of G5 t o L4 emulsion of 10: 1, the image obtained on L4 would be at least comparable in information content with that obtained on G5. For instance, if the exposure t>imewere such as t o blacken G5 emulsion t o an average density of about 2, the signal-to-r.m.s.-noise ratio for the 10 cycles/mm curve in Fig. 8 would be about 0.19. On L4 emulsion, this would correspond t o a density of about 0.2 and although it is difficult t o obtain anything like a precise value from the curves shown in Fig. 9, the signal-to-r.m.s. noise value does not appear t o have fallen much below 0.19. This is in contrast t o the authors’ previous findings where comparisons were only made at a density of unity. This, combined with its more reliable linearity, would tend t o make this emulsion superior to 0 5 emulsion in almost all respects. Speed considerations have been deliberately omitted from the assessment of tfhe relative merits of the systems measured because of the wide variation found from batch t80batch of emulsion and, in fact,
+
64
M. COHEN AND E. KAHAN
from plate to plate in the same batch. Just how great these variations can be is demonstrated by the results obtained by Duchesne and Bijaoui.’
FIQ.9.
ACKNOWLEDGMENTS The authors would like to thank Professor J. D. McGee, F.R.S., for the continuod help and encouragoment given during the course of this work. The cooperation of Dr. M. Duchesne, Dr. P.J. Criboval and Dr. G. Kron in obtaining the linearity measurements on G5 emulsion is greatly appreciated. The micro. clensitometor used for theso measurements was provided by the Royal Society, whose help is gratefully acknowledged.
REFERENCES 1. Kahan, E. and Cohen, M., In “Adv. E.E.P.”, Vot. 28B, p. 725 (1969). 2. Jones, R . C., J. Opt. Soc. Amer. 45, 799 (1965). 3. Brand, 1’. W. J. L., Ph.D. Thesis, University of Edinburgh (1967).
LINEARITY OF OPTICAL AND NITCLEAR EMVLSIONS
65
4. Shaw, It., Photogrrkphic Science &! Engineering, 6, 281 ( I 962). 5. Beckman, J. E.. In. “Adv. E.E.P.”, Vol. 22A, p. 369 (1966). 6. Blackmati. 13. 13. a i d Titkey. J. W., “‘I’hc Mcasiiremrnt, of Power Spectra”, p. 171. Dovcr Publications, New York (1959). 7. Diichest~e,M. and Hijaoui, A., NOUV.R e v . Opt. A p p l . 1, 287 (1970).
DIscussIoN K. u. ARLES: Were the data points shown in your density versus exposure
relationships for tho GS tests original measuronient,~by the investigators or your n~easurenients? E. KAHAN : The data points shown were my mewiired values but, except for Griboval’s measurements, agreed very closely with the part,icipent’s own findings. I n the case of Griboval’s results, whereas my own measurements showod a density versus exposure relationship which was linear over a considerablo range, his own measurement.s on the same plates shom7ed virtually no linear relationship what,soever. It is thought that this discrepancy is due to the different, miorodensitorneters used. J. D. MCGEE: There appears to be 1% tliffownce in kind rat,her than degree between L4 and G5 in their S/Ar characteristics. Any explanation? E. K A H A N : The difference botween L4 and G5 emulsions is a combination of the smaller line-spread in the L4 emulsion and its lower noise value. This shows itself as a “cleaner” appearance of the L4 emulsiori when exposures of similar density are viewed by the naked eye.
P.E.I.D.
INTRODUCTION I n a previous publication1 a comparison was made between Kodak IIa-0 optical emulsion, a type widely used in astronomy, and the Spectracon in conjunction with various types of electron-sensitive emulsions. This was done a t a density of unity, mainly because a t this sort of density the photographic plate presents an acceptable image t o the eye. However, this density is not the optimum working density in either the optical case or the electronographic case as elementary considerations show. Thus, for the linear portion of the H and 1) curve of the optical C, the symbols having their usual meanings. emulsion D = y log E Let E l and E2 be the maximum and minimum exposures in a given image. Then the signal height
+
If for the same image the exposure is increased by a factor of 2, say, then the new signal height
That is, as long as the exposure is such that the linear portion of the H and D curve is reached, further exposure is pointless, and since for a large class of photographic emulsions the noise is proportional to the square root of the density, further exposure only serves to increase the noise with no further increase in the signal. I n the electronographic case, the situation is different. Here the density is directly proportional to the exposure, and not the logarithm 68
54
M. COHEN AND E. K A H A N
of the exposure as in the optical case. Thus, providing that there is not a disproportionate increase in the noise, the signal-to-noiseratio should improve as the exposure for a given object is increased.
LINEARITY OF NUCLEAR EMULSIONS There has been a considerable difference of opinion in the past amongst workers using nuclear emulsions as to the extent of their linearity. In order to make some attempt t o clear up the situation a controlled experiment was carried out in which a single batch of Ilford G5 emulsion (10-pm emulsion on Melinex) was divided up and sent out to laboratories in different parts of the world. The development and fixing were carried out by all participants in an agreed, identical manner, i.e. development, 5 min in Ilford ID-19 ; stop bath, Kodak SB-5 for 30 sec ; fixing, 5 min in Kodak F-5. All of these processes were done in solutions at 20 “C and made up according to precise instructions. Four participants returned their exposed plates to be measured within a reasonable length of time and these results, as measured on a Joyce Loebl Mark IIICS microdensitometer, are shown in Fig. 1. Other participants did not expose the plates sent to them for a very considerable time and, as in the authors’ experience, there is some evidence for aged plates to be somewhat non-linear, these are not included in the results given here. Where the participants gave details of the conditions of their density measurements, i.e. numerical aperture of lenses used and slit size, these were adhered to as far as possible. The authors’ own measurements coincided very closely with those given by the participants, except in the case of the measurements by Griboval whose own measurements showed a considerable divergence from linearity. It is thought that this difference is almost certainly ascribable to the different microdensitometers used, since in this case in particular, the numerical aperture of the objective lens and the area of the scanning slit were the same in both the authors’ measurements and those of Griboval. It is worth noting in this context that the linearity of response of the Joyce Loebl microdensitometer is very easy to check and, providing that care is taken to remove all traces of stray light, optical densities up to 6 can be measured with ease and measurements up to a density of 8 are possible, but with reduced reliability, if suitable precautions are taken. As can be seen from the diagram, there is a strong tendency for the density/exposure relationship to be linear (in the case of Griboval’s results up to D w 7) even though the conditions of exposure varied from 27 kV to 40 kV. Variation of the type of developer, as was done
LINEARITY OF OPTICAL AND NUCLEAR EMULSIONS
55
by Griboval but for which no results are shown in Fig. 1, showed no appreciable change. A peculiar result was obtained by Duchesne. Although a group of 6 plates in all were exposed and processed together, only 3 of these proved to have a linear response, the most nearly linear and least linear results being reproduced in Fig. 1 .
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Grlbovol (Leveloped offer 2 4 n) C Gnboval (Immediate development) %
+ Kahon
Kron CTY Duchesne iShorles1 llneor range) : Duchesne (Longest Ilneor range) Q
Exposure (arbitrary units)
Fro. 1. I)ensity/exposurerelationship f i r Ilford GK emulsion. Kahan, 40 keV electrons through mica; Griboval, 40 keV electrons direct; Kron, z 3 0 keV electrons direct; Duchesne, 27 keV electrons direct.
56
M. COHEN AND E. KAHAN
From these results it would appear that although on the whole Ilford G5 emulsion can be relied upon t o have a linear response, where accurate quantitative work is contemplated each plate must be individually calibrated. The smallest change in density that can be detected with certainty using the Joyce Loebl microdensitometer is about 0.002 and the highest, approximately 7 or 8 ; the dynamic range of the Spectracon, or, indeed, of any other electronographic device when used in this way, is thus a little more than thre2 orders of magnitude.
SIGNALTRANSFER It has been explained in the introduction that for an emulsion having a linear response the signal, which is in fact D , - D,, should increase linearly as the rccorded density incrcases. This change in Oh
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FIG.2. Signal-transfer function as a function of density for Kodak I I a - 0 emulsion.
signal with density waa measured as a function of spatial frequency using a sine-wave grating and, for lack of a better term, is here called the signal transfer. The results for Kodak I I a - 0 emulsion, the Spectracon and Ilford G5 emulsion (10-pm emulsion on Melinex) and the Spectracon and Ilford
57
LINEARITY OF OPTICAL A N D NUCLEAR EMULSIONS
L4 stripping emulsion (5-pn1cniulsion on 10ym gelatine) are shown in Pigs. 2, 3 and 4, respectively. The nuclear emulsions were processed as described in the section dealing with linearity of G5 emulsion and the IIa-0 emulsion was developed for I U min in Johnson Solufin Developer, placed in SB-5 stop bath for 30 see and fixed in Kodak F-5 fixer for 15 min.
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Fro. 3. Signal-transfer function as a function of dronity for the (Spectracon combination.
+05)
It can be seen from Fig. 2 that for I l a - 0 emulsion, as higher densities are reached (greater than 0.9 in the diagram since values for average densities between 0.6 and 0.9 were not measured) the corresponding increase in signal is very small, zero in fact for very low spatial frcquencies. For G5 emulsion (Fig. 3), the Mignal-transfer function starts to deteriorate a t densities greater than 2 but this is because the particular batch of emulsion used was not linear up to the density expected. For the L4 emulsion (Fig. 4), the expected linear increase of signal with average density is found, particularly a t the lower spatial frequencies. The fall-off in response a t the higher spatial frequencies is probably due t o the reduced response of the microdensitometer a t high densities.
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M. COHEN AND E. KAHAN
It should be noted that the values of signal transfer given in the diagrams have not been corrected for slit width or projector lens response. As far as these measurements are concerned only comparative values are necessary and the constancy of this was assured by keeping all conditions constant for each of the measurements.
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FIG.4. Signal-transferfunction EB a function of density for the (Spectracon combinstion.
+ L4)
NOISEPOWER The zero frequency noise power for the three systems measured is shown in Fig. 5. This parameter is in fact the product of the scanning area and the mean square deviation in density and, providing that the noise-power spectrum of the emulsion is flat over the frequency response of the measuring apparatus,a it is independent of the scanning area. The area used in these measurements was 2000 pm2 so that the mean square deviation for any other area can easily be calculated. Approximately 900 independent measurements were made at each individual density to calculate these results.
LINEARITY O F OPTICAL AND NUCLEAR EMULSIONS
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It is immediately apparent from the diagram that for both H a - 0 and L4 emulsions the noise power increases linearly with the density as expected. However, in the case of G5 emulsion, the noise-power increases extremely rapidly with density. This has been found to be so for G5 emulsion by Brand3 when exposing this emulsion t o electrons but not for optical exposure, although this type of noise characteristic has also been found for optical emulsion^.^ It is thought that the rapid
/
Density (0)
FIG.5. Zero-frequencynoise power versus density for Kodak 11s-0optical emulsion and the Spectraoon in conjunction with Ilford G5 and L4 emulsions. Plotted values of noise power for IIe-0 and (Spectracon L4) are actual values x10 and x l 0 0 rcspectively.
+
increase in the noise-power of G5 emulsion with density is due t o grain clumping at these densities. This would appear t o be borne out by the low frequency peaking in the noise-power spectrum shown in Fig. 6. It should be noted that noise-power measurements on nuclear emulsions exposed t o an electronographic device in the normal manner are fraught with difficulty because of the non-uniform response of the photocathode. To overcome this, only those parts of the trace in which there appeared to be no photocathode non-uniformities were accepted for noise-power measurements. Although this was A fairly easy task as far as the L4 emulsion was concerned since the emulsion noise and
60
E. KAHAN
M. COHEN AND
photocathode non-uniformities could be distinguished with a fair degree of certainty, with the G5 emulsion both effects were of a similar nature and it was difficult t o separate them, However, when the various measuring parameters have been taken into account, the present measurements agree reasonably well with the authors’ own previous results and those of Brand. However, in the case of the L4 emulsion, the results obtained here are somewhat lower than have been obtained previously by the authors and could possibly be the result of over-careful selection of the pieces of recording taken for measurement. They are, nevertheless, within the bounds of values calculated on elementary grain statistics.
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FIQ.6. Noise power spectrum for the (Spectracon + G 6 ) combination at a mean density of 2-86.
It was thought that photocathode non-uniformity was not an inherent feature of the system because this is a fixed pattern type of noise and in principle it can be measured and eliminated from subsequent measurements. Further, the extent of this non-uniformity varies widely from tube t o tube and figures quoted for one tube would bear little relationship t o values for another. For this reason, noise arising from this source was eliminated as far as possible in this work.
61
LINEARITY OF OPTICAL A N D NITCLEAR EMIX3IOP;S
SIGNAL-TO-NOISE RATIO The values for signal-to-noise rtatio given here are based upon the assumption that the noise-power spectrum of the emulsion used is flat. This is fairly well established at densities of about unity1, and t o verify that it is still so at higher densities, an analysis was made of the noise-power spectrum for G5 ernulsion exposed t o a mean density of 2-85, i.e. =3. This is shown in Fig. 6 where the values given are absolute, corrections for the slit width and length having been made. The graph shown has been smoothed using a method due to Harln, quoted by Blackman and Tukey6 and is the result of 50 separate tracings, each yielding 25 independent sampling points. As can be seen from the diagram, t h r spectrum is not flat, but fBlls fairly sharply in the low spatial-frequc.nc.y region and then tends to flatten off. This would tend to bear out the presence of grab cluniping mentioned previously. However, the fall-off over the spatial frequencies concerned here (up t o 40 cycleB/rnm for G5) is only about 25% and also density 3 is in any case well ahove the optimum working density of G.5. The zero noise-power of L4 increases directly with the density. This indicates that the distribution of grains is still n random process,
0 30
I
0 25 0 .c
P
;0 2 0 -
0 I
0
0
I
I
0 5
I
10
I
15
1
20
I
Denstry a b o v e fog l e v e l (f og level 0 14)
b h . 7. Sigxral-to-1..m.,.-nolspratio for Kodalc J l a - 0 rmul.iion as w. funrtion of frequency and clunsity above fog level ( D : 0.14). Valitr-< arc for an arbitrary constant, signal, thr same value being U H for ~ F i p . 7, X ant1 9.
62
M. COHEN AND E. KAHAN
even at fairly high densities so that the assumption of a flat power spectrum would appear to be justified. No attempt was made to measure the noise-power spectrum over a range of densities because of the enormous amount of work involved. The signal-to-noise ratio, plotted as signal/r.m.s. noise, for IIa-0 emulsion and the (Spectracon G5) and (Spectracon L4) combinations for the same arbitrary, constant signal are shown in Figs. 7, 8 and 9, respectively. As can be seen from Fig. 7, the signa1-to-r.m.s.noise ratio peaks in the region of 0435D for I I a - 0 emulsion. This density is a little higher than the usually accepted figure (0.5 to 0.6 D) and is probably due to the slow, ultra-fine-grain developer used. The curve for zero spatial frequency on the right of the peak follows the (signal)-'I2 relationship implied in the introduction to this paper and the dotted extension to the curve is the path it would follow if the H and D curve were linear over its entire length. The (Spectracon G5) combination (Fig. 8) peaks at about 1.9 D. As
+
+
+
Density D
+
Fro. 8. Signal-to-r.m.8.-noiseratio for the (Spectracon G6) Combination. The individual points are Hhown for zero spatial frequency only, for the other values of spatial frequency the experimental points lie on the curves.
LINEARITY OF OPTICAL AND NUCLEAR EMULSIONS
63
was pointed out earlier, this particular batch of emulsion turned out to be linear over a smaller region than usual ; had this not been so, the maximum signal-to-r.m.s.-noise ratio would have occurred a t a density a little higher than 1 a 9 and its value would have been correspondingly a little greater. The signal-to-r,m.s.-noiseratio for the (Spectracon + L4) combination (Fig. 9), which had the most nearly linear densitylexposure relationship of the systems compared, increased for zero spatial frequency over the entire range of densities measured, i.e. up to D w 5. It is suspected that the fall-off a t high densities for the higher spatial frequencies is due t o the inadequacy of the microdensitometer at these densities. CONCLUSIONS
Comparing the three systems, it can be seen that, except at zerofrequency, an optimum recording taken on IIa-0 emulsion would be roughly comparable with that taken by means of the Spectracon +G5 combination. However, because of the vastly superior speed of the latter, a comparable image would be obtained in a fraction of the time necessary for direct recording. As far as the (Spectracon L4) combination is concerned, the signalto-r.m.s.-noise values obtained a t optimum density are about 10 times higher than those of the other two systems over all spatial frequencies. It is thus obvious that when it is desired t o detect extremely weak signals, and this is presumably when an image tube would be used in any case, a fine-grain emulsion such as L4 should be used even though it is much slower. It would in fact appear from the results obtained here that, even when the exposure time is limited t o some fixed period, and even for a speed ratio of G5 t o L4 emulsion of 10: 1, the image obtained on L4 would be at least comparable in information content with that obtained on G5. For instance, if the exposure t>imewere such as t o blacken G5 emulsion t o an average density of about 2, the signal-to-r.m.s.-noise ratio for the 10 cycles/mm curve in Fig. 8 would be about 0.19. On L4 emulsion, this would correspond t o a density of about 0.2 and although it is difficult t o obtain anything like a precise value from the curves shown in Fig. 9, the signal-to-r.m.s. noise value does not appear t o have fallen much below 0.19. This is in contrast t o the authors’ previous findings where comparisons were only made at a density of unity. This, combined with its more reliable linearity, would tend t o make this emulsion superior to 0 5 emulsion in almost all respects. Speed considerations have been deliberately omitted from the assessment of tfhe relative merits of the systems measured because of the wide variation found from batch t80batch of emulsion and, in fact,
+
64
M. COHEN AND E. KAHAN
from plate to plate in the same batch. Just how great these variations can be is demonstrated by the results obtained by Duchesne and Bijaoui.’
FIQ.9.
ACKNOWLEDGMENTS The authors would like to thank Professor J. D. McGee, F.R.S., for the continuod help and encouragoment given during the course of this work. The cooperation of Dr. M. Duchesne, Dr. P.J. Criboval and Dr. G. Kron in obtaining the linearity measurements on G5 emulsion is greatly appreciated. The micro. clensitometor used for theso measurements was provided by the Royal Society, whose help is gratefully acknowledged.
REFERENCES 1. Kahan, E. and Cohen, M., In “Adv. E.E.P.”, Vot. 28B, p. 725 (1969). 2. Jones, R . C., J. Opt. Soc. Amer. 45, 799 (1965). 3. Brand, 1’. W. J. L., Ph.D. Thesis, University of Edinburgh (1967).
LINEARITY OF OPTICAL AND NITCLEAR EMVLSIONS
65
4. Shaw, It., Photogrrkphic Science &! Engineering, 6, 281 ( I 962). 5. Beckman, J. E.. In. “Adv. E.E.P.”, Vol. 22A, p. 369 (1966). 6. Blackmati. 13. 13. a i d Titkey. J. W., “‘I’hc Mcasiiremrnt, of Power Spectra”, p. 171. Dovcr Publications, New York (1959). 7. Diichest~e,M. and Hijaoui, A., NOUV.R e v . Opt. A p p l . 1, 287 (1970).
DIscussIoN K. u. ARLES: Were the data points shown in your density versus exposure
relationships for tho GS tests original measuronient,~by the investigators or your n~easurenients? E. KAHAN : The data points shown were my mewiired values but, except for Griboval’s measurements, agreed very closely with the part,icipent’s own findings. I n the case of Griboval’s results, whereas my own measurements showod a density versus exposure relationship which was linear over a considerablo range, his own measurement.s on the same plates shom7ed virtually no linear relationship what,soever. It is thought that this discrepancy is due to the different, miorodensitorneters used. J. D. MCGEE: There appears to be 1% tliffownce in kind rat,her than degree between L4 and G5 in their S/Ar characteristics. Any explanation? E. K A H A N : The difference botween L4 and G5 emulsions is a combination of the smaller line-spread in the L4 emulsion and its lower noise value. This shows itself as a “cleaner” appearance of the L4 emulsiori when exposures of similar density are viewed by the naked eye.
P.E.I.D.