Double-Beam Densitometer and Comparator ROBERT O'B. CARPENTER, Baird Associates, h e . , Cambridge, Mars., AND
JOHN U. WHITE, W h i t e Development Co., Stamford, Conn. A double-beam densitometer is described which has a servo-type automatic balanoing system, a projection comparator, and a scale linear in density fmm 0 to 2.0. This is done by means of preoision logarithmio aperture and a special electronio circuit, which provides a servo-loop gain, a atahility, and a precision of f0.003 density unit, all of which are independent of the density being measured.
I
N 1941 Baird ( 1 ) described a nonrecording densitometer for line spectra utilizing a double-beam, optically balanced arrangement with two vacuum photocells in a bridge circuit to indicate null balance. I n 1946 Carpenter ( 2 ) described a modification of the same instrument in which a light chopper alternates the two beams on a single photomultiplier with a vacuum tube voltmeter to indicate null signal a t the chopping frequency. The use of the optical null method in densitometry has the advantages of inherent stability and freedom from drift. The measurements do not depend directly on the constancy of a photoemissive cathode or the accuracy of a linear electronic ssnplifier. This principle has had extensive application in various photometric devices in recent yoartrs. In the present densitometer the optical null and chopping s y s tems have been combined with an automatic balancing meehanism to make an indicating instrument with terminals for direct connection to B recorder. A second projection system and plateholder have also been added to make the instrument a projection comparator as well as a densitometer. The final indication is presented in density rather than transmittance units with an accurately machined variable aperture as the ultimate standard for measurement. Density units me eonvenient heenuse over large concentration ranges the other murees of error which enter into a quantitative spectrochemical determination, source fluctuations, plate sensitivity fluctuations, and granularity noise, lead to approximately constant error on a lin-
of the instrument's.
Figure 1 shc parts.
The densitometer is built ou a cast duminum hase 26.5 inches long by 18.5 inches wide. This base houses the controls, light sources, and most of the other parts. The projection lenses are in the overhanging arm. The screen, scale, and operating range meter are together under the hood, which also contains the phototube. The plate to be measured lies on the movable platehplder a t the front of the main carriage; the comparison plate IS in back. Each plateholder has independent rack and pinion vertical adjustments for selecting different spectra. The usable area of each plate is 3.5 by 9.25 inches. The holders w e standard for 4 X 10 plates, but 2 X 10 or 4 X 14 can be handled without change. For scanning the speotrum, both plateholders move to ether on the same carriage, remaining in register. A manual trive advances the plate 2 mm. far one revolution of the graduated knob. The scale divisions are 0.02 mm. urith a vernier reading to 2 microns. For automatic scanning a motor and g e a box give two speeds, 5 and 25 microns per second. With the indieator rep o m e time of 2 seconds, these speeds are about right for scanning spectra. taken with 40- and 200-micron slits, respectively. A friction clutch prevents injury to any of the parts and a differential avoids the necessity of disconnecting one drive when another is being used. Thus while the automatic scanning motor is operating, the carriage may be driven slowly by the manual knob, or very rapidly by pushing the carriage by hand. OPTICAL SYSTEM
:he exact arrangement of the optical system is shown in Figure n the sample beam light from a 50-cp. headlight bulb, B1, passes through a condensing system, C1, to a, Banseh and Lamb Microtessar projection lens of 32-mm. focal length, PL1. A plate, F1, is illuminated over an area 0.6 inch long and adjustable from 0.1 to 0.2 inch wide. This is projected a t 1OX mqnification on a. 5-inch screen. The excess length of the projected spectrum is enough to illuminate the whale screen even when prism PI is rotated a few degrees about a vertical axis. This variable is used to rotate the image of the spectrum on the acreen for exact alignment of it8 lines with the slit. -1n the center of the screen, S, is a fixed slit 0.13 mm . wide and 15 mm. long, corresponding t.o a used ?rea of plate 13 X 1500 microns, or 20,000 square nncrons. Operation is possible with any slit havirig are&greater than 2000 square microns. A good rule is that the densitometer slit should be abobault one half the spectrogram line widths, and the horizontal scan a t a rate of about one half the densitometer slit in one response time, 2 seconds for this densitometer. iediately following the slit is a field lens icuses rtn image of the projection lens on ilar aperture 0.050 inch in diameter just it of the 1P21 electron multiplier tube. 'This aperture is the limiting stop in the first b e a m , excluding from t h e detector a l l light that did not come from the projection lens. This makes the instrument insensitive t o
1474
ANALYTICAL CHEMISTRY
normal room light, and reduoes the amount of scatter?-' 1:-L4 measured. The comparison beam for projecting the standard plate lar ta the sample beam, hut has one half the focal len&b,,, uuw same magnification, the same area of illuminated spectrum, and hence twice the angular field of illumination in the condensing system, 42" in this cam. The third heamprovidesavariahle-intensity beam for the mea& nring and balancing system. A two-bladed chopping cylinder alternates the light through the samDle and measuring beams a t 60 oyoles pe; second. -This light-is collimated and passed through two vsriahle apertures, one for aero setting, and one the precision logarithmic measuring aperture. The attenuated light is then refocused onto the sensitive surface of the photomultiplier. The diffusing opal shown is necessary to prevent the two apertures from vignetting each other.
Fm
RECORDER CMIMICTICN
...-...-........,. ~
MSWN,W LINKAGE
, ~
WGARITHMIC APERTURE
The precision logarithmic aperture is in parallel light between two lenses. It operates like two variable-width slits at right angles to each other. For convenience both dits are made in the form of tapered annular openings in large disks on rotating shafts. Figure 3 shows their construction and arrangement. The outer edges of the openings are circular, all the logarithmic shape being incorporated in the separate inner places. The aptperture varies from an open area of 0.459 to 0.0029 square inch a t the rate of a tenfold change in intensity for 90' rotation. Its usable
Figure 4.
Schematic Diagram of Eleotmnies and
Servomechanism
where h i s the opening of each aperture, e is the angle of rotation in degrees, and h, is the opening at B = 0 degrees. The open m a , 4. a h*, of t.he two apertures together follows the logarithmic function accurately, as a result of a slight empirical correction of the ahove relation. The dial is coupled by cable to the aperture shaft with a 3 to 2 ratio to give 270' rotation for the 0 to 2.00 density scale that corresponds to 180' of aperture rotation. A logarithmic aperture based on similar principles, hut having six rather than four sides and a range of density 4.2, has been descrihed by Morrison (4). ELECTRONICS
Figure 2.
Sohematie Diagram of Optical System
The densitometer operates as a self-halancing null indicator in which the intensity of light in the reference beam is automatically and continuously adjusted to make i t equal the intensity in the unknown beam. The two beams of light from the source are chopped 180" out of phase with each other, so that one beam ia closed offwhile the other is open, and vice versa. When the intensities are equal in bath beams, the light falling on the photamultiplier tube is steady with no Bicker of the chopping frequency. When the two beams are out of balance, a flicker appears a t the chopping frequency. This off-balance signal is amplified and used to adjust the variable aperture to eqndilize the intensitiea of the two beams. Its phase indicat.es which beam is more intense and which is less. I n order to obtain good 8emo operation, it is desirable that the aver-all servo gain be independent of the operating point. Because the final indication is logarithmic with respect tQ light transmittance, a special type of electronic circuit (shown in Figure 4) must he used to meet this condition. The performance of the system is evaluated below.
As the aperture is cut to give a uniform optical density scale, its transmittance, T,is given by D = -log T
-lag IIIo
=
(1)
Let V represent the voltage applied to each dynode of a photomultiplier, I the intensity of light falling on it, and n a number which varies from 3 to 9 in commercial photomultipliers and averages ahout 6. Then the made current, i, is given rather accurately by
i
=
K'V" I
=
KV* T
(2)
where K and K' are constants. If now the photomultiplier were operated in the conventional constant dynode voltage arrangement, the amplitude, Ai, of the alternating sign4 for a given offbalance, AD, would be
Ai
Figure 3. Logarithmic Aperture (Densitometer)
=
KAI
=
-KTAD
(3)
V O L U M E 2 5 , NO. 10, O C T O B E R 1 9 5 3
1475
To convert the linear response of the photocell to the desired response, a modification of an ingenious circuit described by Sweet ( 6 ) was used. As shown in Figure 4, the phototube anode voltage developed across the load resistance, R,, is applied to the grid of the 6AG7 control tube, which maintains the phototube mode current constant. Changes in light incident on the photomultiplier are then reflected in changes in dynode voltage (supplied by the plate current in the control tube) rather than changes in the phototube anode current. When the light is chopped the alternating current component of the dynode voltage is coupled by condenser C into the servo amplifier. Setting i in Equation 2 con st ant, J- =
K7’-IItC
(4)
and for a small signal AT
From density 0 to density 2, the transmittance varies by 100 to 1 and the servo gain, A V ~ A Dvaries , by ( By selecting tubes with n = 6 or greater, the gain varies a t most by 2.2, the
eixth root of 100, easily handled by common servo systems. For comparison, the smallest signal variation that the authors were able to obtain over the same transmittanch range by the use of vniiahle p pentodes (“rcniote cutoff”) was four times. If n could
be made to equal infinity, the static response characteristic-Le., the functional relation of dynode voltage V to the incident light intensity-would be truly logarithmic and the alternating current gain independent of T. The actual relation of V to D is readily obtained from a curve of multiplier sensitivity versus Ti ( 6 ) . This relation is shown in Figure 5. The slope AV/AL) of this curve is one factor contributing to the effective over-all servo gain, and is nearly constant. The sensitivity or amplification of the 1P21 varies on the average by a factor of 10 for each increment of 20 volts per stage. Therefore for the required range of 0 to 2 density, a total of about 400 volts swing in the regulator circuit is required. The degree to which the control tube maintains a constant photomultiplier anode current may be found graphically, as in Figure 6. The control tube load, RL,that determines the load line on the pentode characteristics is 500,000 ohms. The change in plate voltage required to vary the photomultiplier sensitivity by 100 times is indicated. The change in photomultiplier anode current can then be read as the grid voltages where the plate potential lines cross the load line. The change is 1.5 volts in l l or 14%. The deg-ee of regulation can also be considered analytically. For the grid potential e, we have e , = R,i
=
Sl‘ = R,K(i,RL)GT
(6)
where S is written for KR,(i,RL)B, the effective sensitivitjr of the photomultiplier, R, is the grid resistor, RL the plate load resistance, and ip the plate current. Taking the differential of Equation 6, Aeo
=
(is Aa,. 7
f SAT
(7)
ZP
But there is also the transconductance relationship between e, and zp:
(8)
Ai, = gmAe, (gm is the transconductance of the tube.)
Putting Equation 8 in
7 and solving,
This equation is in the form of the feedback equation, with the It can bc shown by taking typical feedback factor, f = 6g,/i,. numerical values of the quantities involved that Sf >> I , so that a sufficiently good approximation is
TA -A% is the quantity in which we are interested-namely, 05
I
2
15
25
0: -LOG T
Figure 5. Static Characteristic of Dynode Voltage us. Logarithm of Light Intensity in Sweet Circuit Average 1P21 data from (5)
the
measure of the effectiveness of the regulator tube in maintaining the phototube current i constant-since by Equation 6 i t is proportional to eg. This relation (Equation 10) gives a figure of merit
%!! for the control tube.
For most tubes gm is approxi-
2,
mately proportional to i,, so that the effectiveness of control is somewhat independent of the operating i,. The tube transconductance, gm, increases with screen potential for most tubes. The 6AG7 tube appears to have the highest value of
9. 2,
0
200
400
600
800
eP Figure 6.
Characteristics and Load Line of 6.467 Control Tube Screen potential 140 v o l t s
1000
The function of the variable resistor, R,, is to establish the initial operating point of the 6AG7 regulator tube. The procedure is to put in a transparent plate (the arbitrarily chosen zero density) and adjust R, until the meter indicating the
ANALYTICAL CHEMISTRY
1476
6AG7 plate potential shows approximately 600 volts, which, according to Figure 6, is a convenient maximum operating point for the circuit. Then when a line of density 2.0 is heing read, this same meter will read approximately 200 volts. In terms of Figure 5, the effect of varying R, is to translate the curve horizontally. The same adjustment also, of course, takes care of changesin multiplier sensitivitydue to aging, fatigue, or chmge of tube, since the effective over-all phototube sensitivity is the product of R, and the current sensitivity of the phototube. A drift in lamp intensity would be corrected in the same way. The setting of R.is not cnticd. It is only important that the voltage across the 6AG7 not come within about 100 volts of either Bero or the supply voltage. The only other control is a gain control in the 60-cycle-per-second phase-sensitive amplifier. This control is used to set the servo system to a no-dead-spot, n-hunt condition. The amplifier and servo motor used a-- - l ' ~ l ~ L 1 ~ ~ modified parts from a Brown Instr Elektronik recorder. Chopped WPVCForms
Figure 7. RECORDER CONNECTIOn
The densitometa is very easily from nonrecording to recording. '_..-_..I... terminal of a threeturn Helipot potentiometer is coupled to the log aperture 80 thzt resistance or voltage is proportional to density. This may now be connected to the bridge of any standard strip ohart recording potentiometer. I
9
I
t
PHASING OF CHOPPER
If the approximately square waves in each of the two optical beams are identical in shape and amplitude (equal light intensities) and have exactly 50% duty cycle displaced exactly 180 degrees, we would expect the two square waves to overlap perfectly, givhg a pure direct current output signal. Figure 7 shows some of the wave shapes which are obtained as the various sdjustmenta are made which finally achieve an approximation to this ideal condition. A phasing adjustment is pmvided by moving the chopper motor in ita mount parallel to one beam and perpendicular to the other. This changes the time a t which the perpendicular beam ia cut by the blade without affecting the timing of the parallel beam, thus changing the relative phase of the two beams. Figure 7, A , shows a wave shape caused by improper phasing. Figure 7, B, shows the result of proper phasing, but with duty cycle different from 50%-i.e., open time different from closed time. When both of these conditions are corrected, a wave as in Figure 7, C, is obtained. This indicates that the rise time of the two "square" pulses is different, depending on the width of the beams chopped a t the position of the chopper blade. For this reason the aperture at lens C3, Figure 2 (the zero adjustment), is made rectangular. Only its length is varied, so that its effective center, wave shape, m d phase angle are invariant to the eero setting. The width of the aperture in the direction that the chopper blade moves is chosen 80 that the effective beam width is the same in both beams. This gives a wave as in Figure 7, D. The remaining small lack of perfect overlapping is due to higher harmonics because, even though the rise times are approximately the same, the exact shapes of the rise in the two bee& I are not identical. PERFORMANCE
The instrument is warmed u p and ready to operate within 1 minute after turning on. Owing to the chopped douhle-beam optical null arrangement i t is very insensitive to line voltage fluctu-
5
S . r n k ' ,w 1
0
'
'
" . e .m ' .so'
" L'm
'
1
M
'
'
8.40
. uo'
" -0
'
I
ZDO
DENSIT" SCALE RE*DI*O
Figure 8.
Cumulative Density Error Resulting from Departure from Linearity of Precision Apertures
ations, vibrations, drifts in lamp brightness, amplifier gain, or photocell sensitivity. The uncertainty in density due to reproducibility, dead spot, and stability over longperiods of time ie leas than 0.003 density unit, which is about the scale reading limit and corresponds to a relative accuracy of 0.7% of the transmittance. This precision is obtained at all densities from 0 to 2.0. I n order to prove the above accuracy i t is neceasary to mark 8 spot carefully on a plate and return the slit to precisely the same location for a number of readings, which cannot he observed to vary. The inherent grain noise and fluctuations of sensitivity of a photographic plate are greater than this amount. Using B standard Eastman Kodak calibrated step density film tablet a8 perhaps a good example of a uniformly exposed aud carefully developed negative, a recording scan was t&en across each of the density steps. The root mean square fluctuation in density wa8 found to-vary from less than 0.003 a t clear plate to about 0.007 a t density 2.00. T h i s was with the standard slit, 13 by 1509 microns, an area of approximately 20,000 square microns. At density 1.48the root mean square fluctuations were about 0.005 with standard slit, 0.008with half the slit length (10,000 square micron area), and 0.012 at 5000 square micron area. These rough estimates are approximately in accord with the well-known law (9) that the granularity fluctuations vary inversely as the square root
V O L U M E 25, NO. 10, O C T O B E R 1 9 5 3 of the area. Fx this r c ~ a s O 1 lamong , others, it is desirable in spectrochemical analysis to usc slits in both spectrograph and densitometer which are no smaller than necessary to obtain sufficient resolution. The linearity of the density scale depends upon the precision with which the logarithmic apertures are machined. Each blade is carefully hand filed down to a tool-hardened master. The departure from linearity can be measured and corrected for, if the highest precision is required. This is done by carefully marking two points on density steps differing by about 0.15 and measuring this density difference all along the scale as the zero setting is changed. The results of this measurement on one instrument are shown in Figure 8. Cumulative density error (departure from linearity) is plotted. The average reading is assumed to be the true density difference of the test steps, which automatically makes the cumulative error at density 2.00 vanish. For any differential density reading B - A ( B being more dense), the rorrection to be added is Ea - EB. The light scattered into the 13-micron slit n-hen it is obscured
1477 by a 100-micron wire is less than 1 %-that sity greater than 2 is obtained.
is, a reading of den-
ACKNOWLEDGMENT
The authors would like to express appreciation to C. G. Bearce, Langdon C. Hedrick, and D. E. Williamson for assisting with some of the details of the mechanical and electronic design and the construction of the modpl. LITERATURE CITED
(1) Baird, W. S., J . Opt. SOC.Amer., 31,179 (1941) (2) Carpenter, R. O’B., Ibid., 36, 676 (1946). (3) Jones, L. A , and Higgins, G. C., Zbid., 36, 203 (1946). (4) ;\lorriaon, C.d.,Ibid., 42,90 (1952). (5) Radio Corp. of America, “RCA Handbook.” (6) Sweet, LI.H . , J . O p t . SOC.Amer., 37,432 (1947); Eldronics, 19, 105 (1946).
RECEIVED for re\iew May 6, 1953. Accepted July 10, 1953. Presented a t the Pittsburgh Conference on Analytical Chemistry and Applied Spectrosr o p y . Jfarch 2 to 6, 1953.
Estimating the Tritium Content of Tritiated Water WILMER A. JENKINS’ Department of C h e m i s t r y , California I n s t i t u t e of Technology, Pasadena, Calif. Present methods for the radioactive assay of tritiated water are somewhat laborious and require specialized equipment. For this reason, a simpler method, involving the use of a windowless flow counter, would be desirable. I t was found that a method, based on measuring the activity of solid ammonium chloride which had been rendered radioactive by exchange with tritiated water, could be developed to give reproducible results. The accuracy of the method is at present limited to 15%. In its present state, this method should be particularly useful for the rapid determination of the approximate activity of tritiated water samples in experiments where an accurate figure for the activity is.not necessary.
T
H E advent of solid phase tritium counting techniques ( 2 , 3 ) has opened up new possibilities for the rapid radioactive a m y of tritiated compounds. For experiments which involve tritiated water (HTO) and in which an accurate value for its activity is not necessary, it would be useful to have a method by which its tritium content could be rapidly estimated with fair accuracy. Such a situation might arise, for example, if an investigator were measuring the rate of exchange of tritium between some hydrogen-containing solute and tritiated water and u-ished to know the tritiated water activity only accurately enough to make the correct dilutions of his stock solution so that the solute activities which he was measuring would be in the optimum range for counting. For such an assay method, one would choose a hydrogen-containing compound which was solid a t room temperature and which could be easily made radioactive. Then the solid would be rendered radioactive to a known extent by treating it in an appropriate way with tritiated water of known activity. The activity of the solid could then be measured in a windowless flow counter, thereby determining the ratio
One could then measure the activity of sample of unknonn activity by treating the solid i n the same way with the unknown and measuring the resulting activity of the solid in the flow coun1 Present address, Pigments Department, E. I. du Pont de Neinours 8Co., Wilmington, Del.
ter; the activity of the unknown could then be calculated from the known value of S. In this work, ammonium chloride was the hydrogen-containing solid used. (Preliminary experiments were also carried out with copper sulfate and magnesium perchlorate. The resulting hydrates were found to be unsatisfactory; a steady loss of activity was observed when they were counted, because of volatilization of tritiated water from the solid.) Although the experiments were not as extensive or as complete as might be desired, they served to outline the difficulties and point the m y toward a more complete development of the method as an accurate analytical tool. EXPERIMENTAL
Preparation of Materials. Tritium was obtained from the Argonrie Xational Laboratories in the form of hydrogen gas containing 2.6 curies of tritium. This gas mixture waa converted to water by diluting it with tank hydrogen and passing it slowly over copper oxide at 350’ C. The resulting tritiated water vapor was trapped with liquid air, diluted with inactive water, and distilled several times in an all-borosilicate glass still. An aliquot portion of this water was then completely converted to hydrogen by passing it over magnesium turnings a t 450“ C. (4). The absolute activity of the resulting hydrogen-tritium mixture wa8 measured in an ionization chamber ( 1 ) . This assay method is accurate to about 10%. The major source of uncertainty in this measurement wm the capacitance of the ionization chamber. It is hoped that in the near future, the capacitance can be measured to about 1 or 2%, thereby reducing the error in the determination of tritiated water activity to 2 or 3%. Baker’s Analyzed ammonium chloride, dried at room tempera-
