The Examination of Multicomponent Systems in BiologicalMaterials by Means of a Rapid Scanning Photometer

Dietrich W. Lubbers and Reinhard Wodick

Only photometers scanning a large range of wavelengths provide the amount of information which isnecessary to analyze multicomponent systems in a general form. After a description of a rapid scanningphotometer and a discussion of the recording problems, the mathematical method is described whichallows an optimal analysis of the concentrations of the single components of a multicomponent system.The error involved in this procedure is demonstrated by the calculation of the four nucleotides in a mixture.The long range photometry has been successfully applied to other problems such as measurements byreflected light and analyses of inhomogeneously distributed substances in living tissues.

1. Introduction

To analyze metabolic reactions of the livingorganism, the single components of the reaction shouldbe isolated and studied thoroughly. But such measure-ments have to be supplemented by experiments under-taken under the original conditions in the unimpairedorgan. Especially, the results of kinetic measurementsare dependent on the influence of the surroundingmedium. The single reactions can be understood onlyas a part of a complicated reaction chain which some-times has different branches. Because it is difficult toobtain an exact simulation of such a system, it has someadvantage if measurements are carried out in livingcells or in a whole organ. For this purpose, opticalmeasurements are most suitable. Having a smallenergy they usually do not disturb the cells. Fortu-nately, there are in the cells characteristic pigments thespectral changes of which allow us to follow the chemicalreactions.

Quantitative measurements in cell suspensions aredifficult, because the light is not only absorbed by thepigments, but also scattered by particles or fibers. Inthin sheets of organs, some substances are inhomoge-neously distributed, as, for example, the hemoglobin,which is situated in the capillaries only and not in thesurrounding tissue. Reflection measurements on organsurfaces are even more complicated, and it is difficultto obtain quantitative results.

Under some conditions, the two-wavelength method-'allows quantitative measurements in living cells and

The authors are with the Max Planck Institut fur Arbeit-physiologic, Rheinlanddamm 201, 416 Dortmund, Germany.

Received 23 July 1968.

tissues. But measuring the absorption at two wave-lengths, we obtain only two bits of information for thereactions of the whole chain and for the problem oflight scattering and distribution. The measurementsof Chance4 and his co-workers have shown that, inmany cases, this information is sufficient for obtainingimportant results.

In order to analyze the complex systems moregenerally, we need more information about our system,i.e., the absorption of more wavelengths should beknown.

One could think that the best way to increase theamount of information would be to measure the absorp-tion at all those wavelengths at which big and char-acteristic absorption changes take place during thereaction. But different reaction systems would needdifferent sets of wavelengths which could be providedonly by rather complicated equipment. In Sec. IIwe show in which way the amount of informationnecessary for an optimal analysis can be obtained bymeans of photometers that allow continuous scanningof the needed range, applying mathematical methodsespecially developed for this purpose (Secs. II andIII). Furthermore, this amount of information allowsquantitative measurement of concentrations in theliving tissue using reflected light (Sec. IV) and correc-tion for inhomogeneous distributions (Sec. V).

II. The Rapid Scanning Photometer

Our main experimental question which triggered thedevelopment of a rapid scanning photometer concernedthe mechanism of oxygen transport to the heart tissue.For the analysis of this transport, we had to know thetime course of oxygen uptake during the heart cycle.Inside the cell, the oxygen reacts with the respiratorychain producing energy for chemical reactions and

May 1969 / Vol. 8, No. 5 / APPLIED OPTICS 1055

water. As a small store of oxygen, the heart cellcontains oxygen chemically bound to myoglobin. Theenzymes of the respiratory chain and the myoglobinhave characteristic absorption spectra. Therefor, fastspectrophotometric methods should be able to solveour problem. The main features of such a photometershould be:

(1) in order to get a sufficient amount of informationit must scan spectral ranges of different size;

(2) the scanning time must be in order of 10 msec,otherwise, it would not be possible to obtain undis-turbed spectra of the beating heart;

(3) the sensitivity must be as high as possible,because the concentrations of the substances in the cellare rather small. They cannot be changed arbitrarily;

(4) the expected changes are small, therefore theaccuracy of the method should be high;

(5) in order to follow the reactions continuously,the reproducibility should be so good that additionalcalibrations are not necessary during the measurement;

(6) for practical reasons, the apparatus should havea flat zero line and measure the absorptions in units ofoptical density;

(7) finally, it should be possible to obtain measure-ments every 10 A in a range of 200 nm.

To fulfill these conditions, we constructed in 1957together with Niesel and I(oehler 7 a special photom-eter (Kurzzeitspektralanalysator) which was later onimproved and which is now manufactured as a rapid-scan spectrometer by the Kieler Howaldtswerke, Kiel,Germany.'

In order to scan a suitable range, a plane mirror isturned in the parallel light beam of the monochromator.In our construction, this is preferable to turning theprism or the grating.

To establish the short scanning time of 10 msec, theplane mirror is mounted on a torsion wire in order toallow an oscillation in the resonance frequency (50 Hz).At the frame of the mirror, a coil is fixed which ismoved by the oscillation in a magnetic field. Theamplitude of the oscillation can be changed easily bychanging the electric current in the coil. It is stabilizedby a feedback system using some separate windings ofthe coil as a pickup. The electric power needed fordriving this rather big mirror (5 cm X 7 cm; 0.7 cmthick) only amounts to some hundreds of milliwattsfor a spectral range of 400 nm. With thinner mirrors, asufficient good monochromaticity could not be obtained,because these mirrors didn't remain plane during theoscillation. We have also tried to oscillate the prismor the grating, or even the light source, but the best re-sults were obtained by oscillating the mirror. With arotating wheel on which different mirrors or prisms havebeen mounted, we were not able to achieve the sameoptical quality.

In order to meet the conditions 4, 5, and 6, we con-structed a split beam photometer. This splitting hasbeen achieved by another oscillating mirror which had aresonance frequency of 20 Hz. This mirror had a sizeof 10 mm2. Its construction was much more difficultthan the other one. The poorer optical quality of the

Fig. 1. Block diagram of the rapid spectrometer. The oscil-lating mirror M5 (50 Hz) oscillates the picture of the entranceslit before the exit slit of the monochromator producing the wave-length scan. Leaving the exit slit, the monochromatic lighttravels alternately through the sample and the reference sample.This switching of the light is achieved by the other oscillating

mirror M (12-25 kHz) (Niesel et al.8

).

picture transmitted by this mirror was sufficient forour purpose. The beam splitting mirror allowed use ofthe same part of the light source and the same photo-multiplier. In the construction of the photometer,therefore, the same optical parts (after splitting ahighly symmetrical setup) with the same number ofoptical surfaces could be used. The monochromator isof the Pfund type, the light source is a xenon high pres-sure lamp (Osram XBO 450 W/P). The grating wasmanufactured by Bausch & Lomb (type 33/53/08/26).As a photomultiplier we used the type EMI 9558 (Qcwith quartz window S-20).

The regulation of the changing sensitivity of thephotometric device was accomplished by regulating thevoltage of the photomultiplier by the reference lightbeam. The regulation is very much improved bylogarithmic conversion of both signals and followingsubtraction. By this operation, all the nonlinearitiesconcerning both light beams in the same manner arecancelled. The limit of the linearity is given by thelogarithmic amplifier, the sensitivity is limited by theefficiency of the photomultiplier. The signal-to-noiselevel can be improved by integration.

The required high frequency of the beam splittingmirror gives the frequency range the amplifier has todeal with.

Figure 1 shows the schematic design of therapid scan spectrometer. Figure 2 is the reflectionspectra which can be observed during the cycle ofa beating rabbit heart.9 In order to measure thereflection spectra, the light beam penetrates an inte-grating sphere without disturbance and enters a lightpipe which is almost in contact with the heart surface.The light reflected by the heart returns in the samelight pipe and it is scattered in the integrating spherein the window of which the photomultiplier is situated.The picture is triggered by the R peak of the electro-cardiogram. The recording starts at the bottom. The

1056 APPLIED OPTICS / Vol. 8, No. 5 / May 1969

following spectra are recorded on the top of the earlierones. So a series of reactions can be displayed on thesame oscilloscope picture.

Ill. Recording of the Spectra

In order to analyze the spectra of the rapid scanspectrometer, they must be recorded. The measuringfrequency of the older models is 25,000 data/see, thenewer ones produce some 50,000 data/sec. Thestoring of these data can be lone in different ways.

(1) Direct recording is only possible by photographyof the oscillograms. But this will be a suitable pro-cedure only if the analyses will be made by graphicalmethods. Section IV (4) shows that actually rathercomplicated calculations have to be done in order tocalculate the concentrations with optimal accuracy.These calculations have to be carried out by a computer.Therefore, the data should be recorded in such a waythat they can be easily put into a computer.

(2) The signals can be stored on a magnetic tapeusing frequency modulation as analog signals. Thishas the advantage that the storing can be made at highspeed and the recording at a low one (100:1). Un-fortunately, this lower speed is so high that it stillneeds a light spot uv recorder for registration. Higherreductions of the speed impair the results.

(3) The most efficient way is to use a computerdirectly on line. Since for the calculations storing ofthe molar spectra is necessary, the application of ananalog computer is not possible. One would need ahybrid computer, but the commercially availablemachines are too slow.

Therefore, at the moment it will be best to use adigital computer. The calculations can start during

MbO2 Cc MbO2 Ca 3

Lj

~~~~~~~ c AnL. I

180 -

750 -

30 Q A m p

0- n', I.-

. i,. 1573 rvm

Fig. 2. Series exposure of eight difference spectra taken fron abeating rabbit heart. The ex.posure has been triggered by Rpeak of the ECG and covers a s Ingle heart action. The measure-ments of a single spectrum needs 10 msec. Abscissa-wave-length; ordinate-extinction; MbO2 = oxymyoglobin; Cc =cytochrome C; C, = cytochromoxydase (Fabel und Liibbers9).

the measurements and therefore it is for the most partsufficient to store only a part of the information. Itis another advantage that the results of the calculationscan be used to influence or regulate the reaction or thephotometer. We were using the digital computerPDP of the Digital Equipment Company. Thetwelve-bit signals are directly transferred by databreak into the memory. The necessary multiplicationis done by adding the logarithms of the signals becausethe hardware multiplication of this computer is tooslow. With a memory of 8 k we can analyze threecomponents on line. The storing of the twelve-bitlogarithms results in an error of rounding up which is 2%of the concentration value. The necessary programsare written in machine code and Fortran II (Wodick,1968). For the rapid scan spectrometer with 50,000data/sec we are preparing the calculation with aDD1P 516 (Honeywell) which has eight externalmultiplication units. This allows us to analyze eightcomponents at the same time in an optimal way. Ifthe speed of the reaction is slow, recording is notpossible, because the movements of the organs disturbthe signal. But an averaging by the computer resultsin higher accuracy.

IV. Evaluation of the Concentration from theExtinction Curve Measured by the Rapid ScanSpectrometer

The following different methods were applied.

(1) Having the spectral extinction curve, the con-centrations of the different components can be calcu-lated in the usual way by measuring the extinction atcharacteristic absorption peaks and isosbestic points.This procedure has no advantage over single measure-ments.

(2) For small extinctions the analysis of the absorp-tion curve can be evaluated by measuring the slope or-if there is an absorption peak-by drawing the tangentsand measuring the angle in between. This proceduregives better results than single measurements.' 0 - 3

But also with this method one uses only a part of thetotal available information.

(3) Together with Niesel 4 we tried to use a totalmeasured spectrum by applying the least-squaresmethod for curve fitting. The multicomponent systemconsists in the molar concentration x, x2 ... Xn withthe spectra xo,(X), X2V2(X) ... v(X) meansthe known one molar extinction spectrum of component1. The molar concentration x, ... x, has to becalculated so that the sum of the calculated spectraxlsoi(X) + 2,P2(X) + -- + nnW(X) fits the spectrumof the multicomponent system y(X).

F (x, x2 ... x) = y(X) - [x,,l(x)

+ X,212(X) + * (X) I t'dX = min. (1)Since

d F (X) x = 0, F(X) x, = 0, * * * d F(X) xn = 0,

May 1969 / Vol. 8, No. 5 / APPLIED OPTICS 1057

we find for the concentration of the single componentsX.:

Xp | ,2() dX. (2)

5 (X) is a linear combination of the known molarextinction curve of the components of the system. Inconnection with the rapid scan spectrometer, Niesel" hasconstructed an analog computer for this formula. Theg,(X) function was provided by means of a light spotof an oscilloscope scanning behind a screen which hadthe shape of the different extinction curves. Thisdevice gave a pulse length modulation correspondingto- the extinction and easily could be used for themultiplication with y ( X). We measured the hemo-globin system, but ten years ago the technical difficultieswere considerable, so we could get only 5% accuracy.The same mathematical procedure was later used foranalyzing the nucleotid system."- 2" If the spectra ofdifferent components are similar then this methodshould not be applied.

(4) Our last development enable us to apply anoptimal method: it is this one which gives the smallesterror for the calculated concentrations x... x. Wehave to consider that the spectrum y (X) is only knownwith an errorf(X).

We found that the best way to calculate, describe anddiscuss the analyzing method is to use the mathematicaltools of the functional analysis, especially the ones ofthe Hilbert space (Wodick) .2223 Functions the squareof which can be summed up in the sense of Lesbesguesatisfy the axioms of the Hilbert space if the metric ofthe space is fixed by a scalar product of the followingform:

( )= (j (x) ) jIy(x)g(x)(x)dx (3)

The corresponding scalar product for a finite dimen-sional space results in the formula:

(y/, ) = ( a,0 1 IYJ yiji.i=I i=1

We could show that in the Hilbert space the concen-tration x, is a linear function of the elements y. Fromthis follows (theorem of Frech6t and Riesz) that itmust be possible to describe concentrations by scalarproducts:

x = (y, gY). (8)

The different types of analysing methods are dis-tinguished by different elements gp. ConsideringEq. () we multiply both sides of Eq. (7) by g:

N= Ex (,, . 9)

This expression must be valid for all possible concen-trations xl, x2 ... x,. Therefore, g has to be orthogonalto all sop( 5Z /L)

(so 9) = APE- (10)

(6, means ronecker's symbol). In reverse, thecalculation of the concentration x, is possible by anelement g, which satisfies Eq. (10).

Let us start with an element p of the Hilbert spacewhich has a component h in the part Hy of the space.H, is the part which is spread out by so, but has nocommon region with the part W, of the Hilbert space.

E

2,0

1.5

1.0

E

2.0

1.5

1.0

0.5

(4)

This expression can be applied to the measurementswith the rapid scan spectrometer which has a number ofmeasured values for the spectrum of M = 200-500dependent on the frequency of the oscillating mirrors.

The function a (X) is a weight function which dependson the error function f(X)

a ( = /f2 (X) (5)

By means of the scalar product [Eq. (3) ], a norm canbe defined as

Il yl = (y,y) 12 . (6)

We consider the expression:

NY(X) = x1,VV(X); (7)

>'=1

y and are elements of the Hilbert space characterizedby the scalar product [Eq. (3) ].

300 320 nm A

K:r 2

240 25 260 280 300 320 nm AE

Fig. 3. Spectra of a mixture of nucleotides and its single com-ponents. The upper curve shows the spectrum of the mixture,the lower one the single nucleotide components (pH = 13).AMP = adenosine-3'-phosphate = 28.1 -4 0.6%; CMP =cytidine-3'-phosphate = 23.2 -4 1.1%; GMP = guanosine-3'-phosphate = 32.9 0.8%; UMP = uridine-3'-phosphate =15.8 i 0.7%. The concentration of this arbitrary mixture hasbeen calculated from the 227 values of the spectrum. The errorof this analysis is calculated for the single components on theassumption that the measurements had an error of 2% at thewavelength 245 nm and that this error is constant over the whole

spectral range (Wodick23).

1058 APPLIED OPTICS / Vol. 8, No. 5 / May 1969

I1 , 11 is defined by the following conditions which aresufficient and necessary for the analyzing methoddescribed:

(s1Pu, PA) = 6Vy- (18)

The different analyzing methods are distinguished bythe different q of the part of Q of the Hilbert space.The smallest error,

I AXA12 = hl2/ E Zai, (19)

is obtained if q, equals zero

q, -O .

The element h can be calculated from p,, using themethod of E. Schmidt.

In order to apply this analyzing method for thecalculation of the concentration x, V,(X) must belinearly independent from the other V,(X) (withv F We succeeded in constructing the analyzingmethod for Zm in such a way that it works also if thev,(X) (with v z A) are not linear independent of eachother.

This procedure makes it possible to use all theinformations concerning the concentration x, whichcontains the spectrum of the mixture y(X). Equation(19) allows an estimation of the error. A modi-fication of the method is possible with the addi-tional condition that there is no negative concen-tration x,.

As an example of the application of the methodthe mathematical analysis of the spectra of amixture of four nucleotides (AMP, GMP, CMP,UMT) have been carried out. Figure 3 shows thespectra of the mixture and the four components.Figure 4 gives the corresponding functions ,(X).

For example, if we assume an error of measure-ment of 2% of the extinction at 245 nm and that thiserror is constant over the whole spectral range, we findthe following results: AMP 28.1 4t 0.6%; GMP23.2 i 1.1%; CMP 32.9 ±4 8%; UMT 15.8 i 0.7%.This error describes the maximal accuracy which can beobtained under these circumstances.

. . . . . . . . .240 260 280 300 320 nm X

Fig. 4. The function g(X) for AMP, CMP, GMP, and UMPas a function of the wavelengths 2 ' (Wodick 1968).

The space We will be spread out by the elements sos(with v - ,). Using the method of E. Schmidt (Ortho-normierungsverfahren) from the element p it ispossible to find an element p, for which is(S , T ) = a (11)

This gives the analysing method in its most generalform:

x = (y, Pa-(12)

In case that the function y(X) has the error f(X) wecan write

xlA A,, = ( i4f, ). (13)

y ( X) consists of M measuring values y, of the rapid scanspectrometer. Corresponding to the law of propagationof error, we obtain:

M M

I Ax,, I [ C f.2pi2ai2/( E .) ]§. (14)

With Eq. (5) followsM

Ax I 11 H/( > ai)12 (15)i_1

pa has a component in the direction of o, andcorresponding to its construction, no common regionwith the space W, which is spread out by the sp, (withV 5z g) . q is the projection of p, in the complementaryspace Q of the Hilbert space which is given by

pi = hA -- qp. (16)

Being h. 1 q it can be concluded from the generaliza-tion of the Pythagorean proposition in the Hilbertspace

M

j^X~2= (fl h,f 2+ flqpfI2)/ Zai. (17)

V. Methods for Analyzing by Means ofReflected Light

In several cases, our biological objects do not allowus to measure the spectra with the light passing throughthe sample. We can only analyze the reflected light.24

The reflection depends very much on the special condi-tions which vary from organ to organ. Therefore, wefirst tried to find out if any reproducible relationshipexists between the concentrations measured by lightpassing through the sample and by light reflected by thesample. The measurements were made at the braincortex (hemoglobin-free, perfused guinea pig brain).First the reflection spectra were taken. Then themeasured area of the brain was homogenized anddiluted until further dilution did not change the resultanymore. These values were used to calculate the

May 1969 / Vol. 8, No. 5 / APPLIED OPTICS 1059

2

AMP

(20)

LREk(X), X] = Lof 4 (x, X)e-k(Xl)dx,0

(21)

where k(X) = log Es e(X)ci and the logarithm to thebase e is used instead of the base 10. 4'(x, X) is theprobability density of the light in the sample; it canbe a zigzag path. The function L(k, ) is the Laplacetransformation of the function ql(x, X).

The function L(k) has been measured by addingknown concentrations of hemoglobin to the homogenateof guinea pig brain. By retransformation of theLaplace function, we were able to calculate 4'(x, X).Figure 7 shows the probability density /(x, X) for thepath which the light has taken in the brain. The curveIPT(X) shows a function theoretically calculated byassuming that only light reaches the photomultiplierwhich was scattered only once. For the average of thelight path inside the brain x we obtain 1.5 mm at thewavelength 585 nm

Fig. 5. Reflection spectra of the cortex of a guinea pig brain[normoxia (lower trace) - anoxia (upper trace)]. Abscissa-wavelength; ordinate-extinction. Solid line-measured reflec-

tion spectra; dotted line-graphically constructed spectra."

Fig. 6. Schematic drawing of the path of scattered light. Theright side shows how this way can be simulated by a set of

cuvettes of different thickness."

original concentration in the brain surface. Theexperiments showed that there is a constant relationshipbetween the measurements. So it is possible toobtain the real concentration values by multiplyingthe results of the analysis using reflected light by afactor 3.19.

Figure 5 shows the reflection spectra of a guinea pigbrain changing from normoxia to anoxia. The dottedcurve has been obtained by summing up the componentsgraphically. The concentration of the componentshas been measured in the diluted homogenate. Theextinction curves of the components were taken fromthe literature. The figure shows that both curves fitvery well. We therefore tried to find a mathematicalway to interpret these results.

A light beam entering the surface passes the organ indifferent ways (Fig. 6). This can be simulated by aset of cuvettes which have different thicknesses (Fig.6 right) xi. The mathematical analysis results in theLaplace integral:

= x (x) dx.0

(22)

The shorter the wavelength of the light, the longerbecomes the average path for the light beam. Forexample, at the wavelength of 485 nm, x was 1.7 mm.

There is a discrepancy between the calculated andthe measured curve by the new increase in the range of2-3 mm. This can be explained in the following way.Assuming that no light leaves the sample, we cancalculate the light intensity per unit path of light whichis scattered different times (never, once, twice) (Fig.8). The new increase of 4A can be understood ascaused by multiple scattering. The function 4'(x, X)describes the essential optical properties of the objectanalyzed by means of the reflection photometry. Bythe expression:

LR(X) = Lo J4 (x, ) 10- 2eici-dx,

kmm W(x)

0,48

1 2 3 4 5 6 mm x

Fig. 7. Probability density 1'(x) of the way x which the lighthas taken in the rabbit brain (x = 585 nm). The curve AkT(X)

has been calculated.23

1060 APPLIED OPTICS / Vol. 8, No. 5 / May 1969

b, -1 10

L-1 10

b - L-1 Dob, - P.

------- b.- L-1-b L-1 ---

I

lo(x)

\ 11 (X ) 12 1(X)

2 I 1 2 3

Fig. 8. Intensity of the light per unit way I(x) as a function ofthe way x. Io(x) = no scattering; I(x) = once scattered;

12(x) = twice scattered.23

=w~0%.

EE

0,30-

0,15

0 0,5 1,0 1,5 2,0 g /.Hb

Fig. 9. The influence of inhomogeneous distribution in a two-compartmental system. w = the percentage area of the com-partment 2. Abscissa-hemoglobin concentration; ordinate-

EE = E542- E (Ref. 25).

the intensity of the reflected light LR(X) can be calcu-lated if the function 4'(x, ) and the concentration ciare known.

The relationship between the intensity of the passingand the reflected light,

LD Lol0-Xi eicid/ LO [ 4'(X, X) 10-l eiidx,LR I

is approximately constant in the wavelength range500-600 nm. Therefore it is possible to introduce anequivalent thickness of the layer d which can be appliedfor the solution of the Lambert-Beer's law:

E = log(Lo/L) = Eeicid.

For the value d we found by our measurements in theguinea pig brain: d = 1.57 mm.

VI. Concentration Measurements of anInhomogeneously Distributed Substance

ANJeasurements of the hemoglobin concentration inthe tissue have to consider that the hemoglobin issituated in the blood vessels and capillaries only: thecapillary network covers about 20-40% of the surface.

Therefore the hemoglobin is inhomogeneously dis-tributed. Because the concentration of the hemoglobinis much higher than the concentration of the othercomponents, it is sufficient to divide the analyzed areainto two compartments [t + (1 - t) = 1]. In com-partment 1, the hemoglobin absorbs the light with theextinction El,,. Compartment 2 shows no absorption(white). The extinction is E2,, = 0. If Em means themeasured extinction of the total area, applying theLambert-Beer's law to the two compartmental systemsresults in

Em(XI) = -log[t + (1 - t)0 loEl] (23)

E = Em(Xl) - Em(X2 ) = log t + (1 _ I)10-(X2 )cdt + ( - t) 10-(,1)cd

(24)

Figure 9 shows the results of the calculation. Even ifthe size of compartment two is only 18% (t = w = 1Sc)of compartment 1, the analyzed concentration ismeasured too low. Since this curve has a maximum,it is impossible to find the concentration out of theextinction difference AE (Fig. 9) between 542 nm and558 nm. Higher extinctions are measured relativelytoo low. This system can be simulated easily by acuvette which is only partly in the light beam. Themeasurements fit the calculated values with an errorof 3c. By means of the Eq. (24) a correction can bemade. If the spectra of the components are knownfrom the measured spectrum, the inhomogeneous dis-tribution can be calculated (Lubbers and Wodick25 ).Programs are available in Fortran.2 3 If the degree ofinhomogenity is known, the correction can be made atthe input of the photometer by electronic subtraction.The problem of inhomogenity 6-21 is treated in moredetail by Wodick.23

References1. K. Kramer, Z. Biol. 95, 126 (1934).2. G. A. Millikan, Proc. Roy. Soc. London B123, 218 (1937).3. B. Chance, Sci. 120, 767 (1954).4. B. Chance and G. D. Williams, Adv. Enzymol. 14, 65 (1956).5. D. W. Lubbers und W. Niesel, Naturwiss. 44, 60 (1957).6. D. W. Lubbers und W. Niesel, Pfltigers Arch. 268, 286 (1959).7. W. Niesel, D. W. Lulbbers, und G. Thews, Z. Elektr. Chem.

Ber. Bunsenges. Phys. Chem. 64, 15 (1960).8. W. Niesel, D. W. Lubbers, D. Schneewolf, J. Richter, und W.

Botticher, Rev. Sci. Instrum. 35, 578 (1964).9. H. Fabel und D. W. Lubbers, Biol. Z. 341, 351 (1965).

10. W. Niesel, G. Thews, und D. W. Lubbers, Pflugers Arch. 268,298 (1959).

11. R. Wodick, D. Schwickardi, und D. W. Libbers, PfligersArch. 291, 25 (1966).

12. D. Schwickardi, Med. Diss. Marburg, 1967.13. A. T. Giese and C. S. French, Appl. Spectrosc. 9, 78 (1955).14. D. W. Lubbers und W. Niesel, Naturwiss. 44, 59 (1957).15. W. Niesel, Forschungsber. Deut. Forschungsgem., 1957.16. J. C. Reid and A. W. Pratt, Biochem. Biophys. Res. Commun.

3, 337 (1960).17. J. C. Sternberg, H. S. Stillo, and R. H. Schwendemann,

Anal. Chem. 32, 84 (1960).18. S. K. Vasilenki, S. G. Kamzolova, and D. G. Knorre, Bio-

khim. 27, 1942 (1962).

May 1969 / Vol. 8, No. 5 / APPLIED OPTICS 1061

-- , -T__ - -; 3 4 SX

19. F. P. Zscheile, H. C. Murray, G. A. Baker, and R. G. Peddi- 23. R. Wodick, Inaugural-Dissert. Marburg 1968.cord, Anal. Chem. 34, 1776 (1962). 24. G. Kortum: Kolometrie, Plotometrie und Spektrophotometrie

20. Sh. Lee, D. McMullen, G. L. Brown, and A. R. Stokes, (Springer-Verlag, Berlin, 1963), 4. Aufl.Biochem. J. 94, 314 (1965). 25. D. W. Lubbers und R. Wodick, Pflfigers Arch. 294, 40 (1967).

21. E. G. Richards, European J. Biochem. 4, 256 (1968). 26. A. W. Pollister and H. H. Swift, Science 111, 68 (1950).22. R. Wodick, D. W. Libbers, und E. Piontek, Pflugers Arch. 27. L. Ornstein, Lab. Invest. 1, 251 (1952).

297, 94 (1967). 28. K. Patau, Chromosoma 5, 341 (1952).

Optical Instruments and Techniques

Reading, England

14-19 July 1969

A conference on optical instruments and techniques will be held next July in

Reading, England, in conjunction with the Eighth General Assembly of theInternational Commission for Optics (16 and 18 July). It will be devotedto papers and discussion on new instruments and techniques for spectros-copy, including interferometric methods, stimulated emission, and non-linear phenomena; for systems design of astronomical telescopes; foroptical meterology and optical processing of data including coherent lighttechniques; for image forming systems of novel design. The conferencewill discuss new aspects of mechanical design, advances in assessment andspecification of performance of optical instruments, and recent develop-ments in optical production techniques (including the use of new ma-terials). (In order to avoid overlap with the Commission on Spectroscopyit will not include instrumental systems using essentially standard pro-cedures of analysis by emission or absorption spectroscopy, or spectra ofatoms and molecules.) Languages: English, French and German. Timefor presentation: for contributed papers 15 minutes will be given, with asimilar period for discussion. Offers of contributed papers for presenta-tion should be made not later than 1 March 1969, and should give at leastthe title and an adequate abstract. The provisional program gives thenames of invited speakers with the titles of their papers, and other in-formation such as visits to firms and research organizations. A copy ofit and other information can be obtained from A. Thetford, Applied Optics,New Applied Physical Science Building, The University, Whiteknights,

Reading, Berkshire, England.

1062 APPLIED OPTICS / Vol. 8, No. 5 / May 1969