- Email: [email protected]
[3] Nanosecond absorbance spectrophotometry
32
SPECIALIZED TECHNIQUES
[3]
The identity of I can be pheophytin as Fajer 3~suggested or a combination of several species. These primary processes in rhodopsin and chlorophyll are only an example of the potential uses of picosecond spectroscopy in biology. With extrapolation one can decipher processes with 3 × 10 ':~ sec lifetimes, thus approaching a vibrational period which is essentially the lower limit for chemical and biological events. Acknowledgments The work of Drs. G. E. Busch, D. Huppert, K. J. Kaufmann, T. L. Netzel, W. S. Struve, and V. Sundstrom at Bell Laboratories has formed the basis of this paper. 1 thank Drs. M. L. Applebury, P. L. Dutton, and K. S. Peters for collaboration and discussions on rhodopsin (MLA and KSP) and bacteriochlorophyll (PLD). I thank Drs. D. C. Douglass, E. O. Degenkolb, and L. J. Noe for continuous discussions and suggestions in the development of this manuscript. a.~ j. Fajer, D. C. Brune, M. S. Davis, A. Forman, and L. D. Spaulding,Proc. Natl. Acad. Sci. U.S.A. 72, 4956 (1975).
[3] N a n o s e c o n d
Absorbance Spectrophotometry
By DON DEVAULT It is possible, with a streak camera, to record a whole spectrum in a nanosecond and to record changes in successive nanoseconds. The instruments are expensive ($40,000)' and probably do not have the sensitivity required for biological spectrometry 2 which often deals with transmission changes of the order of only 1%. Furthermore when one is dealing with a known reaction it is usually not necessary to obtain a whole spectrum but only the time course of changes at a few key wavelengths. 3 This chapter ' Some producers of streak cameras: Hadland Photonics, Ltd., Tel: (0442) 832525, U.K. (or Macro Scientific, Inc., Sunnyvale, Calif., Tel: 408-739-9418); Hamamatsu TV Co., Ltd., Hamamatsu, Japan (or Middlesex, New Jersey 08846); Cordin, Salt Lake City, Utah 84119. See also S. Gordon, K. H. Schmidt, and J. E. Martin, Rev. Sci. Instrum. 45,552 (1974). The price given is for a Cordin Model 132 + minimum accessories. The Hamamatsu C979 is $47,000 (1977). (Prices approximate only. Dated because of inflation.) 2 Hamamatsu estimates their dynamic range as possibly 1000 but gives data showing 68. I have no data on the others. However, to make any kind of measurement on a 1% change, the noise should be no more than 0. I%, making imperative a dynamic range of 1000 or a gray-scale resolved to 10 bits. 3 The relative merits of taking an instantaneous whole spectrum at a given time after the stimulus to the sample vs. following the kinetics at a single wavelength is discussed by one of
METHODS IN ENZYMOLOGY, VOL. LIV
Copyright O 1978by AcademicPress, Inc. All rightsof reproduction in any form reserved. ISBN 0-12-181954-X
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
33
will d i s c u s s i n s t r u m e n t a t i o n for m e a s u r i n g the t i m e c o u r s e o f small r a p i d c h a n g e s o f a b s o r b a n c e at a single w a v e l e n g t h ? T o o b t a i n a s p e c t r u m o n e r e p e a t s the e x p e r i m e n t at d i f f e r e n t w a v e l e n g t h s . A c c o r d i n g to t h e title w e a r e d i s c u s s i n g i n s t r u m e n t a t i o n in w h i c h t y p i cal o r limiting t i m e c o n s t a n t s , z, r a n g e f r o m 1000 n s e c d o w n to I n s e c . This c o r r e s p o n d s to b a n d w i d t h s e q u a l to 1/(2~'z) o r 160 k H z to 160 M H z . I n s t r u m e n t s p e c i f i c a t i o n s a r e often in " r i s e t i m e s , " Tr, w h i c h is d e f i n e d in s e v e r a l d i f f e r e n t w a y s '~ v a r y i n g f r o m 1.6 z to 2.3 z. S o m e t i m e s 1 will call z t h e " r e s o l v i n g t i m e . " T e c h n i q u e s at the 1000 n s e c e n d o f the r a n g e a r e not g r e a t l y d i f f e r e n t f r o m s t a n d a r d s p e c t r o p h o t o m e t r y , while t h o s e at t h e 1 n s e c e n d a p p r o a c h the state o f the art. H o w m u c h o f the f o l l o w i n g a d v i c e o n e n e e d s d e p e n d s u p o n h o w far d o w n into the n a n o s e c o n d r a n g e o n e i n t e n d s to go. T h e p a r t s o f a f a s t - a b s o r b a n c e s p e c t r o p h o t o m e t e r a r e (1) t h e m e a s u r i n g light s o u r c e , (2) m e a n s o f c h o o s i n g the m e a s u r i n g w a v e l e n g t h if the s o u r c e is n o t a l r e a d y sufficiently m o n o c h r o m a t i c , (3) a cell h o l d i n g the s p e c i m e n , (4) a d e t e c t o r to m e a s u r e , a m p l i f y , a n d r e c o r d the t r a n s m i t t e d (or p o s s i b l y r e f l e c t e d ) m e a s u r i n g light i n t e n s i t y as a f u n c t i o n o f t i m e , a n d (5) a m e a n s o f s t i m u l a t i n g o r p e r t u r b i n g the s a m p l e .
1. T h e L i g h t S o u r c e T h e m o s t d e m a n d i n g a s p e c t o f fast s p e c t r o p h o t o m e t r y is the n e e d f o r a s u f f i c i e n t l y b r i g h t m e a s u r i n g light s o u r c e . T h e m i n i m u m b r i g h t n e s s is s e t b y t h e n e e d to r e d u c e " s h o t " n o i s e to a s u i t a b l e level. S h o t n o i s e is the n o i s e in t h e o u t p u t w h i c h r e s u l t s f r o m the c o r p u s c u l a r n a t u r e o f the m e a s u r ing light a n d / o r the p h o t o e l e c t r i c c u r r e n t it p r o d u c e s in t h e d e t e c t o r . T h e m o s t critical s t a g e in t h e m e a s u r i n g l i g h t - d e t e c t o r s y s t e m is t h a t at w h i c h the n u m b e r o f s u c h c o r p u s c l e s is a m i n i m u m . In t h e m e a s u r i n g light b e a m this will b e at t h e e n t r a n c e to the d e t e c t o r , a f t e r the l o s s e s d u e to a b s o r p t i o n in the s a m p l e a n d i n e f f i c i e n c i e s in the o p t i c a l p a r t s . In the e l e c t r i c a l p a r t s it will b e t h e p r i m a r y p h o t o e l e c t r i c c u r r e n t b e f o r e a n y a m p l i f i c a t i o n . N o r the pioneers in the field, G. Porter, in "Photochemistry and Reaction Kinetics" (P. G. Ashmore, F. S. Dainton, and T. M Sugden, eds.), pp. 9 3 - I l i . Cambridge Univ. Press, London and New York, 1967. Note that the streak camera aims to do both. 4 Another general discussion of fast spectrophotometry is F. E. Lytle, Anal. Chem. 46, 545A and 817A (1974). Tr is usually defined as the time to rise from 10% to 90% of the ultimate rise. For a sine wave this is (sin-' 0.9)/Trf, wheref is the frequency, taken here to be the bandwidth, or Tr = 2"r sin -l 0.9 = 2.24T. In the case of an exponential approach to a constant displacement, Tr = z In 9 = 2.20 z, where ~-is the time constant of the exponential. Another definition used, but not consistently, in the Tektronix catalogue appears to he the time for ¼ of a cycle of sine wave. This give T,. = 7rr/2 = 1.57r.
34
SPECIALIZED TECHNIQUES
[3]
mally the electric current will have fewer corpuscles (electrons) than there are photons producing them because the quantum efficiency of photoelectron production is usually less than 1. I f n photoelectrons are produced in one sample period the noise, i.e., the root mean square of the deviations from sample to sample, 6 will be X/n. If the noise is required to be less than 0.1% of the signal, then X/n must be less than 0.1% ofn and n must be more than 106. If the sample period is 1 nsec (for a I-nsec resolution of measurement), the photoelectric current must be more than 106 electrons per 10-9 sec or more than 160 p,amperes. Suppose, next, that the material in the cuvette transmits only 10% of the measuring light striking it and that the efficiency of the detector in collecting the transmitted photons and converting to photoelectrons is 10%. Then our example tells us that 108 photons must strike the cuvette per sample period. This is l014 photons sec -1 at ~ = 1000 nsec and 1017photons sec -1 at ~- -- ! nsec. 1017photons o f 500 nm wavelength per second is 40 mW of light energy incident on the cuvette. Figure 1 illustrates our experience with various lamps. For specifications other than those assumed in the example, note that noise/signal will be inversely proportional to the square root of the light intensity, and resolving time for a given noise/signal level will be inversely proportional to the first power of light intensity. It is possible to use smaller measuring light intensity if the experiment can be repeated a large number of times. At 1/100 the light intensity calculated above one could repeat the measurement 100 times and the total amount of light entering during the sum of corresponding sample periods will be the same. A computer would be required to add together the corresponding samples from the different repetitions (Computer of Average Transient). If one uses CAT averaging, some of the following advice needs modification, particularly the needs for measuring-light intensity and for detector capacity. There are problems with maintaining constancy of light intensity during the measuring interval. Our solution for the boosted incandescent light source, used in the slower measurements, is described elsewhere. 7 The high-pressure mercury arc s is constant enough for intervals up to 10 ~sec, but it fluctuates over longer intervals. The Xe flash lamp can be given a reasonably flat top for, say 1 ~sec, by using a pulse that is considerably broader overall. 9 A common method of getting bright light is to transiently 6 Poisson statistics. 7 D. DeVault, in "Rapid Mixing and Sampling Techniques in Biochemistry" (B. Chance et al., eds.), pp. 165-174. Academic Press, New York, 1964. The AHG- 1B sold by several lamp companies running at 900 V and I A. An example of its use is found in M. Seibert and D. DeVault, Biochim. Biophys. Acta 253, 396 (1971). 9 We have used the E.G. and G. Co. FX-101 pulsed with 5J. An example of its use is by M. C. Kung and D. DeVault, P h o t o c h e m . Photobiol. 24, 87 (1976).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY 1018
,
1017
+
1016
+
,
,
+
35
1018
i
,
,
+
+
+
1017
+
+
+
+
JO16
,+
+
+
!i
'°'5 '. ~i, \-?
5
i} Jc ,o"ii
/
ii /
+f /
/~
i o 15
,
.....
+
+
- w-Iz( 55 w)
+
+
i o 14
.....
~ _ . _ . ~ ¢ . w. . . . . . . . . . . .
i o ~3
400
500
600
700
800
900
~,bvelengt h (nm)
FIG. 1. Measuring light available at the sample from several light sources passed thru a Bausch and Lomb 250 mm, Cat. #33-86-40 monochromator with a blue-blazed, 1200 grooves / mm grating. Slit widths, 2.00 mm, corresponding to 6.7-nm bandwidth. (A) 45 watt W-I~ lamp (GE, Q6.6AT2UCL) running at 7.8 V and 7.0 A. (B) The same but boosted for 30 msec to 11.8 V and 9.0 A. (C) 150 W Xe-arc lamp (Hanovia 901C in a Bausch & Lomb housing). (D) 1 kW high-pressure mercury-arc (AH 6-I-B) running at 790 V and 1.36 A. (E) Xe flash lamp (EG&G, FX- 101), operated at 14/zF, 845 V giving 5 J per flash. Note that at wavelengths near an intense line as found in the spectra of some sources the wavelength passed by the monochromator set to wide bandwidth can be much distorted. The pulsed Xe arc is not shown. It can be estimated by moving curve C upward by an amount corresponding to the expected enhancement. × 18 to X I000 are claimed by the papers in footnote 10.
boost an otherwise continuous Xe arc lamp. 1° Taylor e t al. lo use a lightsensing feedback control of the arc to produce constant light, and commercial continuous wave (cw) lasers are stabilized by the same method. "~ Pulsed Xe arcs are described by S. Gordon, K. H. Schmidt, and J. E. Martin, Rev. Sci. lnstrum. 45, 552 (1974); W. B. Taylor, J. C. LeBlanc, D. W. Williams, M. A. Herbert, and H. E. Johns, ibid. 43, 1797 (1972); B. W. Hodgson and J. P. Keene, ibid. p. 493; S. Martellucci and E. Penco. ibid. 37, 783 (1966).
36
SPECIALIZED TECHNIQUES
[3]
If a refinement is necessary, one can use a microscope slide to split off a small fraction of the measuring light before it enters the sample and monitor it with a second detector. When the two detectors are balanced against each other their difference, or their ratio without balancing, will measure the changes of absorption in the sample free from fluctuations of the light source. 11 Note that the use of a bright measuring light in fast measurements does not necessarily mean any greater total exposure of the sample to measuring light. It takes the same total number of photons to make a measurement with a given a c c u r a c y whether the measurement takes a long or short time. H o w e v e r , except when using a discontinuous measuring-light source such as a flash lamp, it may be necessary to avoid excessive pre-exposure to the measuring light before the measurement is made. We use a shutter whose opening gives a signal which starts all the other synchronized a c t i o n s / 2. T h e M o n o c h r o m a t o r In time the tunable, continuously emitting laser lz can be expected to replace the white light source and m o n o c h r o m a t o r . Present continuous wave (cw) lasers can have trouble with stability, and tuning over more than a narrow range requires change of dyes. (Except in a very specialized case, one needs to be able to vary the wavelength of the measuring light: often to scan a spectrum or to monitor different c o m p o n e n t s of a reaction mixture.) If there is a sufficient selection available, interference filters can replace a m o n o c h r o m a t o r and they have the great advantage, in a light-hungry system, of greater overall transmission. Because of the need for maximum amount of light one should use the maximum bandwidth of filter or m o n o c h r o m a t o r consistent with the spectral width of the absorption band whose change is being measured. The 6 - l 0 nm bandwidths are c o m m o n for c y t o c h r o m e or chlorophyll bands. Dual-wavelength s p e c t r o p h o t o m e t r y - - a s employed by Chance 13 and widely used to stabilize against slower, nonspecific changes such as of light scattering or of measuring-light intensity--is not needed in fast spectrophotometry. If one arranges to have a short " b a s e l i n e " on the read-out 11A system using a monitoring photomultiplier and difference amplifier is described by J. C. LeBlanc, A. Fenster, D. W. Williams, M. A. Herbert, and H. E. Johns,Rev. Sci. Instrum. 44, 763 (1973). ~2Tunable cw lasers are produced by Spectra-Physics. Specifications for Model 375 show complete coverage of wavelengths from 430 to 950 nm at 40 mW or more (at least I I different dyes needed). Amplitude stability = + .5% with Model 373 stabilizer. $26,425 (1977) with stabilizer, 2 pump lasers, and special circulator. ~3B. Chance, Rev. Sci. Instrum. 22, 634 (1951).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
37
trace before the stimulus is given to the sample then one has a measurement of the transmission before and after the event in a time too short for slow fluctuations to matter. Of course, if one wants to use two wavelengths simultaneously to extract two separate pieces of information this can be done. 14 While under certain conditions one can place the m o n o c h r o m a t o r after the sample, there are two reasons for at least sometimes placing it before the sample (between the light source and the sample). If the sample is sensitive to the measuring light, monochromating the light before it reaches the sample can greatly reduce the exposure. In this case, one may also put a shutter in the measuring-light path so that exposure begins only a negligible time before the measurement is to be made. 1,~The second reason is that, if the sample is turbid, it would be difficult to find enough light coming from the sample in the proper direction to pass through a monochromator placed after the sample. If the sample is activated by laser flash, it is normally necessary to use a guard filter between sample and detector which absorbs the flash wavelength and passes the measuring light. Often a colored glass filter will do, but sometimes a monochromator after the sample is necessary. 3. Optics In arranging the measuring light optics it is helpful to keep in mind the points at which one finds an " a p e r t u r e " focus and those at which one finds a " s l i t " focus. These are designated A and S respectively in Fig. 2. The slit foci have the characteristic of narrowness, but may not be uniform. For example, if the source is a tungsten filament, the slit focus will show filament structure. The aperture foci have the characteristic of uniform illumination and thus are good for sample illumination unless the sample is narrow. 4. S a m p l e a n d S a m p l e Cell As already mentioned, in contrast to slower measurements, fast measurements tend to be limited by shot noise. The optical density of sample which gives the maximum ratio of signal to shot noise is 0.87, if the total of available measuring light is assumed to be fixed. This value is not critically ~4 p. L. Dutton and J. B. Jackson [Eur. J. Biochem. 30,495 (1972)] and P. L. D u n o n , K. M. Petty, H. S. Bonnet, and S. D. Morse [Biochim. Biophys. Acta 387,536 (1975)] have used 2 wavelengths simultaneously (not time shared) but not below 10/zsec. 1.~ A case in which the pre-exposure to the measuring light of a photosynthetic sample was m e a s u r e d is referenced in footnote 8.
38
SPECIALIZED TECHNIQUES
~ LI
s
A
[3]
M
L2
Grating
sJ ~ Z . _ , _ y ~
S~ L3
Laser
,4 ~
Sample
FIG. 2. Optical considerations. Lens L, focuses the measuring light source onto entrance slit of the monochromator. The conjugate foci of L, are thus "slit loci." Concave mirror M focuses the entrance slit at infinity in the direction of the grating and then focuses the reflections from the grating onto the exit slit. Lens L 4focuses the exit slit to a slit focus forming a narrow portion of the beam before going to the sample. If the sample were narrow it could be placed at this point. Lens L2 focuses the aperture at L ~onto the grating and L3 focuses it onto the aperture at L4. L~ focuses the aperture at Z 4 onto the sample. Its position and focal length can be chosen to give an aperture image at the sample whose size matches the sample size. The slit foci are labeled S and the aperture foci, A.
s h a r p . A n y d e n s i t y n e a r this v a l u e will d o a l m o s t a s well, b u t d e p a r t u r e s b y m o r e t h a n a f a c t o r o f t w o will n o t i c e a b l y d e g r a d e s i g n a l - t o - n o i s e r a t i o . A d e r i v a t i o n o f this n u m b e r is g i v e n in the a p p e n d i x to this a r t i c l e b u t it r e s t s u p o n an o p t i m u m b e t w e e n z e r o o p t i c a l d e n s i t y w h i c h g i v e s no signal, b e c a u s e it c o n t a i n s no s a m p l e , a n d infinite o p t i c a l d e n s i t y w h i c h g i v e s no signal b e c a u s e no light g e t s t h r o u g h . It is f u r t h e r m o d i f i e d b y h o w t h e n o i s e v a r i e s with t h e size o f the signal. S h o t n o i s e is p r o p o r t i o n a l to t h e s q u a r e r o o t o f t h e signal a n d g i v e s 2/ln 10 = 0.87 a s o p t i m u m o p t i c a l d e n s i t y . I f t h e n o i s e w e r e i n d e p e n d e n t o f signal s i z e (as, s a y , a fixed e r r o r in r e a d i n g t h e o u t p u t ) , t h e o p t i m u m w o u l d b e l / l n 10 o r 0.43. T h e o p t i c a l d e n s i t y r e f e r r e d to h e r e is t h a t o f e v e r y t h i n g in t h e s a m p l e i n c l u d i n g i m p u r i t i e s w h i c h a r e p r o p o r t i o n a l to t h e c o n c e n t r a t i o n o f t h e s a m p l e a n d w h i c h a b s o r b t h e m e a s u r i n g light. T h e a s s u m p t i o n is m a d e t h a t t h e a b s o r b i n g i m p u r i t i e s m u s t g o w i t h t h e s a m p l e . If, on t h e o t h e r h a n d , s u c h i m p u r i t i e s c o u l d b e rem o v e d , it w o u l d b e a d v a n t a g e o u s to d o so.
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
39
The optical density of the sample can be adjusted by varying either the concentration or the path length, their product being fixed by the desired optical density. The area of the cuvette could be important, if either the a m o u n t of material available is limited or if the material is sensitive to measuring light. For a fixed optical density, the a m o u n t of material used is proportional to the area. If the area of illumination can be v a r i e d - - a s by changing the focal lengths of the lenses, or changing from an aperture focus to a slit focus, or something in b e t w e e n - - t h e n the larger the area for a given total amount of measuring light, the smaller will be the exposure of each molecule of material. For this reason we have tended to use cuvettes with a large area (15 m m × 15 ram). H o w e v e r , if the amount of sample material were limited, this would place a limit on the area that could be used. 5. T h e D e t e c t o r S y s t e m a. R e a d - o u t D e v i c e . What one uses here m a y depend upon how much m o n e y one can spend. As mentioned in the introduction, we will concentrate on reading out the time course of absorption at a single wavelength. The most versatile instrument for this job is undoubtedly the Tektronix transient digitizer, R7912.16 This instrument will do in the n a n o s e c o n d region what the better-known slower transient digitizers 17 can do in the microsecond region. It digitizes the coordinates of a trace. The digital record can then be stored indefinitely, read out immediately, and/or operated on by c o m p u t e r , as, for example, to add together successive traces to get a " C A T " average. The only other method of digitizing n a n o s e c o n d traces at present is by reading photographs of the traces. 18 The next most expensive read-out system is a fast-storage oscilloscope newly developed by Tektronix, the Model 7834.19 At 2.5 c m / n s e c writing rate it can store transients 2.5 cm high if they take 1 nsec to rise. The Tektronix 7633 `'o stores at i cm/nsec. Other storage scopes known to the writer are not fast enough for nanosecond work. The main advantage of storage oscilloscopes is that they simplify the p h o t o g r a p h y of the trace and avoid wasting film on bad traces. T h e y m a y be a little tricky to adjust to the correct intensity and persistence to get a good stored trace.
~6$20,000 and up. This is sold as part of several systems designated the WP2000 series. 17Biomation, Nicolet, Erdac, Physical Data, and Princeton Applied Research. The Biomation 8100 resolves to about l0 nsec [$9850 (1975)] but none of the others go below 0.5 p.sec. ~ A home-made transient digitizer with a resolution of 2 nsec is described by H. A. Baldis and J. Aazam-Zanganek, Rev. Sci. Instrum. 44, 712 (1973). ~9$10,000 (1977) with one 7A 19, 7B80, and 7B85 plug-ins. Add another $1000 for another 7A !9 if differential input is desired. 2o$6,000 (1977) with 7A18 and 7B50A plug-ins.
40
SPECIALIZED TECHNIQUES
[3]
Nonstorage oscilloscopes should be chosen with camera and phosphor adapted for high photographic writing rate. A 15 cm/nsec writing speed is obtained with either Tektronix 79042' or 7704A. 22The camera 23is another $1200 to $1600. The 7904 has a rise time of 0.8 nsec and the 7704A, 4.7 nsec. b. Detectors. The detector should have a large sensitive area (comparable to the cuvette area or more) to collect as much measuring light as possible from the cuvette. An exception might be a case in which the sample is clear and the transmitted light is still well enough collimated to be focusable to a small area. Usual detectors are photomultipliers, p-i-n type silicon diodes, or vacuum diodes. Photomultipliers have the great advantage of built-in amplification and variable gain. They are good in the upper half (logarithmic) of the nanosecond region (30-1000 nsec). At 30 nsec the minimum cathode current for 0. I% shot noise would be 5 tzA. It is difficult to find a photomultiplier with specifications allowing a larger cathode current than this as would be necessary below 30 nsec. 24 Another problem is that the rise time of many photomultipliers is of the order of 20 nsec due to statistical spread in the transit time of the electrons through the dynodes, although there are ways to solve this problem. 25,26The dynode voltage supply circuit must provide adequate current to meet the demands of high light levels without too much variation of voltage and the last several dynode stages must be bypassed with capacitors. Fatigue effects 27 encountered on a millisecond time scale in photomultipliers are not important at nanosecond speeds, but linearity should be watched. Aside from the expensive gated photomultipliers 24 photodiodes are required below 30 nsec. Fortunately the higher light intensities involved reduce the requirements for amplification and external amplifiers of sufficient gain are feasible. Biplanar vacuum photodiodes z8have very good rise times. However, the greater quantum efficiency of silicon photodiodes 29helps to combat shot noise by giving a larger primary photocurrent 2, $7,200 (1977) with one 7A19, 7B80, and 7B85 plug-ins. Add $1000 for a second 7A19 if differential input is desired. 2z $4,600 (1977) with 7A18 and 7B53A plug-ins. 23 Tektronix model C-51 with writing speed enhancer ($1570) or model C-27, option 04, with writing speed enhancer ($1160). 24 Photomultipliers with cathode current ratings higher than 5 p.A: I.T.T. Co. F4084 (gated), 50 /~A, $3671 (1971); E.G.&G. Co. GPM-50M, gated, 100/zA, $1690 (1971). 2~ Examples of fast photomultipliers: EMI 9810 to 9818 (2 nsec); Amperex XP1020 ( < 2 nsec). 26 Use of optimum voltages and fewer dynodes: A. Fenster, J. C. LeBlanc, W. B. Taylor, and H. E. Johns, Rev. Sci. Instrum. 44,689 (1973); G. Beck, ibid. 47, 537 (1976). 27 See DeVault r and Fenster et al. 26. z8 Biplanar diodes: I.T.T. Co: FWll4; Hamamatsu Co. R617; Instrument Technology Ltd, Hastings, England, TF50. 29 Fast silicon photodiodes of large area: E.G.&G. Co. SGD-444 (100 mm2).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY P.0.
41
@
®
FIG. 3. Diode detector and current-to-voltage signal amplifier. P.D. = SGD-444 photodiode (E.G.&G. Co.);A~ = A 2 = / z A 7 3 3 amplifier(Fairchild Co.);D~-D~6 = IN4148;R~ = R7 = R' 7 = R 4 = R' 4 : 1 kD,;R 2 = R.', = 50,Q;R:~ : R~ = R 6 = R'~ = 20,Q;Rs : R.~ : Rs = R~ : 2001); C, = 0.01 ~F; Cz = C'2 = C3 = C;~ = Cs = C~ = 0.001 ~F; C4 = C'4 = 0.022 g F . R o = Adjusted to give desired ratio between voltage applied at " o f f s e t " and the offset produced in output. O n e of the outputs goes directly to the input of the amplifier s h o w n in Fig. 3. For further gain at slower speeds the two outputs can go to the inputs of, say, a/~A 715 (Fairchild) integrated circuit amplifier. A distinctive feature of this circuit is the use of pin # 4 (emitter of one of the input transistors) of the ~A733 as a current-input terminal. (Normal input is voltage applied to pins 1 and 2.) Shunt feedback is provided internally in the/~A733 by 7 k~Q resistors between output and input on each side of the amplifier. Both share in offsetting the input current so that the output voltage on either side is then ½ X 7 k,Q X (input current), and the effective input impedance, which multiplied by photodiode capacitance gives the time constant, is very small. Details of this design were worked out by Mr. Drew Henderson. The two amplifier stages apparently have a flat response from 0 to 30 M H z with overall transfer impedance (voltage out/current in) of 35 kO on each output.
for a given light intensity. Figure 3 shows a detector-amplifier system, costing not much more than the price of the photodiode ($225) plus labor, which is good to 10 nsec resolving time. c. Matching Detector to Oscilloscope. Normally one will connect detector to oscilloscope with a length of coaxial cable. At the smaller resolving times it is essential to terminate the cable with its characteristic impedence (usually 50-75 1)) to avoid reflections of signal in the cable. This termination becomes the output load resistor of the detector and whatever amplifier may be attached to it. If one uses a very high oscilloscope sensitivity, such as 10 m V/cm, the current required through a 50-1"~resistor to get a 2-cm deflection would be 0.4 mA. If the 0.4 mA corresponds to the I% change in transmission postulated in our earlier example, the total signal would correspond to 40 mA. A current of 40 mA is beyond the output capability of most photomultipliers, and only an extremely bright light source would give this much primary photocurrent from a photodiode. Therefore, an amplifier is ordinarily needed to couple either photomultiplier or photodiode to the connecting cable. By introducing offset (see § d) to the amplifier at an early stage, one makes it unnecessary for the amplifier to handle the whole signal and it need amplify only the changes in
42
SPECIALIZED TECHNIQUES
[3]
signal. H o w e v e r , it is well to amplify beyond the 0.4 mA, postulated above, in order to use a less sensitive scale on the oscilloscope. Photodiodes and photomultipliers are both high-impedance devices putting out a current proportional to the light. The load resistance should be as small as possible to keep the time constant (load resistance × internal capacity) small for fast response. This is accomplished by using shunt feedback in the amplifier. The amplifier in Fig. 3 is able to put out a signal with up to 4 V peak-to-peak. H o w e v e r , it is limited to 10 mA output, and so could not drive 50 or 75 l-I the full 4 V. It can, however, if the amplifier of Fig. 4 is added as an output stage. 3°
RINz
/74
R3
=CI
CI
-~
G FIG. 4. Output(current) amplifier. R i = 27011;R1 = R'~ = 7501~;R2 = R~ = 110ll;Ra = R~ = 911~;R 4 = R~ = 5101~;RL = 7511 (to match RG-59U cable); C1 = C'~ = 0.1/.~F; QI = Q2 = 2N3906; Q'I = Q'2 -- 2N3904. Q2and Q~ should be mounted in good thermal contact with a h e a t sink. Power supply requirements: + V = + 9 V at 130 mA. Input impedance ~ 100 kll at DC; 1 k[l at 16 MHz. Another set of values which have been found useful are: R~ = 20011; R 1 = R '1 = 5101~;R2 = R~ = 1001~;R:~ = R.~ = 511~;R 4 = R ; = 330fL C1 = C'1 = 0.001 txF; ± V = ± 5 V at 130 mA. In contrast to the usual emitter-follower output amplifier this circuit is " p u s h p u l l " - - e q u a l drive for both rising and falling signals. Its rise time appears to be less than 1 nsec.
d. Offset Considerations. When measuring small changes, 2~S, in a large signal S one must offset most o f the signal so that the small change will deflect the trace an easily discernable amount. One must also k n o w what the a m o u n t of offset is so that one can calculate A S / ( 2 . 3 S ) , the change o f optical density. We have d e v e l o p e d an automatic offset circuit that is very useful. 3~ We are trying to publish the circuit e l s e w h e r e , but the principle is ao Other preamplifiers: J. P. Keene, E. D. Black, and E. Hayon, Rev. Sci. Instrum. 40, 1199 ( 1969); G. Diebold and R. Santaro, ibid. 45,773 ( 1974); R. H. Hamstra, Jr. and P. Wendland, Appl. Opt. 11, 1539 (1972). "Pulse amplifiers" with 1 nsec rise times and band pass limited to frequencies above some given value are fairly c o m m o n and can be used for fast measurements if the DC light-intensity data can be obtained by parallel use of a slower DC amplifier. See, for example, J. K. Millard, Rev. Sci. Instrum. 38, 169 (1967). :~ Other offset circuits: S. L. Olsen, L. P. Holmes, and E. M. Eyring, Rev. Sci. lnstrum. 45, 859 (1974); D. A. Whyte, ibid. 47, 379 (1976).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
43
as follows: The output from the signal amplifier goes to both the oscilloscope and also a special amplifier that generates an offset current, a current which is fed to an early stage of the signal amplifier in parallel but opposite in sign to the photo-signal current. In Fig. 3 the entrance point of this offset current is indicated. This current counteracts or offsets the photo-signal. It is generated by only a small deviation in the input to the oscilloscope and to the offset amplifier and is just enough to keep the deviation small. Thus the signal-amplifier and the offset-amplifier form a servoloop that keeps the input to the oscilloscope fixed close to some desired value regardless of the size of the photo-signal. At the time the oscilloscope sweep starts, a signal from the oscilloscope triggers a gate that opens the servoloop and holds the offset constant thereafter at w h a t e v e r value was found at the m o m e n t of opening. Further variations in the photo-signal then record fully on the oscilloscope screen. Before the loop is again closed to make the next m e a s u r e m e n t the actual offset is read from a meter attached to the output of the offset amplifier. This arrangement assures that the oscilloscope trace will start at the desired height on the screen. If the offset adjustment were not automatic, slow unknown variations of light intensity or sample density could throw the trace completely off the screen before it starts. e. B a n d w i d t h V a r i a t i o n . For m a x i m u m signal-to-noise ratio it is necessary to match the bandwidth of the amplifier to the speed of the measurement. The s p e c t r o p h o t o m e t e r will often be used at rates slower than the design maximum. In such a case one should be able to decrease the bandwidth accordingly. We do this with a simple series resistor followed by a capacitor to ground in a box containing a choice of resistors and capacitors. 3z The usual choice is to make ~- ~ 1/200 of the time for one oscilloscope sweep, so that the trace will correspond to at least 200 resolved points. The bandwidth limiter should be applied at a stage before the noise has been amplified to a point where it is clipped by the amplifier swing limits. The suggestion of footnote 32 is excellent in this respect. 6. T h e Stimulus The perturbation administered to the sample could be anything, but it must be fast if it is to be followed by a f a s t m e a s u r e m e n t . The experience of this author is entirely with light flashes, '~'~but radiolysis pulses, 34 tempera:~2Another method is to put a capacitor in parallel with the shunt feedback of the signal amplifier. The capacity times the feedback resistance then gives the "integration time constant." :~'~Pioneering in nanosecond spectroscopy is the group under H. T. Witt. See C, Wolff, H, E. Buchwald, H. R/ippel, K. Witt, and H. T. Witt, Z. Naturfi~rsch.~ Teil 24b, 1038 (1969). :~4j. p. Keene, Nature (London) 188, 843 (1960).
44
SPECIALIZED TECHNIQUES
[3]
ture jumps,35 shock waves, and electric and magnetic field jumps are also possibilities. Rapid mixing is not yet below the microsecond range but one can think of using flash photolysis to generate a reagent in sire to react with a system of interest not itself sensitive to light. The following will consider flash activation. The pulsed laser is certainly the choice flash generator. Q-switching (control of laser-cavity gain to shorten the pulse) or other gatingis necessary to get into the nanosecond range. The coherence (spacial) property of the laser is useful in allowing the laser to be put at some distance (we use 6 m) from the spectrophotometer and readout amplifiers. This helps greatly in reducing electrical interference from the flash-lamp and possibly gating circuits of the laser. The lack of afterglow from the laser (compared to a flash-lamp) is also important because the afterglow can interfere with the spectrophotometric measurements, especially if the sample is turbid. There are at least three common ways of Q-switching the laser. It can be done with (1) a passive, saturatable dye, (2) a rotating prism, or (3) a Pockels cell. The first has the disadvantage that it is hard to synchronize with the scope trigger so as to obtain a reliable amount of base line before the pulse stimulates the sample. However, this objection only applies at the slower end of the nanosecond range. When the base line need be only 100 nsec or less, the signal delay built into the oscilloscope may be sufficient for generating a base line. In this case the oscilloscope may be triggered by a signal from a small photodiode monitoring the laser flash itself. The Pockels cell has the disadvantage that it requires a heavy electrical pulse to activate it just at the moment one is trying to make the spectrophotometric measurement. The electrical isolation must be extra good. The rotating prism is a simple mechanical device and has served well in the author's ruby laser z6 for 14 years. A magnetic pick-up on it gives a signal a fixed number of microseconds before the prism will be in position to cause iasing, and this signal is used to synchronize the oscilloscope in the upper end of the nanosecond range. The "delayed sweep" capability of the oscilloscope is very useful for adjusting base lines. Small delays can be introduced into one signal line or another by the simple use of extra lengths of coaxial cable (about 5 nsec/m). '~7 Delay lines designed for the purpose can also be obtained. :35 By electric discharge through the sample microwave heating, etc. [M. Eigen, Disc. Faraday Soc. 17, 194 (1954); M. Eigen and L. De Maeyer in "Technique of Organic Chemistry" (A. Weissberger, ed.), Vol. VIII, part II, p. 895. Wiley, New York, 1963; M. Eigen in "Nobel Symposium 5" (S. Claesson, ed.), p. 333. Almqvist and Wiksell, Stockholm, 1967]. Also by light flash absorbed in solvent [J. V. Beitz, G. W. Flynn, D. H. Turner, and N. Sutin,J. Am. Chem. Soc. 92, 4130 (1970)]. ~6 TRG-Hadron Model 104. :37This was done in M. C. Kung and D. DeVault, Biochim. Biophys. Acta 501, 217 (1978). Lytle 4 discusses limitations.
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
45
Unless one wants to run out an action spectrum the limited number of wavelengths that may be easily available from Q-switched lasers is not a great disadvantage. The ruby laser's primary output is 694 nm, very good and much more powerful than necessary for stimulating photosynthetic systems. Frequency-doubling gives 347 nm and stimulated Raman effect in hydrogen gas gives 539 nm as the first anti-Stokes line. 3s The 694 nm easily pumps dye lasers to give longer wavelengths. :~ N e o d y m i u m lasers give 1.06 ktm direct, 530 nm doubled, and 265 nm quadrupled. If one uses a cuvette whose horizontal cross-section is square one can introduce the laser light at right angles to the measuring light. H o w e v e r , in this case it is particularly necessary to insure sufficiently uniform activation of sample across the face of the measuring beam to avoid errors in the measurement. If the cuvette has large area presented to measuring-light and short measuring-light path length it will be necessary to introduce the laser light in parallel with the measuring light. This can also be more uniform. The arrangement shown in Fig. 2 is particularly suitable for getting both beams through a narrow aperture as in the side of a cryostat holding the cuvette in its interior.
Acknowledgments The author received valuable advice from Drs. Henry Linschitz and William Parson. The writing of this section was supported by National Science Foundation grants PCM76-15724, PCM76-23744, and PCM77-22086.
A p p e n d i x : D e r i v a t i o n of O p t i m u m S a m p l e D e n s i t y Let Y = 2.3Ecl where • = extinction coefficient, c ---- concentration, and / = path length thru the cuvette. Then: S = Soe ~"
(1)
where So = photodetector current with empty cuvette and S with sample in place. For generality we let the noise, N, in the photodetector current be proportional to arbitrary power, n, of the signal; thus: N = kl S" and No = /,'IS,"
(2)
We also consider two types of spectrophotometric measurement: In case I the measurement is of the total optical density, Y/2.3. In this case: Y= INS,.- InS
(3)
In case II the measurement is of a small change in optical density, AY/2.3. :~sR. W. Minck, R. W. Terhune, and W. G. Rado, Appl. Phys. Lett. 3, 181 (1963). :~' B. Chance, J. A. McCray, and J. Bunkenburg, Nat,re (London) 225, 703 (1970).
46
SPECIALIZED
TECHNIQUES
[3]
In this case: As Ay = In S -- In (S + AS) ~ - S
(4)
W e will a s s u m e that A y remains a fixed fraction o f Y during a n y manipulation o f c or 1" Ay = k~r
(5)
T h e noise in In So is: N o O In So _
No
OS,)
So -- k l S o n i
(6)
T h e noise in In S is: N O In S
N
OS
S
--
k lgOt'--I e(l t/'Y
(7)
and this is practically also the noise in In (S + AS). T h e noise in the overall m e a s u r e m e n t s indicated in (3) and (4) will be the square r o o t o f the sums o f the s q u a r e s o f the noise in the individual terms. T h u s the s q u a r e s o f the signal-to-noise ratios are: y2
Case I: C a s e II:
k~2 So~'-~(l + e 2(1-")Y) k~Y2 2k ,~S o.2, '2 e 2` .... Y
(8)
(9)
W e find the value o f Y which m a x i m i z e s these e x p r e s s i o n s by differentiating with r e s p e c t to Y and setting equal to zero. T h e result is: 1 + e 2(n-l)Y C a s e I:
Case II:
Y -
(10)
I -n
Y-
1
1
?/
(i 1)
C a s e II is a s s u m e d in the b o d y of this paper. I f the s o u r c e o f noise w e r e the reading error, n = 0 and the o p t i m u m value o f Y would be 1. With s h o t noise, n ---- I/2 and k 1 = ~/q/"l" w h e r e q is the c h a r g e o f an electron. In this case the o p t i m u m value of Y is 2 and the c o r r e s p o n d i n g optical d e n s i t y is 2/2.3.
SPECIALIZED TECHNIQUES
[3]
The identity of I can be pheophytin as Fajer 3~suggested or a combination of several species. These primary processes in rhodopsin and chlorophyll are only an example of the potential uses of picosecond spectroscopy in biology. With extrapolation one can decipher processes with 3 × 10 ':~ sec lifetimes, thus approaching a vibrational period which is essentially the lower limit for chemical and biological events. Acknowledgments The work of Drs. G. E. Busch, D. Huppert, K. J. Kaufmann, T. L. Netzel, W. S. Struve, and V. Sundstrom at Bell Laboratories has formed the basis of this paper. 1 thank Drs. M. L. Applebury, P. L. Dutton, and K. S. Peters for collaboration and discussions on rhodopsin (MLA and KSP) and bacteriochlorophyll (PLD). I thank Drs. D. C. Douglass, E. O. Degenkolb, and L. J. Noe for continuous discussions and suggestions in the development of this manuscript. a.~ j. Fajer, D. C. Brune, M. S. Davis, A. Forman, and L. D. Spaulding,Proc. Natl. Acad. Sci. U.S.A. 72, 4956 (1975).
[3] N a n o s e c o n d
Absorbance Spectrophotometry
By DON DEVAULT It is possible, with a streak camera, to record a whole spectrum in a nanosecond and to record changes in successive nanoseconds. The instruments are expensive ($40,000)' and probably do not have the sensitivity required for biological spectrometry 2 which often deals with transmission changes of the order of only 1%. Furthermore when one is dealing with a known reaction it is usually not necessary to obtain a whole spectrum but only the time course of changes at a few key wavelengths. 3 This chapter ' Some producers of streak cameras: Hadland Photonics, Ltd., Tel: (0442) 832525, U.K. (or Macro Scientific, Inc., Sunnyvale, Calif., Tel: 408-739-9418); Hamamatsu TV Co., Ltd., Hamamatsu, Japan (or Middlesex, New Jersey 08846); Cordin, Salt Lake City, Utah 84119. See also S. Gordon, K. H. Schmidt, and J. E. Martin, Rev. Sci. Instrum. 45,552 (1974). The price given is for a Cordin Model 132 + minimum accessories. The Hamamatsu C979 is $47,000 (1977). (Prices approximate only. Dated because of inflation.) 2 Hamamatsu estimates their dynamic range as possibly 1000 but gives data showing 68. I have no data on the others. However, to make any kind of measurement on a 1% change, the noise should be no more than 0. I%, making imperative a dynamic range of 1000 or a gray-scale resolved to 10 bits. 3 The relative merits of taking an instantaneous whole spectrum at a given time after the stimulus to the sample vs. following the kinetics at a single wavelength is discussed by one of
METHODS IN ENZYMOLOGY, VOL. LIV
Copyright O 1978by AcademicPress, Inc. All rightsof reproduction in any form reserved. ISBN 0-12-181954-X
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
33
will d i s c u s s i n s t r u m e n t a t i o n for m e a s u r i n g the t i m e c o u r s e o f small r a p i d c h a n g e s o f a b s o r b a n c e at a single w a v e l e n g t h ? T o o b t a i n a s p e c t r u m o n e r e p e a t s the e x p e r i m e n t at d i f f e r e n t w a v e l e n g t h s . A c c o r d i n g to t h e title w e a r e d i s c u s s i n g i n s t r u m e n t a t i o n in w h i c h t y p i cal o r limiting t i m e c o n s t a n t s , z, r a n g e f r o m 1000 n s e c d o w n to I n s e c . This c o r r e s p o n d s to b a n d w i d t h s e q u a l to 1/(2~'z) o r 160 k H z to 160 M H z . I n s t r u m e n t s p e c i f i c a t i o n s a r e often in " r i s e t i m e s , " Tr, w h i c h is d e f i n e d in s e v e r a l d i f f e r e n t w a y s '~ v a r y i n g f r o m 1.6 z to 2.3 z. S o m e t i m e s 1 will call z t h e " r e s o l v i n g t i m e . " T e c h n i q u e s at the 1000 n s e c e n d o f the r a n g e a r e not g r e a t l y d i f f e r e n t f r o m s t a n d a r d s p e c t r o p h o t o m e t r y , while t h o s e at t h e 1 n s e c e n d a p p r o a c h the state o f the art. H o w m u c h o f the f o l l o w i n g a d v i c e o n e n e e d s d e p e n d s u p o n h o w far d o w n into the n a n o s e c o n d r a n g e o n e i n t e n d s to go. T h e p a r t s o f a f a s t - a b s o r b a n c e s p e c t r o p h o t o m e t e r a r e (1) t h e m e a s u r i n g light s o u r c e , (2) m e a n s o f c h o o s i n g the m e a s u r i n g w a v e l e n g t h if the s o u r c e is n o t a l r e a d y sufficiently m o n o c h r o m a t i c , (3) a cell h o l d i n g the s p e c i m e n , (4) a d e t e c t o r to m e a s u r e , a m p l i f y , a n d r e c o r d the t r a n s m i t t e d (or p o s s i b l y r e f l e c t e d ) m e a s u r i n g light i n t e n s i t y as a f u n c t i o n o f t i m e , a n d (5) a m e a n s o f s t i m u l a t i n g o r p e r t u r b i n g the s a m p l e .
1. T h e L i g h t S o u r c e T h e m o s t d e m a n d i n g a s p e c t o f fast s p e c t r o p h o t o m e t r y is the n e e d f o r a s u f f i c i e n t l y b r i g h t m e a s u r i n g light s o u r c e . T h e m i n i m u m b r i g h t n e s s is s e t b y t h e n e e d to r e d u c e " s h o t " n o i s e to a s u i t a b l e level. S h o t n o i s e is the n o i s e in t h e o u t p u t w h i c h r e s u l t s f r o m the c o r p u s c u l a r n a t u r e o f the m e a s u r ing light a n d / o r the p h o t o e l e c t r i c c u r r e n t it p r o d u c e s in t h e d e t e c t o r . T h e m o s t critical s t a g e in t h e m e a s u r i n g l i g h t - d e t e c t o r s y s t e m is t h a t at w h i c h the n u m b e r o f s u c h c o r p u s c l e s is a m i n i m u m . In t h e m e a s u r i n g light b e a m this will b e at t h e e n t r a n c e to the d e t e c t o r , a f t e r the l o s s e s d u e to a b s o r p t i o n in the s a m p l e a n d i n e f f i c i e n c i e s in the o p t i c a l p a r t s . In the e l e c t r i c a l p a r t s it will b e t h e p r i m a r y p h o t o e l e c t r i c c u r r e n t b e f o r e a n y a m p l i f i c a t i o n . N o r the pioneers in the field, G. Porter, in "Photochemistry and Reaction Kinetics" (P. G. Ashmore, F. S. Dainton, and T. M Sugden, eds.), pp. 9 3 - I l i . Cambridge Univ. Press, London and New York, 1967. Note that the streak camera aims to do both. 4 Another general discussion of fast spectrophotometry is F. E. Lytle, Anal. Chem. 46, 545A and 817A (1974). Tr is usually defined as the time to rise from 10% to 90% of the ultimate rise. For a sine wave this is (sin-' 0.9)/Trf, wheref is the frequency, taken here to be the bandwidth, or Tr = 2"r sin -l 0.9 = 2.24T. In the case of an exponential approach to a constant displacement, Tr = z In 9 = 2.20 z, where ~-is the time constant of the exponential. Another definition used, but not consistently, in the Tektronix catalogue appears to he the time for ¼ of a cycle of sine wave. This give T,. = 7rr/2 = 1.57r.
34
SPECIALIZED TECHNIQUES
[3]
mally the electric current will have fewer corpuscles (electrons) than there are photons producing them because the quantum efficiency of photoelectron production is usually less than 1. I f n photoelectrons are produced in one sample period the noise, i.e., the root mean square of the deviations from sample to sample, 6 will be X/n. If the noise is required to be less than 0.1% of the signal, then X/n must be less than 0.1% ofn and n must be more than 106. If the sample period is 1 nsec (for a I-nsec resolution of measurement), the photoelectric current must be more than 106 electrons per 10-9 sec or more than 160 p,amperes. Suppose, next, that the material in the cuvette transmits only 10% of the measuring light striking it and that the efficiency of the detector in collecting the transmitted photons and converting to photoelectrons is 10%. Then our example tells us that 108 photons must strike the cuvette per sample period. This is l014 photons sec -1 at ~ = 1000 nsec and 1017photons sec -1 at ~- -- ! nsec. 1017photons o f 500 nm wavelength per second is 40 mW of light energy incident on the cuvette. Figure 1 illustrates our experience with various lamps. For specifications other than those assumed in the example, note that noise/signal will be inversely proportional to the square root of the light intensity, and resolving time for a given noise/signal level will be inversely proportional to the first power of light intensity. It is possible to use smaller measuring light intensity if the experiment can be repeated a large number of times. At 1/100 the light intensity calculated above one could repeat the measurement 100 times and the total amount of light entering during the sum of corresponding sample periods will be the same. A computer would be required to add together the corresponding samples from the different repetitions (Computer of Average Transient). If one uses CAT averaging, some of the following advice needs modification, particularly the needs for measuring-light intensity and for detector capacity. There are problems with maintaining constancy of light intensity during the measuring interval. Our solution for the boosted incandescent light source, used in the slower measurements, is described elsewhere. 7 The high-pressure mercury arc s is constant enough for intervals up to 10 ~sec, but it fluctuates over longer intervals. The Xe flash lamp can be given a reasonably flat top for, say 1 ~sec, by using a pulse that is considerably broader overall. 9 A common method of getting bright light is to transiently 6 Poisson statistics. 7 D. DeVault, in "Rapid Mixing and Sampling Techniques in Biochemistry" (B. Chance et al., eds.), pp. 165-174. Academic Press, New York, 1964. The AHG- 1B sold by several lamp companies running at 900 V and I A. An example of its use is found in M. Seibert and D. DeVault, Biochim. Biophys. Acta 253, 396 (1971). 9 We have used the E.G. and G. Co. FX-101 pulsed with 5J. An example of its use is by M. C. Kung and D. DeVault, P h o t o c h e m . Photobiol. 24, 87 (1976).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY 1018
,
1017
+
1016
+
,
,
+
35
1018
i
,
,
+
+
+
1017
+
+
+
+
JO16
,+
+
+
!i
'°'5 '. ~i, \-?
5
i} Jc ,o"ii
/
ii /
+f /
/~
i o 15
,
.....
+
+
- w-Iz( 55 w)
+
+
i o 14
.....
~ _ . _ . ~ ¢ . w. . . . . . . . . . . .
i o ~3
400
500
600
700
800
900
~,bvelengt h (nm)
FIG. 1. Measuring light available at the sample from several light sources passed thru a Bausch and Lomb 250 mm, Cat. #33-86-40 monochromator with a blue-blazed, 1200 grooves / mm grating. Slit widths, 2.00 mm, corresponding to 6.7-nm bandwidth. (A) 45 watt W-I~ lamp (GE, Q6.6AT2UCL) running at 7.8 V and 7.0 A. (B) The same but boosted for 30 msec to 11.8 V and 9.0 A. (C) 150 W Xe-arc lamp (Hanovia 901C in a Bausch & Lomb housing). (D) 1 kW high-pressure mercury-arc (AH 6-I-B) running at 790 V and 1.36 A. (E) Xe flash lamp (EG&G, FX- 101), operated at 14/zF, 845 V giving 5 J per flash. Note that at wavelengths near an intense line as found in the spectra of some sources the wavelength passed by the monochromator set to wide bandwidth can be much distorted. The pulsed Xe arc is not shown. It can be estimated by moving curve C upward by an amount corresponding to the expected enhancement. × 18 to X I000 are claimed by the papers in footnote 10.
boost an otherwise continuous Xe arc lamp. 1° Taylor e t al. lo use a lightsensing feedback control of the arc to produce constant light, and commercial continuous wave (cw) lasers are stabilized by the same method. "~ Pulsed Xe arcs are described by S. Gordon, K. H. Schmidt, and J. E. Martin, Rev. Sci. lnstrum. 45, 552 (1974); W. B. Taylor, J. C. LeBlanc, D. W. Williams, M. A. Herbert, and H. E. Johns, ibid. 43, 1797 (1972); B. W. Hodgson and J. P. Keene, ibid. p. 493; S. Martellucci and E. Penco. ibid. 37, 783 (1966).
36
SPECIALIZED TECHNIQUES
[3]
If a refinement is necessary, one can use a microscope slide to split off a small fraction of the measuring light before it enters the sample and monitor it with a second detector. When the two detectors are balanced against each other their difference, or their ratio without balancing, will measure the changes of absorption in the sample free from fluctuations of the light source. 11 Note that the use of a bright measuring light in fast measurements does not necessarily mean any greater total exposure of the sample to measuring light. It takes the same total number of photons to make a measurement with a given a c c u r a c y whether the measurement takes a long or short time. H o w e v e r , except when using a discontinuous measuring-light source such as a flash lamp, it may be necessary to avoid excessive pre-exposure to the measuring light before the measurement is made. We use a shutter whose opening gives a signal which starts all the other synchronized a c t i o n s / 2. T h e M o n o c h r o m a t o r In time the tunable, continuously emitting laser lz can be expected to replace the white light source and m o n o c h r o m a t o r . Present continuous wave (cw) lasers can have trouble with stability, and tuning over more than a narrow range requires change of dyes. (Except in a very specialized case, one needs to be able to vary the wavelength of the measuring light: often to scan a spectrum or to monitor different c o m p o n e n t s of a reaction mixture.) If there is a sufficient selection available, interference filters can replace a m o n o c h r o m a t o r and they have the great advantage, in a light-hungry system, of greater overall transmission. Because of the need for maximum amount of light one should use the maximum bandwidth of filter or m o n o c h r o m a t o r consistent with the spectral width of the absorption band whose change is being measured. The 6 - l 0 nm bandwidths are c o m m o n for c y t o c h r o m e or chlorophyll bands. Dual-wavelength s p e c t r o p h o t o m e t r y - - a s employed by Chance 13 and widely used to stabilize against slower, nonspecific changes such as of light scattering or of measuring-light intensity--is not needed in fast spectrophotometry. If one arranges to have a short " b a s e l i n e " on the read-out 11A system using a monitoring photomultiplier and difference amplifier is described by J. C. LeBlanc, A. Fenster, D. W. Williams, M. A. Herbert, and H. E. Johns,Rev. Sci. Instrum. 44, 763 (1973). ~2Tunable cw lasers are produced by Spectra-Physics. Specifications for Model 375 show complete coverage of wavelengths from 430 to 950 nm at 40 mW or more (at least I I different dyes needed). Amplitude stability = + .5% with Model 373 stabilizer. $26,425 (1977) with stabilizer, 2 pump lasers, and special circulator. ~3B. Chance, Rev. Sci. Instrum. 22, 634 (1951).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
37
trace before the stimulus is given to the sample then one has a measurement of the transmission before and after the event in a time too short for slow fluctuations to matter. Of course, if one wants to use two wavelengths simultaneously to extract two separate pieces of information this can be done. 14 While under certain conditions one can place the m o n o c h r o m a t o r after the sample, there are two reasons for at least sometimes placing it before the sample (between the light source and the sample). If the sample is sensitive to the measuring light, monochromating the light before it reaches the sample can greatly reduce the exposure. In this case, one may also put a shutter in the measuring-light path so that exposure begins only a negligible time before the measurement is to be made. 1,~The second reason is that, if the sample is turbid, it would be difficult to find enough light coming from the sample in the proper direction to pass through a monochromator placed after the sample. If the sample is activated by laser flash, it is normally necessary to use a guard filter between sample and detector which absorbs the flash wavelength and passes the measuring light. Often a colored glass filter will do, but sometimes a monochromator after the sample is necessary. 3. Optics In arranging the measuring light optics it is helpful to keep in mind the points at which one finds an " a p e r t u r e " focus and those at which one finds a " s l i t " focus. These are designated A and S respectively in Fig. 2. The slit foci have the characteristic of narrowness, but may not be uniform. For example, if the source is a tungsten filament, the slit focus will show filament structure. The aperture foci have the characteristic of uniform illumination and thus are good for sample illumination unless the sample is narrow. 4. S a m p l e a n d S a m p l e Cell As already mentioned, in contrast to slower measurements, fast measurements tend to be limited by shot noise. The optical density of sample which gives the maximum ratio of signal to shot noise is 0.87, if the total of available measuring light is assumed to be fixed. This value is not critically ~4 p. L. Dutton and J. B. Jackson [Eur. J. Biochem. 30,495 (1972)] and P. L. D u n o n , K. M. Petty, H. S. Bonnet, and S. D. Morse [Biochim. Biophys. Acta 387,536 (1975)] have used 2 wavelengths simultaneously (not time shared) but not below 10/zsec. 1.~ A case in which the pre-exposure to the measuring light of a photosynthetic sample was m e a s u r e d is referenced in footnote 8.
38
SPECIALIZED TECHNIQUES
~ LI
s
A
[3]
M
L2
Grating
sJ ~ Z . _ , _ y ~
S~ L3
Laser
,4 ~
Sample
FIG. 2. Optical considerations. Lens L, focuses the measuring light source onto entrance slit of the monochromator. The conjugate foci of L, are thus "slit loci." Concave mirror M focuses the entrance slit at infinity in the direction of the grating and then focuses the reflections from the grating onto the exit slit. Lens L 4focuses the exit slit to a slit focus forming a narrow portion of the beam before going to the sample. If the sample were narrow it could be placed at this point. Lens L2 focuses the aperture at L ~onto the grating and L3 focuses it onto the aperture at L4. L~ focuses the aperture at Z 4 onto the sample. Its position and focal length can be chosen to give an aperture image at the sample whose size matches the sample size. The slit foci are labeled S and the aperture foci, A.
s h a r p . A n y d e n s i t y n e a r this v a l u e will d o a l m o s t a s well, b u t d e p a r t u r e s b y m o r e t h a n a f a c t o r o f t w o will n o t i c e a b l y d e g r a d e s i g n a l - t o - n o i s e r a t i o . A d e r i v a t i o n o f this n u m b e r is g i v e n in the a p p e n d i x to this a r t i c l e b u t it r e s t s u p o n an o p t i m u m b e t w e e n z e r o o p t i c a l d e n s i t y w h i c h g i v e s no signal, b e c a u s e it c o n t a i n s no s a m p l e , a n d infinite o p t i c a l d e n s i t y w h i c h g i v e s no signal b e c a u s e no light g e t s t h r o u g h . It is f u r t h e r m o d i f i e d b y h o w t h e n o i s e v a r i e s with t h e size o f the signal. S h o t n o i s e is p r o p o r t i o n a l to t h e s q u a r e r o o t o f t h e signal a n d g i v e s 2/ln 10 = 0.87 a s o p t i m u m o p t i c a l d e n s i t y . I f t h e n o i s e w e r e i n d e p e n d e n t o f signal s i z e (as, s a y , a fixed e r r o r in r e a d i n g t h e o u t p u t ) , t h e o p t i m u m w o u l d b e l / l n 10 o r 0.43. T h e o p t i c a l d e n s i t y r e f e r r e d to h e r e is t h a t o f e v e r y t h i n g in t h e s a m p l e i n c l u d i n g i m p u r i t i e s w h i c h a r e p r o p o r t i o n a l to t h e c o n c e n t r a t i o n o f t h e s a m p l e a n d w h i c h a b s o r b t h e m e a s u r i n g light. T h e a s s u m p t i o n is m a d e t h a t t h e a b s o r b i n g i m p u r i t i e s m u s t g o w i t h t h e s a m p l e . If, on t h e o t h e r h a n d , s u c h i m p u r i t i e s c o u l d b e rem o v e d , it w o u l d b e a d v a n t a g e o u s to d o so.
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
39
The optical density of the sample can be adjusted by varying either the concentration or the path length, their product being fixed by the desired optical density. The area of the cuvette could be important, if either the a m o u n t of material available is limited or if the material is sensitive to measuring light. For a fixed optical density, the a m o u n t of material used is proportional to the area. If the area of illumination can be v a r i e d - - a s by changing the focal lengths of the lenses, or changing from an aperture focus to a slit focus, or something in b e t w e e n - - t h e n the larger the area for a given total amount of measuring light, the smaller will be the exposure of each molecule of material. For this reason we have tended to use cuvettes with a large area (15 m m × 15 ram). H o w e v e r , if the amount of sample material were limited, this would place a limit on the area that could be used. 5. T h e D e t e c t o r S y s t e m a. R e a d - o u t D e v i c e . What one uses here m a y depend upon how much m o n e y one can spend. As mentioned in the introduction, we will concentrate on reading out the time course of absorption at a single wavelength. The most versatile instrument for this job is undoubtedly the Tektronix transient digitizer, R7912.16 This instrument will do in the n a n o s e c o n d region what the better-known slower transient digitizers 17 can do in the microsecond region. It digitizes the coordinates of a trace. The digital record can then be stored indefinitely, read out immediately, and/or operated on by c o m p u t e r , as, for example, to add together successive traces to get a " C A T " average. The only other method of digitizing n a n o s e c o n d traces at present is by reading photographs of the traces. 18 The next most expensive read-out system is a fast-storage oscilloscope newly developed by Tektronix, the Model 7834.19 At 2.5 c m / n s e c writing rate it can store transients 2.5 cm high if they take 1 nsec to rise. The Tektronix 7633 `'o stores at i cm/nsec. Other storage scopes known to the writer are not fast enough for nanosecond work. The main advantage of storage oscilloscopes is that they simplify the p h o t o g r a p h y of the trace and avoid wasting film on bad traces. T h e y m a y be a little tricky to adjust to the correct intensity and persistence to get a good stored trace.
~6$20,000 and up. This is sold as part of several systems designated the WP2000 series. 17Biomation, Nicolet, Erdac, Physical Data, and Princeton Applied Research. The Biomation 8100 resolves to about l0 nsec [$9850 (1975)] but none of the others go below 0.5 p.sec. ~ A home-made transient digitizer with a resolution of 2 nsec is described by H. A. Baldis and J. Aazam-Zanganek, Rev. Sci. Instrum. 44, 712 (1973). ~9$10,000 (1977) with one 7A 19, 7B80, and 7B85 plug-ins. Add another $1000 for another 7A !9 if differential input is desired. 2o$6,000 (1977) with 7A18 and 7B50A plug-ins.
40
SPECIALIZED TECHNIQUES
[3]
Nonstorage oscilloscopes should be chosen with camera and phosphor adapted for high photographic writing rate. A 15 cm/nsec writing speed is obtained with either Tektronix 79042' or 7704A. 22The camera 23is another $1200 to $1600. The 7904 has a rise time of 0.8 nsec and the 7704A, 4.7 nsec. b. Detectors. The detector should have a large sensitive area (comparable to the cuvette area or more) to collect as much measuring light as possible from the cuvette. An exception might be a case in which the sample is clear and the transmitted light is still well enough collimated to be focusable to a small area. Usual detectors are photomultipliers, p-i-n type silicon diodes, or vacuum diodes. Photomultipliers have the great advantage of built-in amplification and variable gain. They are good in the upper half (logarithmic) of the nanosecond region (30-1000 nsec). At 30 nsec the minimum cathode current for 0. I% shot noise would be 5 tzA. It is difficult to find a photomultiplier with specifications allowing a larger cathode current than this as would be necessary below 30 nsec. 24 Another problem is that the rise time of many photomultipliers is of the order of 20 nsec due to statistical spread in the transit time of the electrons through the dynodes, although there are ways to solve this problem. 25,26The dynode voltage supply circuit must provide adequate current to meet the demands of high light levels without too much variation of voltage and the last several dynode stages must be bypassed with capacitors. Fatigue effects 27 encountered on a millisecond time scale in photomultipliers are not important at nanosecond speeds, but linearity should be watched. Aside from the expensive gated photomultipliers 24 photodiodes are required below 30 nsec. Fortunately the higher light intensities involved reduce the requirements for amplification and external amplifiers of sufficient gain are feasible. Biplanar vacuum photodiodes z8have very good rise times. However, the greater quantum efficiency of silicon photodiodes 29helps to combat shot noise by giving a larger primary photocurrent 2, $7,200 (1977) with one 7A19, 7B80, and 7B85 plug-ins. Add $1000 for a second 7A19 if differential input is desired. 2z $4,600 (1977) with 7A18 and 7B53A plug-ins. 23 Tektronix model C-51 with writing speed enhancer ($1570) or model C-27, option 04, with writing speed enhancer ($1160). 24 Photomultipliers with cathode current ratings higher than 5 p.A: I.T.T. Co. F4084 (gated), 50 /~A, $3671 (1971); E.G.&G. Co. GPM-50M, gated, 100/zA, $1690 (1971). 2~ Examples of fast photomultipliers: EMI 9810 to 9818 (2 nsec); Amperex XP1020 ( < 2 nsec). 26 Use of optimum voltages and fewer dynodes: A. Fenster, J. C. LeBlanc, W. B. Taylor, and H. E. Johns, Rev. Sci. Instrum. 44,689 (1973); G. Beck, ibid. 47, 537 (1976). 27 See DeVault r and Fenster et al. 26. z8 Biplanar diodes: I.T.T. Co: FWll4; Hamamatsu Co. R617; Instrument Technology Ltd, Hastings, England, TF50. 29 Fast silicon photodiodes of large area: E.G.&G. Co. SGD-444 (100 mm2).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY P.0.
41
@
®
FIG. 3. Diode detector and current-to-voltage signal amplifier. P.D. = SGD-444 photodiode (E.G.&G. Co.);A~ = A 2 = / z A 7 3 3 amplifier(Fairchild Co.);D~-D~6 = IN4148;R~ = R7 = R' 7 = R 4 = R' 4 : 1 kD,;R 2 = R.', = 50,Q;R:~ : R~ = R 6 = R'~ = 20,Q;Rs : R.~ : Rs = R~ : 2001); C, = 0.01 ~F; Cz = C'2 = C3 = C;~ = Cs = C~ = 0.001 ~F; C4 = C'4 = 0.022 g F . R o = Adjusted to give desired ratio between voltage applied at " o f f s e t " and the offset produced in output. O n e of the outputs goes directly to the input of the amplifier s h o w n in Fig. 3. For further gain at slower speeds the two outputs can go to the inputs of, say, a/~A 715 (Fairchild) integrated circuit amplifier. A distinctive feature of this circuit is the use of pin # 4 (emitter of one of the input transistors) of the ~A733 as a current-input terminal. (Normal input is voltage applied to pins 1 and 2.) Shunt feedback is provided internally in the/~A733 by 7 k~Q resistors between output and input on each side of the amplifier. Both share in offsetting the input current so that the output voltage on either side is then ½ X 7 k,Q X (input current), and the effective input impedance, which multiplied by photodiode capacitance gives the time constant, is very small. Details of this design were worked out by Mr. Drew Henderson. The two amplifier stages apparently have a flat response from 0 to 30 M H z with overall transfer impedance (voltage out/current in) of 35 kO on each output.
for a given light intensity. Figure 3 shows a detector-amplifier system, costing not much more than the price of the photodiode ($225) plus labor, which is good to 10 nsec resolving time. c. Matching Detector to Oscilloscope. Normally one will connect detector to oscilloscope with a length of coaxial cable. At the smaller resolving times it is essential to terminate the cable with its characteristic impedence (usually 50-75 1)) to avoid reflections of signal in the cable. This termination becomes the output load resistor of the detector and whatever amplifier may be attached to it. If one uses a very high oscilloscope sensitivity, such as 10 m V/cm, the current required through a 50-1"~resistor to get a 2-cm deflection would be 0.4 mA. If the 0.4 mA corresponds to the I% change in transmission postulated in our earlier example, the total signal would correspond to 40 mA. A current of 40 mA is beyond the output capability of most photomultipliers, and only an extremely bright light source would give this much primary photocurrent from a photodiode. Therefore, an amplifier is ordinarily needed to couple either photomultiplier or photodiode to the connecting cable. By introducing offset (see § d) to the amplifier at an early stage, one makes it unnecessary for the amplifier to handle the whole signal and it need amplify only the changes in
42
SPECIALIZED TECHNIQUES
[3]
signal. H o w e v e r , it is well to amplify beyond the 0.4 mA, postulated above, in order to use a less sensitive scale on the oscilloscope. Photodiodes and photomultipliers are both high-impedance devices putting out a current proportional to the light. The load resistance should be as small as possible to keep the time constant (load resistance × internal capacity) small for fast response. This is accomplished by using shunt feedback in the amplifier. The amplifier in Fig. 3 is able to put out a signal with up to 4 V peak-to-peak. H o w e v e r , it is limited to 10 mA output, and so could not drive 50 or 75 l-I the full 4 V. It can, however, if the amplifier of Fig. 4 is added as an output stage. 3°
RINz
/74
R3
=CI
CI
-~
G FIG. 4. Output(current) amplifier. R i = 27011;R1 = R'~ = 7501~;R2 = R~ = 110ll;Ra = R~ = 911~;R 4 = R~ = 5101~;RL = 7511 (to match RG-59U cable); C1 = C'~ = 0.1/.~F; QI = Q2 = 2N3906; Q'I = Q'2 -- 2N3904. Q2and Q~ should be mounted in good thermal contact with a h e a t sink. Power supply requirements: + V = + 9 V at 130 mA. Input impedance ~ 100 kll at DC; 1 k[l at 16 MHz. Another set of values which have been found useful are: R~ = 20011; R 1 = R '1 = 5101~;R2 = R~ = 1001~;R:~ = R.~ = 511~;R 4 = R ; = 330fL C1 = C'1 = 0.001 txF; ± V = ± 5 V at 130 mA. In contrast to the usual emitter-follower output amplifier this circuit is " p u s h p u l l " - - e q u a l drive for both rising and falling signals. Its rise time appears to be less than 1 nsec.
d. Offset Considerations. When measuring small changes, 2~S, in a large signal S one must offset most o f the signal so that the small change will deflect the trace an easily discernable amount. One must also k n o w what the a m o u n t of offset is so that one can calculate A S / ( 2 . 3 S ) , the change o f optical density. We have d e v e l o p e d an automatic offset circuit that is very useful. 3~ We are trying to publish the circuit e l s e w h e r e , but the principle is ao Other preamplifiers: J. P. Keene, E. D. Black, and E. Hayon, Rev. Sci. Instrum. 40, 1199 ( 1969); G. Diebold and R. Santaro, ibid. 45,773 ( 1974); R. H. Hamstra, Jr. and P. Wendland, Appl. Opt. 11, 1539 (1972). "Pulse amplifiers" with 1 nsec rise times and band pass limited to frequencies above some given value are fairly c o m m o n and can be used for fast measurements if the DC light-intensity data can be obtained by parallel use of a slower DC amplifier. See, for example, J. K. Millard, Rev. Sci. Instrum. 38, 169 (1967). :~ Other offset circuits: S. L. Olsen, L. P. Holmes, and E. M. Eyring, Rev. Sci. lnstrum. 45, 859 (1974); D. A. Whyte, ibid. 47, 379 (1976).
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
43
as follows: The output from the signal amplifier goes to both the oscilloscope and also a special amplifier that generates an offset current, a current which is fed to an early stage of the signal amplifier in parallel but opposite in sign to the photo-signal current. In Fig. 3 the entrance point of this offset current is indicated. This current counteracts or offsets the photo-signal. It is generated by only a small deviation in the input to the oscilloscope and to the offset amplifier and is just enough to keep the deviation small. Thus the signal-amplifier and the offset-amplifier form a servoloop that keeps the input to the oscilloscope fixed close to some desired value regardless of the size of the photo-signal. At the time the oscilloscope sweep starts, a signal from the oscilloscope triggers a gate that opens the servoloop and holds the offset constant thereafter at w h a t e v e r value was found at the m o m e n t of opening. Further variations in the photo-signal then record fully on the oscilloscope screen. Before the loop is again closed to make the next m e a s u r e m e n t the actual offset is read from a meter attached to the output of the offset amplifier. This arrangement assures that the oscilloscope trace will start at the desired height on the screen. If the offset adjustment were not automatic, slow unknown variations of light intensity or sample density could throw the trace completely off the screen before it starts. e. B a n d w i d t h V a r i a t i o n . For m a x i m u m signal-to-noise ratio it is necessary to match the bandwidth of the amplifier to the speed of the measurement. The s p e c t r o p h o t o m e t e r will often be used at rates slower than the design maximum. In such a case one should be able to decrease the bandwidth accordingly. We do this with a simple series resistor followed by a capacitor to ground in a box containing a choice of resistors and capacitors. 3z The usual choice is to make ~- ~ 1/200 of the time for one oscilloscope sweep, so that the trace will correspond to at least 200 resolved points. The bandwidth limiter should be applied at a stage before the noise has been amplified to a point where it is clipped by the amplifier swing limits. The suggestion of footnote 32 is excellent in this respect. 6. T h e Stimulus The perturbation administered to the sample could be anything, but it must be fast if it is to be followed by a f a s t m e a s u r e m e n t . The experience of this author is entirely with light flashes, '~'~but radiolysis pulses, 34 tempera:~2Another method is to put a capacitor in parallel with the shunt feedback of the signal amplifier. The capacity times the feedback resistance then gives the "integration time constant." :~'~Pioneering in nanosecond spectroscopy is the group under H. T. Witt. See C, Wolff, H, E. Buchwald, H. R/ippel, K. Witt, and H. T. Witt, Z. Naturfi~rsch.~ Teil 24b, 1038 (1969). :~4j. p. Keene, Nature (London) 188, 843 (1960).
44
SPECIALIZED TECHNIQUES
[3]
ture jumps,35 shock waves, and electric and magnetic field jumps are also possibilities. Rapid mixing is not yet below the microsecond range but one can think of using flash photolysis to generate a reagent in sire to react with a system of interest not itself sensitive to light. The following will consider flash activation. The pulsed laser is certainly the choice flash generator. Q-switching (control of laser-cavity gain to shorten the pulse) or other gatingis necessary to get into the nanosecond range. The coherence (spacial) property of the laser is useful in allowing the laser to be put at some distance (we use 6 m) from the spectrophotometer and readout amplifiers. This helps greatly in reducing electrical interference from the flash-lamp and possibly gating circuits of the laser. The lack of afterglow from the laser (compared to a flash-lamp) is also important because the afterglow can interfere with the spectrophotometric measurements, especially if the sample is turbid. There are at least three common ways of Q-switching the laser. It can be done with (1) a passive, saturatable dye, (2) a rotating prism, or (3) a Pockels cell. The first has the disadvantage that it is hard to synchronize with the scope trigger so as to obtain a reliable amount of base line before the pulse stimulates the sample. However, this objection only applies at the slower end of the nanosecond range. When the base line need be only 100 nsec or less, the signal delay built into the oscilloscope may be sufficient for generating a base line. In this case the oscilloscope may be triggered by a signal from a small photodiode monitoring the laser flash itself. The Pockels cell has the disadvantage that it requires a heavy electrical pulse to activate it just at the moment one is trying to make the spectrophotometric measurement. The electrical isolation must be extra good. The rotating prism is a simple mechanical device and has served well in the author's ruby laser z6 for 14 years. A magnetic pick-up on it gives a signal a fixed number of microseconds before the prism will be in position to cause iasing, and this signal is used to synchronize the oscilloscope in the upper end of the nanosecond range. The "delayed sweep" capability of the oscilloscope is very useful for adjusting base lines. Small delays can be introduced into one signal line or another by the simple use of extra lengths of coaxial cable (about 5 nsec/m). '~7 Delay lines designed for the purpose can also be obtained. :35 By electric discharge through the sample microwave heating, etc. [M. Eigen, Disc. Faraday Soc. 17, 194 (1954); M. Eigen and L. De Maeyer in "Technique of Organic Chemistry" (A. Weissberger, ed.), Vol. VIII, part II, p. 895. Wiley, New York, 1963; M. Eigen in "Nobel Symposium 5" (S. Claesson, ed.), p. 333. Almqvist and Wiksell, Stockholm, 1967]. Also by light flash absorbed in solvent [J. V. Beitz, G. W. Flynn, D. H. Turner, and N. Sutin,J. Am. Chem. Soc. 92, 4130 (1970)]. ~6 TRG-Hadron Model 104. :37This was done in M. C. Kung and D. DeVault, Biochim. Biophys. Acta 501, 217 (1978). Lytle 4 discusses limitations.
[3]
NANOSECOND ABSORBANCE SPECTROPHOTOMETRY
45
Unless one wants to run out an action spectrum the limited number of wavelengths that may be easily available from Q-switched lasers is not a great disadvantage. The ruby laser's primary output is 694 nm, very good and much more powerful than necessary for stimulating photosynthetic systems. Frequency-doubling gives 347 nm and stimulated Raman effect in hydrogen gas gives 539 nm as the first anti-Stokes line. 3s The 694 nm easily pumps dye lasers to give longer wavelengths. :~ N e o d y m i u m lasers give 1.06 ktm direct, 530 nm doubled, and 265 nm quadrupled. If one uses a cuvette whose horizontal cross-section is square one can introduce the laser light at right angles to the measuring light. H o w e v e r , in this case it is particularly necessary to insure sufficiently uniform activation of sample across the face of the measuring beam to avoid errors in the measurement. If the cuvette has large area presented to measuring-light and short measuring-light path length it will be necessary to introduce the laser light in parallel with the measuring light. This can also be more uniform. The arrangement shown in Fig. 2 is particularly suitable for getting both beams through a narrow aperture as in the side of a cryostat holding the cuvette in its interior.
Acknowledgments The author received valuable advice from Drs. Henry Linschitz and William Parson. The writing of this section was supported by National Science Foundation grants PCM76-15724, PCM76-23744, and PCM77-22086.
A p p e n d i x : D e r i v a t i o n of O p t i m u m S a m p l e D e n s i t y Let Y = 2.3Ecl where • = extinction coefficient, c ---- concentration, and / = path length thru the cuvette. Then: S = Soe ~"
(1)
where So = photodetector current with empty cuvette and S with sample in place. For generality we let the noise, N, in the photodetector current be proportional to arbitrary power, n, of the signal; thus: N = kl S" and No = /,'IS,"
(2)
We also consider two types of spectrophotometric measurement: In case I the measurement is of the total optical density, Y/2.3. In this case: Y= INS,.- InS
(3)
In case II the measurement is of a small change in optical density, AY/2.3. :~sR. W. Minck, R. W. Terhune, and W. G. Rado, Appl. Phys. Lett. 3, 181 (1963). :~' B. Chance, J. A. McCray, and J. Bunkenburg, Nat,re (London) 225, 703 (1970).
46
SPECIALIZED
TECHNIQUES
[3]
In this case: As Ay = In S -- In (S + AS) ~ - S
(4)
W e will a s s u m e that A y remains a fixed fraction o f Y during a n y manipulation o f c or 1" Ay = k~r
(5)
T h e noise in In So is: N o O In So _
No
OS,)
So -- k l S o n i
(6)
T h e noise in In S is: N O In S
N
OS
S
--
k lgOt'--I e(l t/'Y
(7)
and this is practically also the noise in In (S + AS). T h e noise in the overall m e a s u r e m e n t s indicated in (3) and (4) will be the square r o o t o f the sums o f the s q u a r e s o f the noise in the individual terms. T h u s the s q u a r e s o f the signal-to-noise ratios are: y2
Case I: C a s e II:
k~2 So~'-~(l + e 2(1-")Y) k~Y2 2k ,~S o.2, '2 e 2` .... Y
(8)
(9)
W e find the value o f Y which m a x i m i z e s these e x p r e s s i o n s by differentiating with r e s p e c t to Y and setting equal to zero. T h e result is: 1 + e 2(n-l)Y C a s e I:
Case II:
Y -
(10)
I -n
Y-
1
1
?/
(i 1)
C a s e II is a s s u m e d in the b o d y of this paper. I f the s o u r c e o f noise w e r e the reading error, n = 0 and the o p t i m u m value o f Y would be 1. With s h o t noise, n ---- I/2 and k 1 = ~/q/"l" w h e r e q is the c h a r g e o f an electron. In this case the o p t i m u m value of Y is 2 and the c o r r e s p o n d i n g optical d e n s i t y is 2/2.3.