Basic Principles of the Single Photon Counting Lifetime Measurement

2

Basic Principles of the Single Photon Counting Lifetime Measurement

2.1

The Standard Experiment

A s c h e m a t i c d i a g r a m of a c o n v e n t i o n a l single p h o t o n c o u n t i n g i n s t r u m e n t is s h o w n in Fig. 2 . 1 . T h e single p h o t o n c o u n t i n g m e a s u r e m e n t relies o n t h e c o n c e p t t h a t t h e p r o b a b i l i t y d i s t r i b u t i o n for e m i s s i o n of a single p h o t o n after

FLUORESCENCE CHANNEL

TRIGGER CHANNEL

!—>|TAC|<- -

-

Figure 2.1 Block diagram of a conventional single photon counting apparatus. — optical signal; electronic signal; L, excitation source; T, trigger [Antenna, (fibre optic) and photomultiplier tube, etc.]; S, sample holder; F i , F 2, filter or monochromator; P M , fast photomultiplier tube; D 1 D?2, delay lines; L E D , leading edge timing discriminator; C F T D , constant fraction timing discriminator; TAC, timeto-amplitude converter; A D C , analogue-to-digital converter; DS, data store (multi­ channel analyser or computer). 36

2. Basic

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37

a n e x c i t a t i o n e v e n t yields t h e a c t u a l i n t e n s i t y a g a i n s t t i m e d i s t r i b u t i o n of all t h e p h o t o n s e m i t t e d a s a r e s u l t of t h e e x c i t a t i o n . By s a m p l i n g t h e single p h o t o n e m i s s i o n f o l l o w i n g a l a r g e n u m b e r of e x c i t a t i o n flashes, t h e e x p e r i ­ m e n t constructs this probability distribution. W i t h reference t o t h i s d i a g r a m , t h e e x p e r i m e n t is c a r r i e d o u t a s follows: t h e t r i g g e r T, w h i c h c o u l d b e a p h o t o m u l t i p l i e r , a n a n t e n n a p i c k - u p , o r a l o g i c a l sync, p u l s e f r o m t h e e l e c t r o n i c s p u l s i n g t h e e x c i t a t i o n s o u r c e , g e n e r a t e s a n electrical p u l s e a t a t i m e e x a c t l y c o r r e l a t e d w i t h t h e t i m e of g e n e r a t i o n of t h e o p t i c a l p u l s e . T h e t r i g g e r p u l s e is r o u t e d , p e r h a p s t h r o u g h a d i s c r i m i n a t o r , t o t h e s t a r t i n p u t of t h e t i m e - t o - a m p l i t u d e c o n v e r t e r , ( T A C ) w h i c h i n i t i a t e s c h a r g i n g of a c a p a c i t o r . I n t h e m e a n t i m e t h e o p t i c a l p u l s e excites t h e s a m p l e , w h i c h s u b s e q u e n t l y fluoresces. A n a p e r t u r e h a s b e e n a d j u s t e d s o t h a t a t m o s t o n e p h o t o n is " d e t e c t e d " for e a c h e x c i t i n g e v e n t . T h e s i g n a l r e s u l t i n g f r o m t h i s p h o t o n s t o p s t h e c h a r g i n g r a m p in t h e T A C , w h i c h p u t s o u t a p u l s e , t h e a m p l i t u d e of w h i c h is p r o p o r t i o n a l t o t h e c h a r g e in t h e c a p a c i t o r , a n d h e n c e t o t h e t i m e difference b e t w e e n S T A R T a n d S T O P p u l s e s . T h e T A C o u t p u t p u l s e is g i v e n a n u m e r i c a l v a l u e in t h e a n a l o g u e - t o - d i g i t a l c o n v e r t e r a n d a c o u n t is s t o r e d in t h e d a t a s t o r a g e d e v i c e in a n a d d r e s s c o r r e s p o n d i n g t o t h a t n u m b e r . E x c i t a t i o n a n d d a t a s t o r a g e a r e r e p e a t e d in t h i s w a y u n t i l t h e h i s t o g r a m of n u m b e r of c o u n t s a g a i n s t a d d r e s s n u m b e r in t h e s t o r a g e d e v i c e r e p r e s e n t s , t o s o m e r e q u i r e d p r e c i s i o n , t h e d e c a y c u r v e of t h e s a m p l e . If d e c o n v o l u t i o n is n e c e s s a r y , t h e t i m e profile of t h e e x c i t a t i o n p u l s e is c o l l e c t e d in t h e s a m e w a y b y r e p l a c i n g t h e s a m p l e b y a light s c a t t e r e r .

2.2

Details

2.2.1

Statistics

In a n ideal time-correlation experiment each p h o t o n emitted by the s a m p l e as a r e s u l t of a g i v e n e x c i t a t i o n flash w o u l d b e t i m e d a n d r e c o r d e d . I n fact t h e r e s p o n s e t i m e of t h e d e t e c t i o n e q u i p m e n t a n d t h e m o d e of o p e r a t i o n of t h e T A C r e n d e r it n e c e s s a r y t o t i m e o n l y t h e first p h o t o n in a g i v e n t i m e i n t e r v a l after t h e o c c u r r e n c e of t h e flash. T h e s t a t i s t i c s of g e n e r a l p h o t o n c o u n t i n g h a v e b e e n d i s c u s s e d b y M o r t o n (1968); a s i m p l e r d i s c u s s i o n is g i v e n h e r e following Pfeffer et al. (1962) a n d W a h l (1975). D u r i n g o n e e x c i t a t i o n cycle a n a v e r a g e n u m b e r of p h o t o n s , z i m p i n g e o n h t h e c a t h o d e of t h e fluorescence p h o t o m u l t i p l i e r d u r i n g t h e t i m e i n t e r v a l ί,·_ 21 to i / + , 1c o/r r e2s p o n d i n g t o t h e t i m e w i d t h of a d d r e s s i ( u s u a l l y a c h a n n e l in a m u l t i c h a n n e l a n a l y s e r ) in t h e d a t a s t o r e . T h e s e p h o t o n s eject a n a v e r a g e n u m b e r vv of p h o t o e l e c t r o n s f r o m t h e p h o t o c a t h o d e , t h u s

f

W; -

qz

i9

(2.1)

/

38

Time-correlated

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w h e r e q is t h e q u a n t u m efficiency of t h e p h o t o c a t h o d e . T h e p r o b a b i l i t y of e m i s s i o n of / p h o t o e l e c t r o n s in t h e ith t i m e i n t e r v a l is g i v e n b y t h e P o i s s o n d i s t r i b u t i o n ( M a n d e l a n d Wolf, 1965):

m Pi® = -jfe-

(2.2)

with

00

Ift=l

(2-3)

/=o T h e r e f o r e ( K o e c h l i n , 1961):

w w

(2.4)

P,(/) = w e - '

(2.5)

Po(0 = e - '

i

Pi> i(0 = 1 - Po(0 w = 1- e "

Wi

'-

wfi~ (2.6)

After a l a r g e n u m b e r of e x c i t a t i o n cycles (N ), E t h e ith t i m e i n t e r v a l , N , is

t h e n u m b e r of a n o d e p u l s e s in

A

N

(i) A = NElPl

If w «

t

+

(i)l

Pl>1

(2.7)

1, t h e n p (i) = w

1

and

i

(2.8)

? P i > i ( 0 = w. <
T h e r e f o r e t h e n u m b e r of a n o d e p u l s e s , i V , is p r o p o r t i o n a l t o t h e i n t e n s i t y of A t h e fluorescence a t t i m e i, since

«

N Wi

E

= Nq .

EZi

(2.9)

B e c a u s e t h e T A C d e t e c t s o n l y t h e first p h o t o n in a g i v e n t i m e i n t e r v a l for a g i v e n e x c i t a t i o n cycle, N is n o t t h e n u m b e r of c o u n t s in t h e ith c h a n n e l . T h i s A n u m b e r , N is r e l a t e d t o N b y t h e e q u a t i o n ( C o a t e s , 1968):

h

A

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39

Since j

t h e n u m b e r of detected a n o d e p u l s e s , if Ν «Ν it follows t h a t Ni = N . Ό Ε A C o n s e q u e n t l y t h e c o u n t in c h a n n e l i is a m e a s u r e of t h e f l u o r e s c e n c e i n t e n s i t y at time t.

(

G e n e r a l l y , Ν is m e a s u r e d a t t h e o u t p u t of t h e T A C a n d Ν /Ν Ό Ό Ε kept below a c e r t a i n limit. If N is n o t v e r y m u c h less t h a n ΛΓ , d a t a c a n b e c o r r e c t e d D Ε u s i n g E q u a t i o n 2.10 p r o v i d e d t h a t w , « 1 (see S e c t i o n 6.4). C o l l e c t i o n a t h i g h Ν /Ν Ό Ε r a t i o s n e e d n o t l e a d t o d i s t o r t e d c u r v e s if p i l e - u p i n s p e c t i o n is p e r f o r m e d (see S e c t i o n 5.2.5(b)). H o w e v e r , it is s i m p l e r a n d p r o b a b l y j u s t a s efficient, w h e n d a t a t r a n s f e r a n d a n a l y s i s a r e t a k e n i n t o a c c o u n t , t o k e e p t h e r a t i o Ν /Ν below a certain value.

ΌΕ

It is c l e a r t h a t c h o i c e of a v a l u e for N /N ( D E = F D) will d e p e n d o n t h e level of d i s t o r t i o n t h a t c a n b e a c c e p t e d . Y g u e r a b i d e (1972) h a s d i s c u s s e d t h i s p o i n t ; u s i n g n u m e r i c a l c a l c u l a t i o n s w i t h E q u a t i o n 2.10 h e c o n c l u d e d t h a t a n F a s D h i g h a s 0.05 w a s t o l e r a b l e since a t t h i s c o u n t r a t e d i s t o r t i o n s in t h e e a r l y c h a n n e l s a r e negligible, w h i l e t h e y a m o u n t t o o n l y a few p e r c e n t in t h e l a t e c h a n n e l s . H o w e v e r , e m p i r i c a l tests in o u r l a b o r a t o r y i n d i c a t e t h a t significant d i s t o r t i o n s a r e still p r e s e n t w h e n F is a s h i g h a s 0.05. I n fact m o s t w o r k e r s D k e e p F l o w e r t h a n 0.01 o r 0.02. As far a s p i l e - u p d i s t o r t i o n s a r e c o n c e r n e d , D t h e l o w e r t h e v a l u e of F t h e b e t t e r ; t h e r e f o r e , if c o l l e c t i o n t i m e s a r e s h o r t (as D for i n s t a n c e in i n s t r u m e n t s w i t h a c a v i t y d u m p e d l a s e r a s e x c i t a t i o n s o u r c e ) a n F of 0.005 o r e v e n 0.002 is m o r e u s u a l . It s h o u l d b e p o i n t e d o u t t h a t D e x c i t a t i o n s o u r c e s in S P C i n s t r u m e n t s a r e c o m p a r a t i v e l y w e a k in i n t e n s i t y a n d in m a n y e x p e r i m e n t s t h e l o w level of d e t e c t e d p h o t o n s , JV , r e n d e r s D d i s c u s s i o n of t o l e r a b l e F v a l u e s s o m e w h a t a c a d e m i c . I n c o n c l u s i o n , t h e r e ­ D fore, w h e n p u l s e p i l e - u p d i s t o r t i o n s a r e t o b e a v o i d e d b y l i m i t i n g t h e n u m b e r of d e t e c t e d p h o t o n s a v a l u e of F in t h e r e g i o n of 0.001 o r l o w e r is t o b e D preferred.

2.2.2

Sensitivity, precision and time resolution

W h e n t h e fluorescence p h o t o m u l t i p l i e r ( t h e P M ) is o p e r a t e d in t h e single p h o t o n m o d e , m a n y of t h e d i s t o r t i o n s n o r m a l l y a c c o m p a n y i n g p h o t o ­ m u l t i p l i e r d e t e c t i o n a n d a s s o c i a t e d r e c o r d i n g c i r c u i t r y a r e a v o i d e d , since t h e P M is u s e d m e r e l y t o t i m e t h e a r r i v a l of a p h o t o n a t t h e p h o t o c a t h o d e . I n a d d i t i o n , a m p l i t u d e j i t t e r in t h e e x c i t i n g light p u l s e is i r r e l e v a n t p r o v i d e d t h a t t h e p u l s e s h a p e r e m a i n s c o n s t a n t . T h e S P C t e c h n i q u e t h e r e f o r e h a s all t h e a d v a n t a g e s of d i g i t a l s i g n a l p r o c e s s i n g a n d in a d d i t i o n , a t least for d e c a y t i m e m e a s u r e m e n t s (see C h a p t e r 7 for s p e c t r o s c o p i c m e a s u r e m e n t s ) , is c o n c e r n e d o n l y w i t h t h e t i m e s of o c c u r r e n c e of e v e n t s a n d n o t w i t h i n t e n s i t i e s .

40

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T h e effect of P M n o i s e is g r e a t l y r e d u c e d in m a n y e x p e r i m e n t s b y t h e m o d e of o p e r a t i o n of t h e T A C . W h e n t h e T A C h a s r e c e i v e d t h e S T A R T p u l s e it r e m a i n s " d e a d " for s o m e fixed t i m e before t h e v o l t a g e s w e e p (see S e c t i o n 5.2.5) is i n i t i a t e d . D u r i n g t h e v o l t a g e s w e e p , w h i c h c a n c o n t i n u e for a t i m e set b y t h e o p e r a t o r (called t h e T A C r a n g e ) , it c a n a c c e p t a t m o s t o n e s i g n a l r e s u l t i n g f r o m e i t h e r n o i s e o r fluorescence. A t t h e e n d of t h e T A C r a n g e , o r after r e c e i v i n g t h e S T O P s i g n a l , it r e m a i n s " d e a d " u n t i l t h e n e x t S T A R T s i g n a l a r r i v e s . S i n c e t h e T A C r a n g e is u s u a l l y set t o s p a n t h e m a x i m u m in t h e p h o t o n d i s t r i b u t i o n f u n c t i o n , d a t a c o l l e c t i o n o c c u r s a t t i m e s of e n h a n c e d s i g n a l - t o - n o i s e r a t i o . T h e r e f o r e , a P M n o i s e c o u n t r a t e of s a y 1000 H z after t h e C F T D d i s c r i m i n a t o r m a y b e r e d u c e d b y a f a c t o r of 100 after t h e T A C w h e n t h e t r i g g e r p u l s e is u s e d t o s t a r t t h e v o l t a g e s w e e p . O t h e r w i s e (see S e c t i o n 2.2.6) n o i s e r e d u c t i o n will b e less. G e n e r a l l y b a c k g r o u n d n o i s e offers n o s e r i o u s difficulties since t h e P M is c h o s e n w i t h l o w n o i s e c h a r a c t e r i s t i c s a n d c o r r e c t i o n for b a c k g r o u n d is q u i t e s t r a i g h t f o r ­ w a r d ( S e c t i o n 2.2.5). Sensitivity in S P C i n s t r u m e n t s h a s s o m e t i m e s b e e n r e p o r t e d in t e r m s of t h e r e c i p r o c a l of t h e p r o d u c t ( o p t i c a l d e n s i t y in 1 c m p a t h l e n g t h χ q u a n t u m yield) for t h e6 s a m p l e , t7h e d e c a y t i m e of w h i c h h a s b e e n m e a s u r e d . F i g u r e s a s h i g h a s 1 0 a n d 1 0 h a v e b e e n r e p o r t e d for flash l a m p ( W a r e , 1 9 7 1 ; Y g u e r a b i d e , 1972) a n d l a s e r - b a s e d s y s t e m s ( H a r r i s et al, 1977). U n l e s s t h e d e g r e e of light a t t e n u a t i o n in m o n o c h r o m a t o r s a n d filters is specified, t h i s figure is v i r t u a l l y m e a n i n g l e s s . A n o t h e r a p p r o a c h is s u g g e s t e d b y K n i g h t a n d S e l i n g e r (1973) w h o u s e d a c o n c r e t e e x a m p l e . T h e y d e t e c t e d ( T A C c o n v e r ­ sions) 10 p h o t o n s p e r s e c o n d o n a T A C r4a n g e of 80 n s w h e n t h e v a p o u r o v e r c r y s t a l l i n e a n t h r a c e n e a t 2 0 ° C (P= 1 0 ~ T o r r ) w a s e x c i t e d a t 337.1 n m . Slit w i d t h s a n d m o d e of filtering, h o w e v e r , w e r e n o t specified. H a u g e n a n d L y t l e (1981) h a v e e v a l u a t e d t h e sensitivity of t h e i r i n s t r u m e n t a s ( c o u n t s a c t u a l l y measured)/(counts that should be measured), the latter calculated from k n o w n q u a n t i t i e s s u c h a s n u m b e r of e x c i t a t i o n p h o t o n s p e r s e c o n d , o p t i c a l d e n s i t y of s a m p l e , q u a n t u m yield, / - n u m b e r of o p t i c s , reflections a n d a i r g l a s s interfaces, s p a t i a l a p e r t u r e s , q u a n t u m efficiency of P M p h o t o c a t h o d e - 1 filters -1 a t t h e a p p r o p r i a t e w a v e l e1n g3t h s . ( T h e y a c h i e v e d 2.0 a n d t r13 a n s m i s s i o n of χ 1 0 counts M s o u t of a p o s s i b l e 2.8 χ 1 0 . ) T h i s a p p r o a c h , w h i l e r i g o r o u s , is difficult t o follow in s o m e e x p e r i m e n t s . W e s u g g e s t , t h e r e f o r e , t h a t if sensitivity is t o b e specified it s h o u l d b e d o n e in t e r m s of o p t i c a l d e n s i t y a n d q u a n t u m yield w i t h full d e t a i l s of slit w i d t h s a n d filters a l s o specified. I n a fluorescence d e c a y c u r v e c o l l e c t e d b y t h e S P C t e c h n i q u e t h e r e a r e t w o d i s t i n c t t y p e s of n o i s e . O n e , r e s u l t i n g f r o m p h o t o m u l t i p l i e r d a r k c o u n t s , is a c o n s t a n t b a c k g r o u n d a n d is easily t r e a t e d (see S e c t i o n 2.2.5). T h e o t h e r , a c o u n t i n g e r r o r , v a r i e s f r o m c h a n n e l t o c h a n n e l a n d is of m o r e f u n d a m e n t a l i m p o r t a n c e . I n t h e d a t a s t o r e r e s u l t i n g f r o m a n S P C e x p e r i m e n t t h e r e is, in a

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41

g i v e n t i m e i n t e r v a l ( c h a n n e l ) , a finite n o n - z e r o c h a n c e of o b s e r v i n g a n y i n t e g r a l n u m b e r of c o u n t s . T h e p r o b a b i l i t y of o b s e r v i n g a n y specific n u m b e r of c o u n t s is g i v e n b y t h e P2o i s s o n p r o b a b i l i t y f u n c t i o n ( B e v i n g t o n , 1969), w i t h a m e a n μ a n d v a r i a n c e σ = μ. E v e r y c o u n t in e v e r y c h a n n e l r e p r e s e n t s a n e s t i m a t e of t h e m e a n2 of a P o i s s o n d i s t r i b u t i o n of c o u n t s for t h a t c h a n n e l . H e n c e t h e v a r i a n c e σ e q u a l s t h e n u m b e r of c o u n t s in t h a t c h a n n e l , N a n d h t h e u n c e r t a i n t y in t h e n u m b e r of c o u n t s a is g i v e n b y

t

ff(= V N . -

(2-11)

T h e i m p l i c a t i o n s of t h i s c o u n t i n g e r r o r in c o n n e c t i o n w i t h d a t a a n a l y s i s a r e d i s c u s s e d in C h a p t e r 6. H e r e w e c a n m a k e u s e of t h i s u n c e r t a i n t y t o e s t i m a t e t h e n u m b e r of d e t e c t e d c o u n t s t h a t a r e n e c e s s a r y t o r e c o r d a d e c a y c u r v e w i t h a g i v e n p r e c i s i o n ( Y g u e r a b i d e , 1972). If w e w i s h t o h a v e a p r e c i s i o n of 5 % in t h e n u m b e r of c o u n t s , N in c h a n n e l h i, w h e r e t h e c u r v e h a s d e c a y e d t o 1 % of its m a x i m u m v a l u e , t h e n 0.05 = l / a f = l/y/Ni a n d N = 4 0 0 . C o n s e q u e n t l y t h e n u m b e r of c o u n t s in t h e c h a n n e l of t m a x i m u m c o u n t s s h o u l d b e 4 0 0 0 0 . T h i s figure r e p r e s e n t s a v e r y r o u g h e s t i m a4t e . E x p e r i m e n t a l l y it will p r o b a b l y b e sufficient t o a c c u m u l a t e 1 o r 2 χ 1 0 c o u n t s in t h e m a x i m u m for a single e x p o n e n t i a l d e c a y . T h e r e q u i r e ­ m e n t s for m u l t i p l e e x p o n e n t i a l d e c a y s a r e m o r e s e v e r e a n d d e p e n d o n t h e lifetime v a l u e s a n d t h e i4n t e n s i t i e s of e a c h c o m p o n e n t . F o r s u c h d e c a y s a p e a k c o u n t of a t least 3 χ 1 0 s h o u l d p r o b a b l y b e a c c u m u l a t e d , b u t f r e q u e n t l y t h e c h o i c e of t h e a c c e p t a b l e n u m b e r of c o u n t s will b e a c o m p r o m i s e b e t w e e n h i g h p r e c i s i o n a n d a v o i d a n c e of d i s t o r t i o n s r e s u l t i n g f r o m l o n g - t e r m i n s t a b i l i t y in t h e e x c i t a t i o n s o u r c e . F o r m e a s u r e m e n t5s of t6h e d e c a y of fluorescence a n i s o t r o p y , p e a k c o u n t s of t h e o r d e r of 1 0 o r 1 0 m a y b e a d v i s a b l e b e c a u s e t h e d e c a y t i m e s e x t r a c t e d d e p e n d o n t h e s u b t r a c t i o n of t w o d e c a y c u r v e s (see C h a p t e r 8). M a n y f a c t o r s c o n t r i b u t e t o t h e u n c e r t a i n t i e s in t h e lifetimes t h a t a r e derived from an S P C m e a s u r e m e n t . These include excitation pulse instability, s p r e a d in t h e p h o t o m u l t i p l i e r t r a n s i t t i m e , j i t t e r in t h e e l e c t r o n i c s a n d u n c e r t a i n t y in t h e c h a n n e l c a l i b r a t i o n . I t is i m p o r t a n t t o r e a l i z e t h a t t h e w i d t h of t h e p u m p p u l s e profile is i r r e l e v a n t if t h e s h a p e of t h e profile r e m a i n s a b s o l u t e l y c o n s t a n t . H o w e v e r , n o e x c i t a t i o n s o u r c e is perfectly s t a b l e a n d i n s t a b i l i t i e s a r e u s u a l l y p r o p o r t i o n a l t o t h e p u l s e w i d t h . H e n c e it is d e s i r a b l e t o h a v e a s n a r r o w a p u l s e w i d t h a s p o s s i b l e . S i m i l a r l y , t r a n s i t t i m e s p r e a d will in g e n e r a l b e s m a l l e r in a P M t u b e w i t h a s h o r t e r t r a n s i t t i m e ; h e n c e t h e s e a r c h for faster a n d faster d e t e c t i o n d e v i c e s . I t m u s t a l s o b e r e a l i z e d t h a t t h e S P C e x p e r i m e n t is, e s s e n t i a l l y , a n a v e r a g i n g t e c h n i q u e w i t h t h e c o n s e q u e n c e t h a t t h e t r a n s i t t i m e s p r e a d (typically 1 t o 2 n s for m o d e r n t u b e s ) d o e s n o t l e a d t o t h e s a m e s p r e a d in t h e m e a s u r e d lifetime. T h e y a r e p r o p o r t i o n a l b u t t h e l a t t e r c a n b e m a d e a s s m a l l a s r e q u i r e d t o a c e r t a i n limit, g i v e n perfect

42

Time-correlated

Single

Photon

Counting

s t a b i l i t y in t h e o t h e r e x p e r i m e n t a l c o n d i t i o n s , b y i n c r e a s i n g t h e n u m b e r of c o l l e c t e d c o u n t s . T h e d e t e r m i n a t i o n of t h i s limit is b a s i c a l l y e m p i r i c a l . S o m e a u t h o r s set it o n t h e b a s i s of t h e s h o r t e s t lifetimes t h e y h a v e m e a s u r e d w i t h c o n f i d e n c e . T h u s W a r e (1971) r e p o r t e d a limit of 0.8 n s w h i l e Y g u e r a b i d e (1972) r e p o r t e d 0.5 n s . O t h e r s prefer t o e s t i m a t e t h e t i m e r e s o l u t i o n a s s o m e f r a c t i o n of t h e full w i d t h a t half m a x i m u m ( F W H M ) of t h e i n s t r u m e n t r e s p o n s e f u n c t i o n . T h i s f u n c t i o n is t h e c u r v e t h a t r e s u l t s w h e n t h e p u m p p u l s e profile is m e a s u r e d in t h e w a y d e s c r i b e d in S e c t i o n 2.1 a n d is a c o n v o l u t i o n of t h e t r u e p u m p p u l s e profile w i t h t h e r e s p o n s e f u n c t i o n of t h e d e t e c t o r . W e s t (1979) p u t s t h i s f r a c t i o n a s o n e t e n t h for single e x p o n e n t i a l s a n d o n e fifth for d o u b l e e x p o n e n t i a l s , w h e r e a s o n e fifteenth is r e c o m m e n d e d b y G r i n w a l d (1976) a n d C r a m e r a n d S p e a r s (1978). O n p u l s e d l a s e r b a s e d S P C e q u i p m e n t , i n s t r u m e n t r e s p o n s e f u n c t i o n s c a n b e a s l o w a s 75 p s ( M u r a o et ai, 1982); l o w e r limits of a b o u t 5 p s o n m e a s u r a b l e lifetimes a r e t h e r e f o r e set b y t h e o n e fifteenth c r i t e r i o n . W e believe t h a t t h i s figure is u n r e a l i s t i c a n d t h a t e r r o r s of a t least 1 0 0 % s h o u l d p r o b a b l y b e q u o t e d for lifetimes u p t o 60 p s if t h e r e s u l t of a single m e a s u r e m e n t is given. T h e figures for t i m e r e s o l u t i o n g i v e n in t h e p r e c e d i n g p a r a g r a p h a r e r u l e s of t h u m b b a s e d o n a u t h o r s ' c o n f i d e n c e in t h e lifetimes t h e y h a v e m e a s u r e d . If a m o r e e x a c t e s t i m a t e is p r e f e r r e d , t h e f o l l o w i n g e x p e r i m e n t ( Z i m m e r m a n a n d C u t l e r , 1975) m a y b e p e r f o r m e d . T w o p u m p p u l s e profiles a r e m e a s u r e d , a l e n g t h of t i m e c o r r e s p o n d i n g t o t h e t i m e n e e d e d t o collect a n o r d i n a r y d e c a y curve being allowed to elapse between the two measurements. Deconvolution of o n e p u m p p u l s e profile w i t h t h e o t h e r will yield a " d e c a y " t i m e , w h i c h is a m e a s u r e of t h e t i m e r e s o l u t i o n of t h e i n s t r u m e n t . T h i s e x p e r i m e n t h a s y i e l d e d v a l u e s of 18 p s ( Z i m m e r m a n a n d C u t l e r , 1975) for i n s t r u m e n t s w i t h flash l a m p e x c i t a t i o n . K o e s t e r a n d D o w b e n (1978), u s i n g a m e t h o d b a s e d o n t h e o p t i c a l p r o p e r t i e s of t h e c a v i t y - d u m p e r in t h e i r d y e l a s e r e x c i t a t i o n s o u r c e , d e t e r m i n e d a t i m i n g r e s o l u t i o n of 25 p s w h e r e a s for a similar e x c i t a t i o n s o u r c e u s i n g t h e m e t h o d p r o p o s e d b y Z i m m e r m a n w e e s t i m a t e t h e r e s o l u t i o n a t 50 p s . I n s p i t e of t h e s e l o w v a l u e s , q u o t e d in r e c e n t p u b l i c a t i o n s , t h e p r o s p e c t i v e u s e r s h o u l d n o t e x p e c t t o b e a b l e t o m e a s u r e lifetimes less t h a n 5 0 0 p s u n t i l e a c h c o m p o n e n t of his i n s t r u m e n t h a s b e e n p r o p e r l y o p t i m i z e d . E v e n t h e n , c o n s t a n t checks o n excitation source stability a n d electronic jitter m u s t be p e r f o r m e d if d e c a y t i m e s less t h a n 100 p s a r e t o b e b e l i e v e d . S h o r t d e c a y t i m e s in t w o - c o m p o n e n t d e c a y c u r v e s p r e s e n t e v e n m o r e difficulties. T h e s e d e c a y s s h o u l d b e m e a s u r e d a n u m b e r of t i m e s in o r d e r t o c o m p e n s a t e for r a n d o m e r r o r s . T h e d e t e c t i o n of s y s t e m a t i c e r r o r s c a n best b e a c h i e v e d b y c o m p a r i s o n of t h e r e s u l t s of S P C a n a l y s i s w i t h r e s u l t s of i n d e p e n d e n t e x p e r i m e n t s . W e s t r o n g l y c a u t i o n a g a i n s t t h e a d o p t i o n of m o d e l s b a s e d o n e x t r a c t e d lifetimes f r o m t w o - c o m p o n e n t d e c a y s of less t h a n 100 p s u n l e s s t h e m o d e l is justified on other grounds.

2. Basic

2.2.3

Principles

of Lifetime

Measurement

43

Convolution

If t h e flash of light t h a t excites t h e s a m p l e w e r e infinitely n a r r o w , a n d if t h e r e s p o n s e of t h e d e t e c t i o n s y s t e m w e r e infinitely fast, t h e o b s e r v e d d e c a y c u r v e w o u l d r e p r e s e n t t h e t r u e d e c a y , o r (5-pulse r e s p o n s e , of t h e s a m p l e . W e s h a l l refer t o t h i s f u n c t i o n a s

G(t).

T h e f o r m of t h e o b s e r v e d d e c a y , / ( r ) , w h e n t h e e x c i t a t i o n f u n c t i o n , E(t), is n o t a ^ - f u n c t i o n c a n b e d e d u c e d f r o m t h e t h e o r y of i m p u l s e f u n c t i o n s a n d leads to the c o n v o l u t i o n concept. C o n v o l u t i o n , or folding together, occurs because molecules excited by p h o t o n s at early times are decaying while o t h e r s a r e b e i n g e x c i t e d b y p h o t o n s in t h e tail of t h e e x c i t a t i o n p u l s e . A s i m p l e d e d u c t i o n of t h e c o n v o l u t i o n e q u a t i o n is b a s e d o n t h e d i a g r a m in F i g . 2.2. T h e p u m p p u l s e is a s s u m e d t o b e a s u m of <5-pulses of a m p l i t u d e

E(t')

a t a n y t i m e t'. S i n c e t h e n u m b e r of s a m p l e m o l e c u l e s e x c i t e d a t t i m e t' is p r o p o r t i o n a l t o E{t') t h e n u m b e r a t a n y l a t e r t i m e x — t' is p r o p o r t i o n a l t o E(t')G(x

—1'\

T h e t o t a l n u m b e r of e x c i t e d s t a t e m o l e c u l e s a t t i m e x, w r i t t e n

[^4*](x) is t h e n a s u m o v e r all t i m e s t' p r e c e d i n g t i m e χ o r , for a n infinité s u m , D 4 * ] ( x ) O C ] E(t')G(x

- t')dt'.

(2.12)

ο W e h a v e so far n e g l e c t e d d i s t o r t i o n s i n t r o d u c e d b y t h e d e t e c t i o n s y s t e m .

Figure 2.2 Schematic representation of the effect of convolution. E(t) idealized p u m p pulse profile; G(t) decay law (assumed single exponential) of sample.

Time-correlated

44

Single Photon

Counting

T h e i r effect c a n b e e v a l u a t e d t h r o u g h t h e u s e of L a p l a c e t r a n s f o r m s . S u p p o s e t h a t H(t) is t h e (5-pulse r e s p o n s e of t h e d e t e c t i o n s y s t e m , a n d P(t) t h e m e a s u r e d t i m e profile of t h e p u m p p u l s e , i.e., t h e i n s t r u m e n t r e s p o n s e f u n c t i o n . P(t) is a c o n v o l u t i o n of E(t) a n d H(t), w h i c h w e shall w r i t e a s P{t) = E{t)®H{t).

(2.13)

W r i t i n g t h e L a p l a c e t r a n s f o r m of a f u n c t i o n X(t) a s x(s) w i t h

00

x{s) = L\_X(t)~\ = J*

st Q~ X(t)dt,

0

it follows t h a t p(s) = e(s).h(s).

(2-14)

a(s) = e(s).g(s)

(2.15)

i(s) = a(s).h(s).

(2.16)

Similarly

and

Therefore

i(s) = e(s).g(s).h{s) = p(s).g(s)

(2.17)

and

I(t) =

P(t)®G(t)

= \p{t')G{t-t')àt\

ο

(2.18)

w h e r e I(t) r e p r e s e n t s t h e ^ - f u n c t i o n r e s p o n s e of t h e s a m p l e d i s t o r t e d b y c o n v o l u t i o n w i t h b o t h t h e p u m p p u l s e a n d t h e d e t e c t o r r e s p o n s e , i.e., t h e measured decay curve. E q u a t i o n 2.18, t h e c o n v o l u t i o n i n t e g r a l , c a n b e s o l v e d for G(t) if I(t) a n d P{t\ m e a s u r e d u n d e r t h e s a m e c o n d i t i o n s of i n s t r u m e n t a l d i s t o r t i o n , a r e k n o w n . M e t h o d s for s o l v i n g t h e c o n v o l u t i o n i n t e g r a l , o r v a r i a n t s thereof, a r e d i s c u s s e d in C h a p t e r 6. C o n v o l u t i o n will o b v i o u s l y b e c o m e less significant a s P(t) b e c o m e s n a r r o w e r w i t h r e s p e c t t o G(t). E r r o r s a t t e n d a n t u p o n failure t o d e c o n v o l v e , i n t h e c a s e of i n s t r u m e n t r e s p o n s e f u n c t i o n s of v a r y i n g F W H M , h a v e b e e n e s t i m a t e d ( S h a v e r a n d C l i n e L o v e , 1975), b u t o n l y for single e x p o n e n t i a l decays. Before a d e c i s i o n is r e a c h e d t h a t t h e a s s u m p t i o n I(t) = G(t) is v a l i d it m u s t

2. Basic

Principles

of Lifetime

Measurement

45

b e b o r n e in m i n d t h a t P(t) r e p r e s e n t s t h e i n s t r u m e n t r e s p o n s e f u n c t i o n a n d not simply the excitation pulse. M a n y i n s t r u m e n t response functions, while h a v i n g q u i t e a n a r r o w F W H M (as s h o r t a s 75 p s in s o m e i n s t r u m e n t s ) , h a v e a n e x t e n d e d tail, u s u a l l y w i t h a s e c o n d a r y p e a k r e s u l t i n g f r o m p h o t o ­ m u l t i p l i e r effects ( L e w i s et al, 1973). If t h i s tail c a n n o t b e e l i m i n a t e d it is n e a n i n g l e s s t o c o n s i d e r o n l y t h e F W H M of P{t) in d e c i d i n g w h e t h e r d e c o n v o l u t i o n is n e c e s s a r y o r n o t . I n a d d i t i o n , t h e s a m p l e d e c a y f u n c t i o n m a y c o n t a i n a s h o r t - l i v e d c o m p o n e n t w h i c h m a y b e o v e r l o o k e d if c o n v o ­ l u t i o n is n o t t a k e n i n t o a c c o u n t . F o r i n s t a n c e , L o p e z - D e l g a d o et al (1974) s t a t e t h a t w i t h a n i n s t r u m e n t r e s p o n s e f u n c t i o n of F W H M 1.4 n s , lifetimes g r e a t e r t h a n 4 n s c a n b e d e r i v e d d i r e c t l y f r o m t h e m e a s u r e d I(t) w i t h o u t d e c o n v o l u t i o n . A s a n e x a m p l e t h e y r e p o r t t h e d e c a y t i m e of q u i n i n e b i s u l p h a t e in 0 . 1 N H S O a s 18.8 ns; significantly, t h e r e is n o w s t r o n g

2

4

e v i d e n c e t h a t a single e x p o n e n t i a l f u n c t i o n is a n i n a p p r o p r i a t e m o d e l for t h e d e c a y of t h i s f l u o r e s c e n c e ( H a r r i s a n d Selinger, 1979; M e e c h et al, 1982). W e t h e r e f o r e s u g g e s t t h a t all d e c a y c u r v e s s h o u l d b e d e c o n v o l v e d , i r r e s p e c t i v e of t h e lifetime v a l u e s . W h e n b o t h P(t) a n d I(t) a r e e m p l o y e d in d a t a a n a l y s i s it is u s u a l l y a s s u m e d t h a t t h e c o u n t i n g e r r o r s in P(t) a r e negligible. E x p e r i m e n t s in o u r l a b o r a t o r y h a v e c o n f i r m e d t h e v a l i d i t y of t h i s a s s u m p t i o n , i n s t r u m e n t r e s p o n s e f u n c t i o n s c o l l e c t e d w i t h v a r y i n g n u m b e r s of c o u n t s y i e l d i n g i d e n t i c a l r e s u l t s . P r o v i s i o n for i n c l u d i n g t h e e r r o r s in P(t) in t h e u n c e r t a i n t y in I(t) is t h e r e f o r e u n n e c e s s a r y b u t c a n b e m a d e (see C h a p t e r 6).

2.2.4

Measurement of the instrument response function

T h e v a l i d i t y of t h e c o n v o l u t i o n i n t e g r a l r e q u i r e s t h a t t h e f u n c t i o n s I(t) a n d P(t) s h o u l d b e m e a s u r e d u n d e r t h e s a m e c o n d i t i o n s of d i s t o r t i o n . I n p r a c t i c e o n e tries t o s c a t t e r f r o m t h e s a m e v o l u m e a s t h a t f r o m w h i c h fluorescence is v i e w e d , t h e r e b y e q u a l i z i n g t h e i l l u m i n a t e d a r e a s of t h e P M t u b e p h o t o c a t h o d e , u p o n w h i c h t h e r e s p o n s e f u n c t i o n , H(t) d e p e n d s . C o l l o i d a l s u s p e n ­ s i o n s s u c h a s L u d o x * , g l y c o g e n ( W e b e r a n d T e a l e , 1957), b a r i u m s u l p h a t e (Bailey a n d R o l l e f s o n , 1953) o r s i m p l y m i l k ( M i l l a r et al, 1980) c a n b e s u b s t i t u t e d for t h e s a m p l e a n d , a t t h e a p p r o p r i a t e c o n c e n t r a t i o n , will closely, b u t n o t e x a c t l y , m i m i c t h e e m i s s i o n g e o m e t r y ( D e m a s a n d C r o s b y , 1971). S o m e of t h e s e s u s p e n s i o n s , h o w e v e r , fluoresce u n d e r s h o r t w a v e l e n g t h e x c i t a t i o n (300 n m ) ( E a s t m a n , 1967) a n d a r e t h e r e f o r e t o b e a v o i d e d a t t h e s e w a v e l e n g t h s . A l u m i n i u m o r silver foil o r , b e t t e r , r o u g h e n e d q u a r t z , m a y b e u s e d a s a diffuse reflector. A s c r e e n c o a t e d w i t h m a g n e s i u m o x i d e c a n a l s o *Ludox is a Trade name for an aqueous suspension of silica manufactured by Ε. I. du Pont de Nemour Co., Wilmington, Delaware, USA.

46

Time-correlated

Single

Photon

Counting

serve a s a s c a t t e r e r . A m o n o c h r o m a t o r b e t w e e n t h e s a m p l e a n d P M t u b e r e n d e r s t h e c h o i c e of s c a t t e r e r o r reflector less i m p o r t a n t , b u t if t h e P M t u b e p h o t o c a t h o d e views t h e fluorescing o r s c a t t e r i n g a r e a d i r e c t l y t h e c o r r e c t m e t h o d should be determined empirically using a s t a n d a r d sample (Section 2.4) a n d d e c o n v o l u t i o n . As m i g h t b e e x p e c t e d , t h e p h o t o m u l t i p l i e r r e s p o n s e , H(t% is d e p e n d e n t o n t h e e n e r g y of t h e i n c i d e n t r a d i a t i o n . S i n c e fluorescence is n o r m a l l y S t o k e s shifted f r o m e x c i t a t i o n it m a y n o t b e p o s s i b l e t o m e a s u r e I(t) a n d P(t) a t t h e s a m e w a v e l e n g t h . P u l s e s f r o m h y d r o g e n a n d d e u t e r i u m flash l a m p s a n d f r o m storage ring r a d i a t i o n are t h o u g h t to be wavelength invariant, so t h a t the i n s t r u m e n t r e s p o n s e f u n c t i o n for s u c h s o u r c e s c a n b e m e a s u r e d a t t h e w a v e l e n g t h of t h e fluorescence. M e a s u r e m e n t of P(t) for o t h e r e x c i t a t i o n s o u r c e s is d i s c u s s e d in S e c t i o n 2.3. L o n g - t e r m drift in t h e t i m e profile of t h e e x c i t a t i o n s o u r c e c a n b e t r e a t e d e i t h e r e x p e r i m e n t a l l y o r in t h e d a t a a n a l y s i s . T h e f o r m e r is p r o b a b l y p r e f e r a b l e . A slight e l a b o r a t i o n of t h e s i m p l e e x p e r i m e n t e n t a i l s t h e c o l l e c t i o n of o n e i n s t r u m e n t r e s p o n s e f u n c t i o n , t h e n of t h e d e c a y c u r v e , a n d t h e n of a second i n s t r u m e n t response function (these c o u n t s c a n be simply a d d e d to the c o u n t s in t h e first i n s t r u m e n t r e s p o n s e f u n c t i o n in t h e d a t a store). A n instrument that automatically switches d a t a collection between instrument r e s p o n s e f u n c t i o n a n d d e c a y c u r v e after a c e r t a i n n u m b e r of e x c i t a t i o n cycles h a s b e e n d e s c r i b e d b y H a z a n et al. (1974). A s p e c i a l cell h o l d e r c a r r i e s t h e s c a t t e r i n g s o l u t i o n a n d t h e s a m p l e o n e a b o v e t h e o t h e r . T h e h o l d e r is m o v e d u p a n d d o w n b y a p n e u m a t i c p i s t o n a n d t h e e n t i r e o p e r a t i o n of d e c a y c u r v e a n d i n s t r u m e n t r e s p o n s e f u n c t i o n c o l l e c t i o n , a n d b a c k g r o u n d s u b t r a c t i o n is controlled electronically a n d repeated until the required precision has been r e a c h e d . F o r l o n g c o l l e c t i o n t i m e s t h i s p r o c e d u r e h a s m u c h t o r e c o m m e n d it a n d s h o u l d l e a d t o a n i m p r o v e m e n t in m e a s u r e d d e c a y t i m e s . M o r e e l e g a n t d e v i c e s t h a n a p n e u m a t i c p i s t o n for a l t e r n a t i n g b e t w e e n s c a t t e r i n g s o l u t i o n a n d s a m p l e h a v e b e e n d e s c r i b e d ( E a s t e r et ai, 1976; R a y n e r et ai, 1976). S h o r t - t e r m drift o r j i t t e r in t h e p u m p p u l s e profile is less easily c o r r e c t e d for a n d s h o u l d b e e l i m i n a t e d b y o p t i m i z a t i o n of t h e o p e r a t i n g c o n d i t i o n s in t h e excitation source.

2.2.5

Correction for constant background

I n a g o o d S P C i n s t r u m e n t t h e r e is u s u a l l y a v e r y l o w n o i s e level a r i s i n g f r o m l e a k e d r o o m light a n d t h e r m i o n i c n o i s e in t h e p h o t o m u l t i p l i e r t u b e . T h e r e a s o n is t h a t t h e fast P M t u b e s c h o s e n for single p h o t o n c o u n t i n g h a v e v e r y g o o d d a r k n o i s e c h a r a c t e r i s t i c s . M o s t u.v.-sensitive t u b e s d o n o t n e e d t o b e c o o l e d b u t it is a d v i s a b l e t o o p e r a t e r e d sensitive t u b e s a t a l o w t e m p e r a t u r e . All m e a s u r e d c u r v e s m u s t b e c o r r e c t e d for d a r k n o i s e since l o n g l o w - i n t e n s i t y

2. Basic

Principles

of Lifetime

Measurement

47

lifetimes a r e s o m e t i m e s difficult t o d i s t i n g u i s h f r o m t h e b a c k g r o u n d . T h e r e a r e t h r e e c o m m o n l y u s e d m e t h o d s for b a c k g r o u n d c o r r e c t i o n . S i m p l e s t a n d m o s t w i d e l y u s e d is t h e d i s p l a c e m e n t of t h e d e c a y c u r v e in t h e d a t a s t o r a g e c h a n n e l s s o t h a t t h e first t e n o r t w e n t y c h a n n e l s a r e u s e d t o a c c u m u l a t e o n l y b a c k g r o u n d c o u n t s . T h i s b a c k g r o u n d level is t h e n e s t i m a t e d f r o m a r e c o u n t of t h e d a t a a n d s u b t r a c t e d f r o m t h e c u r v e c h a n n e l b y c h a n n e l . A j u s t i f i c a t i o n for t h i s s u b t r a c t i o n h a s b e e n g i v e n b y K n i g h t a n d S e l i n g e r (1973) w h o s h o w e d t h a t t h e o b s e r v e d d e c a y f u n c t i o n l(t) is g i v e n b y I(t) = CJ (t)

0

+ C

2j

(2.19)

w h e r e C is t h e c o n s t a n t b a c k g r o u n d c o m p o n e n t . 2 A n a u t o m a t e d v e r s i o n of b a c k g r o u n d s u b t r a c t i o n h a s b e e n d e s c r i b e d b y H a z a n et al. (1974). I n t h i s v e r s i o n t h e a n a l y s e r is r u n in s u b t r a c t m o d e w i t h a n e x c i t a t i o n s h u t t e r c l o s e d , for e x a c t l y t h e s a m e n u m b e r of e x c i t a t i o n cycles a s a r e u s e d w i t h t h e a n a l y s e r in a d d m o d e a n d t h e s h u t t e r o p e n . T h i s p r o c e d u r e is a l s o justified o n s t a t i s t i c a l g r o u n d s b u t i n v o l v e s r a t h e r p r e c i s e t i m i n g a n d is p e r h a p s m o s t s u i t a b l e for a fully a u t o m a t e d s y s t e m s u c h a s t h a t described by the authors. M o r e q u e s t i o n a b l e is t h e i n c l u s i o n of t h e c o n s t a n t b a c k g r o u n d a s a v a r i a b l e p a r a m e t e r in l e a s t - s q u a r e s fitting p r o c e d u r e ( R o b b i n s et al, 1980). T h e r e a p p e a r s t o b e n o a d v a n t a g e in i n c r e a s i n g t h e n u m b e r of fitting p a r a m e t e r s in t h i s w a y , e s p e c i a l l y in m u l t i - e x p o n e n t i a l d e c a y s w h e n a v a r i a b l e shift p a r a m e t e r is a l s o i n c l u d e d . S u b t r a c t i o n of t h e b a c k g r o u n d b e f o r e d e c o n v o l u t i o n is t h e r e f o r e q u i t e s a t i s f a c t o r y . C a r e s h o u l d b e t a k e n , if b a c k g r o u n d is e s t i m a t e d f r o m c h a n n e l s c o r r e s p o n d i n g t o a n o n - l i n e a r r e g i o n of t h e T A C , t h a t sufficient c h a n n e l s t o give p r o p e r a v e r a g i n g a r e u s e d . I n a d d i t i o n t h e t i m e s c a l e s h o u l d b e s u c h t h a t in t h e c h a n n e l s b e f o r e t h e c u r v e t h e p r o b a b i l i t y of c o l l e c t i n g s i g n a l p h o t o n s r e s u l t i n g f r o m p r e v i o u s e x c i t a t i o n e v e n t s is negligible.

2.2.6

Operation at high excitation repetition rate

W h e n t h e r e p e t i t i o n r a t e of t h e e x c i t a t i o n s o u r c e is s o h i g h t h a t t h e T A C h a s n o t t i m e t o r e s e t b e t w e e n t h e o c c u r r e n c e of s u c c e s s i v e e x c i t a t i o n p u l s e s , d i s t o r t i o n s will b e p r e s e n t in t h e d e c a y c u r v e if t h e d a t a c o l l e c t i o n is p e r f o r m e d in t h e c o n v e5n t i o n a l f a s h i o n . T h e p r e s e n t g e n e r a t i o n of T A C s c a n o p e r a t e a t 1 o r 2 χ 1 0 H z S T A R T r a t e ( H a u g e n et al, 1979) a n d t h e r e f o r e c a n b e o p e r a t e d in c o n v e n t i o n a l m o d e w i t h m o s t flash l a m p e x c i t a t i o n s o u r c e s a n d w i t h l a s e r s o u r c e s t h a t e m p l o y a P o c k e l s cell. M o d e l o c k e d i o n lasers, cavity d u m p e d dye lasers a n d s t o r a g e rings usually o p e r a t e optimally a t r e p e t i t i o n r a t e s in t h e M H z r e g i o n . C o n s e q u e n t l y , for t h e s e e x c i t a t i o n s o u r c e s , t h e s t a n d a r d m o d e of d a t a c o l l e c t i o n is n o t s u i t a b l e .

48

Time-correlated

Single

Photon

Counting

I n o n e v a r i a n t of t h e c o n v e n t i o n a l t e c h n i q u e ( W i l d et al, 1977) a n i n h i b i t f u n c t i o n is u s e d in s u c h a w a y t h a t d a t a c o l l e c t i o n is b l o c k e d d u r i n g p e r i o d s of T A C r e c o v e r y . F u l l a d v a n t a g e of t h e h i g h r e p e t i t i o n r a t e of e x c i t a t i o n is, t h e r e f o r e , n o t t a k e n . A m o r e c o m m o n v a r i a n t , a n d o n e t h a t a l s o offers s o m e a d v a n t a g e s for l o w r e p e t i t i o n r a t e e x c i t a t i o n s o u r c e s , is o p e r a t i o n of t h e T A C in " r e v e r s e " m o d e ( S w o r d s , 1977; L o p e z - D e l g a d o et ai, 1974). F l u o r e s c e n c e s i g n a l s a r e r o u t e d t o t h e S T A R T i n p u t of t h e T A C a n d t h e t r i g g e r s i g n a l s t o t h e S T O P i n p u t . It is p r e f e r a b l e t o a r r a n g e t h e d e l a y s ( D i a n d D in F i g . 2.1) 2 s o t h a t t h e T A C s w e e p is s t o p p e d b y a t r i g g e r s i g n a l c o r r e s p o n d i n g t o t h e e x c i t a t i o n cycle in w h i c h t h e S T A R T s i g n a l o c c u r r e d . If t h e d e l a y s a r e n o t s o a r r a n g e d t h e i n t e r - p u l s e s e p a r a t i o n in t h e e x c i t a t i o n s o u r c e m u s t b e v e r y stable. T h e a d v a n t a g e of t h i s t e c h n i q u e is t h a t , for h i g h r e p e t i t i o n r a t e s o u r c e s , m a n y m o r e of t h e fluorescence s i g n a l s (after s u i t a b l e r e d u c t i o n t o a v o i d p u l s e pile-up) are processed by the T A C . In a similar way, however, a c o r r e s p o n d ­ ingly l a r g e r n u m b e r of t h e d a r k n o i s e s i g n a l s a r e p r o c e s s e d , a n d t h e n e e d for a l o w n o i s e fluorescence P M t u b e is t h e r e f o r e g r e a t e r . I n all o t h e r r e s p e c t s it is s i m i l a r t o t h e c o n v e n t i o n a l m o d e e x c e p t t h a t t h e c u r v e s a r e c o l l e c t e d in t h e d a t a store with time increasing from higher to lower channel n u m b e r s . A n e x a m p l e of a p u m p p u l s e a n d a d e c a y c u r v e c o l l e c t e d w i t h t h e T A C in " r e v e r s e " m o d e is s h o w n in F i g . 2.3. It is u s u a l t o a d j u s t d a t a s u c h a s t h e s e t o t h e m o r e c o n v e n t i o n a l a r r a n g e m e n t before d a t a a n a l y s i s .

CHANNELS

Figure 2.3 Decay curve of 1-methylindole in methylcyclohexane measured with the TAC operated in "reverse" mode. 1 channel = 0.082 ns.

2. Basic

2.3

Principles

of Lifetime

49

Measurement

Experiments to Correct for Wavelength-dependent P M Distortion

I n t h e d e r i v a t i o n of t h e c o n v o l u t i o n i n t e g r a l , E q u a t i o n 2.18, w a v e l e n g t h d e p e n d e n t effects o n p u m p p u l s e s h a p e a n d d e t e c t o r r e s p o n s e w e r e n e g l e c t e d . When

they are taken into account

w e s h o u l d w r i t e for t h e

instrument response function P(A ,i) or

E

measured

Ρ(λ^ί)

Ρ(λ ,ή

= Ε(λ ,ί)®Η(λ ,ή

(2.20)

Ρ(λ„ΐ)

= Ε(λ„ή®Η(λ„ή,

(2.21)

Ε

Ε

Ε

where λ

Ε signifies t h e w a v e l e n g t h of e x c i t a t i o n a n d Xt t h e w a v e l e n g t h a t w h i c h

t h e e m i s s i o n is o b s e r v e d . T h e m e a s u r e d d e c a y c u r v e s h o u l d b e w r i t t e n Ι(λ„ί)

= Ε(λ ή®β(λ„ή®Η(λ„ή.

Ε9

(2.22)

If t h e p u m p p u l s e s h a p e is w a v e l e n g t h i n d e p e n d e n t , Ε(λ ,ή Ε = Ε(λ^ί) a n d w h e n t h e i n s t r u m e n t r e s p o n s e f u n c t i o n is m e a s u r e d a t t h e w a v e l e n g t h of e m i s s i o n o b s e r v a t i o n E q u a t i o n 2.22 is s o l u b l e since Ι(λ„ΐ)

=

Ε(λ„ή®β(λ„ΐ)®Η(λ„ΐ)

= P(k„t)®G(k t).

t9

(2.23)

T h e w a v e l e n g t h d e p e n d e n c e of p u m p p u l s e profiles is d i s c u s s e d in C h a p t e r 3. H e r e it m a y b e n o t e d t h a t o n l y h y d r o g e n a n d d e u t e r i u m flash l a m p s a n d storage ring r a d i a t i o n h a v e pulse shapes t h a t are believed t o be c o n s t a n t over a wide wavelength range. F o r other sources, the p u m p pulse shape m u s t be m e a s u r e d a t t h e e x c i t a t i o n w a v e l e n g t h a n d s o m e s o r t of c o r r e c t i o n a p p l i e d . It h a s b e e n s u g g e s t e d ( R i c k a , 1981) t h a t in c e r t a i n e x p e r i m e n t s in w h i c h two or m o r e decays are m e a s u r e d at the same emission wavelength, having b e e n e x c i t e d a t t h e s a m e e x c i t a t i o n w a v e l e n g t h , t h e r e is n o n e e d t o m e a s u r e a n i n s t r u m e n t r e s p o n s e f u n c t i o n since, if t h e d e c a y f u n c t i o n s a r e r e l a t e d (e.g., in a fluorescence d e p o l a r i z a t i o n m e a s u r e m e n t ) , t h e d e c a y c u r v e s c a n b e m a n i p u l a t e d a n d t h e d e s i r e d i n f o r m a t i o n e x t r a c t e d . W h i l e it is i n d e e d p o s s i b l e t o a n a l y s e s o m e k i n d s of d e c a y d a t a in t h i s w a y , w e w o u l d s t r o n g l y s u g g e s t t h a t all d e c a y c u r v e s s h o u l d b e d e c o n v o l v e d in o r d e r t o a s c e r t a i n w h e t h e r t h e d a t a a r e d i s t o r t i o n free. M a t h e m a t i c a l t r e a t m e n t of t h i s w a v e l e n g t h - d e p e n d e n t d i s t o r t i o n is d i s c u s s e d in C h a p t e r 6. I n g e n e r a l , it is preferable to eliminate experimental distortions by instrumental techniques r a t h e r t h a n c o r r e c t for t h e m in d a t a a n a l y s i s . H e n c e , s o m e effort h a s b e e n m a d e b y w o r k e r s in t h e S P C field t o d e v e l o p e x p e r i m e n t s b y w h i c h t h e effect of a w a v e l e n g t h - d e p e n d e n t P M r e s p o n s e m a y b e c o u n t e r a c t e d . T h e first s u c h e x p e r i m e n t a p p e a r s t o b e t h a t of W a h l et al (1974), w h o p r o p o s e d t h e u s e of a s a m p l e w i t h a w e l l - k n o w n single e x p o n e n t i a l d e c a y

50

Time-correlated

Single

Photon

Counting

t i m e . I n e s s e n c e t h e i r m e t h o d r e s t s o n t h e s o l u t i o n of E q u a t i o n 2.22 for t h e reference c o m p o u n d . T h e c o n v o l u t i o n p r o d u c t (Ε(λ ί)®Η(λ ή

Ε9

is t h e n

&9

c a l c u l a t e d , a n d m a y b e s u b s t i t u t e d in E q u a t i o n 2.22 w h e n I(t) is m e a s u r e d for a n u n k n o w n d e c a y . T h e d i s a d v a n t a g e s of t h e e x p e r i m e n t a r e t h a t r e f e r e n c e c o m p o u n d s m u s t b e f o u n d for e a c h e m i s s i o n w a v e l e n g t h a n d t h a t t h e e r r o r s i n v o l v e d in t h e t w o d e c o n v o l u t i o n s a s well a s t h e s m a l l n u m b e r of c o m ­ p o u n d s w i t h a definitely k n o w n single e x p o n e n t i a l d e c a y m u s t l e a d t o l a r g e e r r o r s in t h e r e c o v e r e d G(t). B r i t t e n a n d L o c k w o o d (1976) m o d i f i e d t h e m e t h o d j u s t d e s c r i b e d s o t h a t a k n o w l e d g e of t h e e x a c t lifetime of t h e reference c o m p o u n d w a s n o t r e q u i r e d . I n s t e a d , t w o reference c o m p o u n d s , t h e d e c a y s of w h i c h a r e k n o w n t o b e single e x p o n e n t i a l , b u t t h e lifetimes of w h i c h n e e d n o t b e k n o w n a c c u r a t e l y , a r e u s e d t o d e t e r m i n e t h e f u n c t i o n E(À t)®H(À t).

E9

Since this m e t h o d entails

e9

p r e p a r a t i o n of t w o h i g h l y p u r e s a m p l e s a t e a c h e m i s s i o n w a v e l e n g t h of i n t e r e s t its p r a c t i c a b i l i t y is h i g h l y q u e s t i o n a b l e . W o n g a n d H a l p e r n (1976) f o u n d t h a t , b y a d j u s t i n g t h e m e a s u r e d f u n c t i o n Ρ{λ ,ί)

s o t h a t all c o u n t s a t

Ε

t i m e s l o n g e r t h a n 3.6 n s after t h e f u n c t i o n m a x i m u m w e r e r e d u c e d b y 2 0 % , a function

w a s o b t a i n e d t h a t y i e l d e d successful

results w h e n used in t h e

d e c o n v o l u t i o n of d e c a y c u r v e s of c e r t a i n s a m p l e s . S u c h a n e n t i r e l y e m p i r i c a l t e c h n i q u e is n o t r e c o m m e n d e d

since it c o u l d s e r i o u s l y m a s k r e a l n o n -

e x p o n e n t i a l i t y in t h e d e c a y c u r v e s of i n t e r e s t . P r o b a b l y t h e l e a s t o b j e c t i o n a b l e of t h e t e c h n i q u e s i n v o l v i n g

reference

c o m p o u n d s w a s p r o p o s e d b y S z a b o a n d c o - w o r k e r s ( R a y n e r et ai, 1976, 1977). C o n s i d e r a c o m p o u n d , R, w h i c h a b s o r b s a t a w a v e l e n g t h A , s h o r t e r

a

t h a n t h e w a v e l e n g t h of e x c i t a t i o n of t h e s a m p l e , a n d t h a t e m i t s b o t h a t t h i s excitation wavelength a n d at the wavelength at which the sample's emission is o b s e r v e d . I n a d d i t i o n , a s s u m e Rt h a t t h e d eR c a y of t h i s reference c o m p o u n d is w a v e l e n g t h i n d e p e n d e n t [i.e., G (À t)

tions: R Ρ(λ ί) Ε9 a n d 7 (/l ,i) e

E9

( E q u a t i o n 2.20); I(X ,t) ( E q u a t i o n 2.25).

Ε9

Ι (λ„ί)

R

C o n v o l v e I(À t)

e9

t) ® G ( / l , t) ®

Ά9

R E

= Ε(λ 1)

® G (À 1)

= Ε(λ ή®

Ά9

R C9

Ε9

Ε9

® Η(λ ή

(2.24)

Ε9

e9

κE

a n d Ρ(λ ί)

Η(λ 1)

G (À t)®H(À t)

with 7 (A ,i) t o get

Ε9

( E q u a t i o n 2.24);

R

= Ε{λ

Ι(λ„ t) ® Ι (λ 1)

e9

Ε9

Λ9

κ

S i n c e I (k t)

e

( E q u a t i o n 2.22); Ι (λ ή

e

R

/ ( λ 1)

R

κ e m e a s u r e s f o u r func­ = G (A ,i)]. O n

(2.25)

e9

R

= G(A , t) ® / ( A , t) ® Ρ(λ 1).

e

e

(2.26)

Ε9

h a v e b e e n m e a s u r e d , E q u a t i o n 2.26 is d e c o n v o l v e d

t o yield t h e d e c a y of i n t e r e s t , G(X t).

Q9

Although

the proposers

of t h i s

technique have achieved excellent results, s o m e d r a w b a c k s a r e o b v i o u s . F o r instance

t h e reference

compound,

R, m u s t

have

a broad

fluorescence

2. Basic

Principles

of Lifetime

Measurement

51

w a v e l e n g t h r a n g e s u i t a b l e for e a c h s a m p l e of i n t e r e s t . It is t h e r e f o r e likely t h a t a n u m b e r of reference c o m p o u n d s , all in a h i g h s t a t e of p u r i t y , will b e r e q u i r e d . I n a d d i t i o n , t h e d e c a y of t h e reference fluorescence must be w a v e l e n g t h i n d e p e n d e n t ; t h i s p r o p e r t y of d e c a y t i m e s h a s b e e n i n v e s t i g a t e d o n l y t o a v e r y l i m i t e d e x t e n t . F i n a l l y , p r o p a g a t e d e r r o r s a r e likely t o b e v e r y l a r g e since four f u n c t i o n s r a t h e r t h a n t w o a r e i n v o l v e d in d e c o n v o l u t i o n . N e v e r t h e l e s s , t h e r a t i o c o r r e c t i o n t e c h n i q u e is a t p r e s e n t t h e b e s t a l t e r n a t i v e t o t h e z e r o - t i m e shift o u t l i n e d in C h a p t e r 6 in e x p e r i m e n t s affected b y a wavelength-dependent P M response.

2.4

Standards

I n t h e f o l l o w i n g f o u r c h a p t e r s w e d e s c r i b e t h e i n d i v i d u a l c o m p o n e n t s of a n S P C fluorimeter a n d t h e m a t h e m a t i c a l m e t h o d s w i t h w h i c h S P C d a t a a r e a n a l y s e d . D u r i n g t h e c o u r s e of t h i s d e s c r i p t i o n w e s h a l l e m p h a s i z e t h a t a l a r g e n u m b e r of i n s t r u m e n t a l a n d m a t h e m a t i c a l f a c t o r s , s o m e of t h e m q u i t e s u b t l e , m a y interfere w i t h t h e s u c c e s s of a fluorescence lifetime m e a s u r e m e n t . F o r e x a m p l e , excessive d i s c r i m i n a t i o n of t h e fluorescence P M p u l s e s c a n b i a s t h e d a t a c o l l e c t i o n t o w a r d s m u l t i p h o t o n e v e n t s in s u c h a w a y t h a t , w h i l e m e a s u r e d lifetimes will b e in e r r o r , s i m p l e c r i t e r i a b y w h i c h d a t a a n a l y s i s is j u d g e d m a y i n d i c a t e success. C o n s e q u e n t l y it is of t h e u t m o s t i m p o r t a n c e t o h a v e a v a i l a b l e a r a n g e of s t a n d a r d c o m p o u n d s w i t h definitely e s t a b l i s h e d single e x p o n e n t i a l d e c a y t i m e s , w h i c h c a n b e u s e d t o t e s t t h e p e r f o r m a n c e of the instrument. R e c e n t l y w e h a v e , t o g e t h e r w i t h o u r c o l l e a g u e s , r e v i e w e d t h e l i t e r a t u r e for s t a n d a r d c o m p o u n d s a n d p r e p a r e d a list of lifetimes t h a t w e h a v e m e a s u r e d o u r s e l v e s ( L a m p e r t et al, 1983). I n g e n e r a l , t h e a g r e e m e n t b e t w e e n lifetimes m e a s u r e d in different l a b o r a t o r i e s is g o o d , b u t t h e r e a r e s o m e s t a r t l i n g d i s c r e p a n c i e s . T h e s e d i s c r e p a n c i e s m a y a r i s e f r o m different s t a t e s of p u r i t y of s o l v e n t o r s o l u t e , f r o m s t r o n g t e m p e r a t u r e d e p e n d e n c e in t h e lifetime of interest or from maladjusted i n s t r u m e n t s or i n a d e q u a t e m a t h e m a t i c a l analy­ sis t e c h n i q u e s . F o r o n e c o m p o u n d , q u i n i n e b i s u l p h a t e in s u l p h u r i c a c i d , t h e r e p o r t e d lifetimes s h o w a w i d e v a r i a t i o n . W e b e l i e v e t h a t t h i s c o m p o u n d h a s a d o u b l e e x p o n e n t i a l fluorescence d e c a y ( M e e c h et ai, 1982) a n d w e s t r o n g l y c a u t i o n a g a i n s t its u s e a s a fluorescence lifetime s t a n d a r d . P e r h a p s t h e m o s t p o p u l a r s t a n d a r d is a d i l u t e s o l u t i o n of a n t h r a c e n e in c y c l o h e x a n e , t h e d e c a y t i m e of w h i c h a t 2 5 ° C is i n d e p e n d e n t of e x c i t a t i o n a n d e m i s s i o n w a v e l e n g t h . Before u s e b o t h t h e a n t h r a c e n e a n d c y c l o h e x a n e m u s t b e r i g o r o u s l y p u r i f i e d a s r e s i d u a l i m p u r i t i e s h a v e in t h e p a s t led s o m e w o r k e r s t o a s s u m e a r a t h e r l o w v a l u e for t h e d e c a y t i m e . I t s h o u l d a l s o b e n o t e d t h a t t h e d e c a y t i m e is t e m p e r a t u r e , viscosity a n d c o n c e n t r a t i o n d e p e n d e n t ( B l a t t et al, 1982). I n

52

Time-correlated

Single

Photon

Counting

Table 2.1

Compound P P O "a PPO Anthracene Anthracene 1 -Cyanonaphthalene 1 -Cyanonaphthalene 1-Methylindole 3-Methylindole 3-Methylindole C 1,2-Dimethylindole DMNA

a bP P O is the CA t 0.3 Torr

Solvent Cyclohexane Cyclohexane (undegassed) Cyclohexane Cyclohexane (undegassed) Hexane 5 Vapour Cyclohexane Cyclohexane Ethanol Ethanol CH C1

2 2

Wavelength of observation of emission/nm

Lifetime, T /ns

0

440 440

1.42 1.28

405 405

5.23 4.10

345 345 330 330 330 330 375

18.23 23.77 6.24 4.36 8.17 5.71 2.40

symbol for 2,5-diphenyloxazole. vibrationally relaxed with 1 atmosphere cyclohexane; t= 185°C. D M N A is the symbol for N,N-dimethyl-l-naphthylamine.

T a b l e 2.1 w e list a n u m b e r of c o m p o u n d s t h a t c a n b e purified b y s t a n d a r d t e c h n i q u e s a n d t h a t h a v e single e x p o n e n t i a l d e c a y t i m e s . T h e lifetimes h a v e b e e n m e a s u r e d a t l e a s t twice o n o u r S P C i n s t r u m e n t , w h i c h e m p l o y s a s y n c h r o n o u s l y p u m p e d d y e l a s e r a s a n e x c i t a t i o n s o u r c e . T h e m e t h o d of d a t a a n a l y s i s w a s r e i t e r a t i v e l e a s t - s q u a r e s fitting (see C h a p t e r 6). F u r t h e r lists of s t a n d a r d c o m p o u n d s a r e g i v e n b y B i r k s (1970) a n d B e r l m a n (1965) b u t m a n y of t h e r e s u l t s in t h e s e p u b l i c a t i o n s w e r e o b t a i n e d w i t h i n a c c u r a t e , o r a t least, u n s o p h i s t i c a t e d t e c h n i q u e s a n d it is n o w a d v i s a b l e t o rely o n m o r e r e c e n t data. W e h a v e n o t t r e a t e d t h e t r a n s f e r of d a t a t o a c o m p u t e r , n o r d o w e c o n s i d e r t h e t y p e of c o m p u t e r t o b e u s e d s i n c e t h e r e will b e e n o r m o u s v a r i a t i o n f r o m laboratory to laboratory.

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2. Basic

Principles

of Lifetime

Measurement

53

Birks, J. B. (1970). "Photophysics of Aromatic Molecules", pp. 120-132. WileyInterscience, New York. Blatt, E., Treloar, E. F , Ghiggino, Κ. P. and Gilbert, R. G. (1981). J. Phys. Chem. 85, 2810-2813. Britten, A. and Lock wood, G. (1976). Mol. Photochem. 7, 79-84. Coates, P. D. (1968). J. Phys. E. Ser. 2 1, 878-879. Cramer, L. E. and Spears, K. G. (1978). J. Amer. Chem. Soc. 100, 221-227. Demas, J. N. and Crosby, G. A. (1971). J. Phys. Chem. 75, 991-1024. Easter, J. H., De Toma, R. P. and Brand, L. (1976). Biophys. J. 16, 571-583. Eastman, J. W. (1967). Photochem. and Photobiol. 6, 55-72. Grinwald, A. (1976). Anal. Biochem. 75, 260-280. Harris, J. M., Gray, L. M., Pelletier, M. J. and Lytle, J. E. (1977). Mol. Photochem. 8, 161-174. Harris, C. M. and Selinger, Β. K. (1979). Aust. J. Chem. 32, 2111-2129. Haugen, G. R , Wallin, B. W. and Lytle, J. E. (1979). Rev. Sci. Instrum. 50, 64-72. Haugen, G. R. and Lytle, J. E. (1981). Anal. Chem. 53, 1554-1559. Hazan, G., Grinwald, Α., Maytal, M. and Steinberg, I. Z. (1974). Rev. Sci. Instrum. 45, 1602-1604. Imasaka, J., K a w a b a t a , Y. and Ishibashi, N . (1981). Rev. Sci. Instrum. 52, 1473-1477. Knight, A. E. W. and Selinger, Β. K. (1973). Aust. J. Chem. 26, 1-27. Koechlin, Y. (1961). Thesis. University of Paris. Koester, V. J. and Dowben, R. J. (1978). Rev. Sci. Instrum. 49, 1186-1191. Lampert, R. L., Chewter, L. Α., Phillips, D., O'Connor, D. V., Roberts, A. J. and Meech, S. R. (1983). Anal. Chem. 55, 68-73. Lewis, C , Ware, W. R., Doemeny, L. J. and Nemzek, T. L. (1973). Rev. Sci. Instrum. 44, 107-114. Lopez-Delgado, R., Tramer, A. and M u n r o , I. H. (1974). Chem. Phys. 5, 320-326. Mandel, L. and Wolf, E. (1965). Rev. Mod. Phys. 37, 231-287. Meech, S. R., O'Connor, D. V. and Phillips, D. (1982). Chem. Phys. Lett. 88, 22-24. Millar, D. P., Robbins, R. J. and Zewail, A. H. (1980). Proc. Natl. Acad. Sci. USA 77, 5593-5597. M o r t o n , G. A. (1968). Appl. Optics 7, 1-10. M u r a o , T., Yamazaki, I. and Yoshihara, K. (1982). Appl. Optics 21, 2297-2300. O'Connor, D. V. (1977). Thesis. University of Western Ontario. Pfeffer, G., Lami, H , Laustriat, G. and Coche, A. (1962). Comptes Rendus 254, 1035-1037. Rayner, D. M., M c K i n n o n , A. E., Szabo, A. G. and Hackett, P. A. (1976). Canad. J. Chem. 54, 3246-3259. Rayner, D. M., M c K i n n o n , A. E. and Szabo, A. G. (1977). Rev. Sci. Instrum. 48, 1050-1054. Ricka, J. (1981). Rev. Sci. Instrum. 52, 195-199. Robbins, R. J., Fleming, G. R., Beddard, G. S., Robinson, G. W., Thistlewaite, P. J. and Wolfe, G. J. (1980). J. Amer. Chem. Soc. 103, 6271-6279. Shave, L. A. and Clive Love, L. J. (1975). Appl. Spectrosc. 29, 485-489. Swords, M. (1977). Thesis. University of Southampton. Wahl, Ph., Auchet, J. B. and Donzel, B. (1974). Rev. Sci. Instrum. 45, 2 8 - 3 2 . Wahl, P. R. (1975). New Tech. Biophys. Cell. Biol. 2, 2 3 3 - 2 4 1 . Ware, W. R. (1971). In "Creation and Detection of the Excited State", Vol. 1A (Lamola, Α. Α., ed.) p. 250. Marcel-Dekker, New York. Weber, G. and Teale, F. W. J. (1957). Trans. Faraday Soc. 53, 646-655.

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West, M. A. (1979). In "Photochemistry", Vol. 10 (Bryce-Smith, D., ed.) p. 40. The Chemical Society, London. Wild, U. P., Holzwarth, A. R. and G o o d , Η. P. (1977). Rev. Sci. Instrum. 48, 1621-1627. Wong, D. K. and Halpern, A. M. (1976). Photochem. and Photobiol. 24, 6 0 9 - 6 1 1 . Yguerabide, J. (1972). Meth. Enzymol. 26, 498-578. Zimmerman, H. E. and Cutler, J. P. (1975). Chem. Commun. 598-599.