LIGHT ABSORPTION BY FIGMENTS in VWO 1863 



(/) Calculation of True Absorption Spectra from Transmission and Fluores- 

 cence Spectra of Suspensions 



Duysens (1952) suggested two methods to determine the true absorp- 

 tion of light in small colored particles, such as Chlorella cells. The first 

 method (Duysens and Huiskamp, 1953) is based on comparison of the 

 intensities of fluorescence emitted "forward" and "backward" (in relation 

 to the incident beam). If the particles are idealized as tiny plane-parallel 

 vessels (thickness d) filled with pigment solution and illuminated normally 

 to their "front wall," the intensity of fluorescence of wave length X/ excited 

 by monochromatic light of wave length Xj, emitted through the "front 

 wall" into a solid angle o-, is: 



(37C.8) Fl = ^ f^^ he'^^'^'fih, Xi)e'"^'' dx 



while that of the fluorescence escaping through the "rear wall" of the par- 

 ticle (into an equal solid angle) is : 



(37C.9) Fx, = ^ /;/or"^^^/(V, XOr-^^^'^-^^ dx 



where f(\f\i) is the yield of fluorescence of wave length X/, excited by 

 Xi, while a^f and ax.- are the (natural) absorption coefficients for these two 

 wave lengths of the pigment solution inside the particle. 



According to equations (37C.8) and (37C.9), the ratio of the "forward" 

 and the "backward" fluorescence emissions is a function of the products 

 ax^d and a^id. If a second relationship between these two products is 

 known, a^i and ax/ can be calculated from relative measurements of 

 fluorescence intensity in the two directions. In applying this method to a 

 suspension of Chlorella cells, Duysens and Huiskamp (1953) used the 

 relationship: 

 (37C.9A) (1 - exp(-«Xid))/(l - exp(-ax/rf)) = DpM/Dp.\f 



in which i)p,x.- and Dp^/ are the optical densities of the cell suspension at the 

 two wave lengths. (This relationship follows from equation 37C.1G, 

 derived below.) The wave length of the incident light (Xi) was 420 m/x, 

 that of the measured fluorescence (X/), 680 m/x. 



The suspension was diluted so strongly that the transmission of the 

 vessel was > 80%. Since the transmission of each single cell is about 40%, 

 practical absence of mutual shading of the cells was assured. (This is a 

 necessary condition for the application of the above equations, derived for 

 individual particles, to the fluorescence emission of the suspension as a 

 whole.) The calculation was further improved by assuming spherical 

 rather than plane-parallel particles. An absorption of 64% was calculated 

 in this way for a single Chlorella cell, at 680 mju. 



