Group Abstract Group Abstract

Message Boards Message Boards

0
|
7.2K Views
|
5 Replies
|
0 Total Likes
View groups...
Share
Share this post:

Fluorescence lifetime

Hafizah Halip
Posted 6 years ago

Hello, I am new to Mathematica software and I am having problem to start my coding in Mathematica. to be honest, a bit clueless, I want to do simulation for fluorescence lifetime measurement. Here is my equation,

my main equation

Here, ? is the initial fluorescence intensity emitted by the sample when irradiated by laser pulses; ? is the fluorescence lifetime; ? denotes the repetition angular frequency of the short-pulsed laser; T is the period of pulse repetition (T = 2?/?); ? is the phase difference between the excitation pulse sequence and reference signal of the lock-in amplifier. Three phase-difference values of 0, ?/4, and ?/2 were considered.

Next, I want to do

enter image description here

where multiple fluorescence lifetime is used.

Can anyone help me how to do simulation for equation 1 and equation 2? Thank you very much!
POSTED BY: Hafizah Halip
5 Replies
Sort By:
Bill Nelson
Bill Nelson
Posted 6 years ago

I apologize if I misunderstood or wasn't clear.

In each of those the first line defines a function to do your integration and the second and third lines show example usage.

Asking Mathematica to evaluate this

i[tau_,phi_]:=Integrate[alpha E^(-t/tau)Cos[omega t+phi],{t,0,T}];
i[1,0]

then it will perform your integration with those two parameter values and should immediately display this

(alpha*(E^T - Cos[omega*T] + omega*Sin[omega*T]))/(E^T*(1 + omega^2))

Likewise asking Mathematica to evaluate

i[tau1_,tau2_,phi_]:=Integrate[(alpha1 E^(-t/tau1)+alpha2 E^(-t/tau2))Cos[omega t+phi],{t,0,T}];
i[1/2,1,Pi/2]

will perform your integration with those three parameter values and should immediately display

((alpha2*E^T*(-(E^T*omega) + omega*Cos[omega*T] + Sin[omega*T]))/(1 + omega^2) + 
 (alpha1*(-(E^(2*T)*omega) + omega*Cos[omega*T] + 2*Sin[omega*T]))/(4 + omega^2))/E^(2*T)

If I still don't have this correct then please let me know and we will try to resolve this.
POSTED BY: Bill Nelson
Hafizah Halip
Hafizah Halip
Posted 6 years ago

thank you so much for your explanation, I really appreciate it.

if i want to change the value of phi to 0. and then change to to phi = pi/2 and lastly phi = pi/4, i should change the value phi with i[1,0] i[1,pi/2] and i[1,pi/2]?

also, how can i display in on a graph? enter image description here

Attachments:
try3.nb
POSTED BY: Hafizah Halip
Bill Nelson
Bill Nelson
Posted 6 years ago
POSTED BY: Bill Nelson
Bill Nelson
Bill Nelson
Posted 6 years ago

Do these do what you want?

i[tau_,phi_]:=Integrate[alpha E^(-t/tau)Cos[omega t+phi],{t,0,T}];
i[1,0]
i[2,Pi/4]

and

i[tau1_,tau2_,phi_]:=Integrate[(alpha1 E^(-t/tau1)+alpha2 E^(-t/tau2))Cos[omega t+phi],{t,0,T}]
i[1,2,0]
i[1/2,1,Pi/2]
POSTED BY: Bill Nelson
Hafizah Halip
Hafizah Halip
Posted 6 years ago

thank you so much for replying my question. may i know what is the i[1,0] i[2,Pi/4] for?
POSTED BY: Hafizah Halip
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard