**4.3 Time modulation**

10 VLSI Design

distance of its path length, x, traveled in the material. The absorption coefficient, , is defined relative to the concentration, M, and the cross section, S, of the absorbing molecules

 I(x) = I(0) . exp (.x) = I(0) . exp (-S.MxN) (4.1.1) Where I(x) is the light intensity at distance x, I(0) the incident light intensity at x = 0, and N

Changes of the analyte concentration in the sample can alter the absorption coefficient . An absorption based sensor measures these changes by the transmitted light intensity in terms

A = log[I(0)/ I(x)] (4.1.2)

Wavelength modulation can provide us with more information than just the intensity modulation. Several numbers of fixed wavelength sources are used simultaneously and their responses, intensity, are detected using photo detectors. Several sources that are modulated at different electrical frequencies can be used simultaneously in order to use a single photo

Fluorescence occurs when an atom or a molecule makes a transition from a higher energy state to a lower one and emits lights. Excitation and subsequent emission can occur not only by photoluminescence but also by chemical reaction (chemiluminescence) or biological reaction (Bioluminescence). In resonance fluorescence, absorption and emission take place between the same two energy levels, and therefore the wavelength of the excitation and emission lights are the same. In non-resonant fluorescence, emission occurs either at higher wavelength than excitation wavelength (Stokes Fluorescence), or lower wavelength than

where *k*t is the total fluorescence rate, in sec-1, and *N* is proportional to the number of

 = *N0* 

Lamda X (a) Intensity vs. wavelength

matter versus the wavelength. (b) corresponding schematic for measurement.

Fig. 4.2. (a) Attenuation of the optical intensity as it travels along the x axis throught the

(b)

/d*t* of the fluorescence

/d*t* = -*k*t *. N* (4.2.1)

 *.* exp(-*k*<sup>t</sup> **.** *t*) (4.2.2)

Light Source Sample Filter Detector

detector. One of the wavelengths could serve as a reference channel for calibration.

excitation wavelength (anti- Stokes Fluorescence). The decay rate d*N*

I(0)

electrons excited due to the fluorescent state in a time t. Hence

(Svanberg, 2001).

of absorbance (A) units:

for a two level system is

log I

d*N*

 *N*

I(x)

**4.2 Wavelength modulation** 

Avogado's number (6.022 x 1023 mol-1).

Time modulation is essentially a subclass of intensity modulation. In time domain fluoremetry (TDF), a pulsed light source generates the photoluminescence. The fluorescence decay signal is measured as a function of time, and the decay curve determines the lifetime of the chemical sample. In time modulation base sensors measure the halftime of the sample.

Fig. 4.3. (a) Fluorescence decay curve (b) corresponding schematic for measurement
