The distinction between irradiance and fluence rate. The former considers optical power through a surface of unit area in a direction parallel to the surface normal (a). The latter considers the total optical power through though a sphere of unit surface area in all directions (b) 

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Context 1

... to explaining the details regarding treatment light quantification, it is important to define two quantities, irradiance and fluence rate, and their differences relevant to biophotonic applications in turbid media such as biological tissues. Although both quantities have the same units, their meanings are in fact vastly different. Irradiance, commonly denoted H, describes the power density [mW · cm -2 ] at a point P(x,y,z) through a surface of unit area in the direction of a surface normal r. Shown in the Figure 1 is a surface of unit area within an environment containing diffuse light. Irradiance is calculated by integrating all optical power through the surface that travel in the same hemisphere of r. In terms of clinical PDT, irradiance is the quantity of interest when an external collimated treatment light is delivered to a tissue surface such as the skin, the esophagus (van Veen et al. (2002)) or the surface of the bladder ( Star et al. (2008)). Fluence rate, commonly denoted as Φ, is the three-dimensional analogue of irradiance as it describes the power density [mW · cm -2 ] through a sphere of unit surface area, as shown in Figure 1b. Fluence rate can be derived from irradiance by integrating irradiance through a full solid angle of 4π sr. In PDT and other light-based therapies ( Robinson et al. (1998); Amabile et al. (2006)), fluence rate is used to quantify treatment light when it is delivered to a tissue volume using devices such as isotropic diffusing tip fibers. Since this delivered light travels omnidirectionally, the power delivered in all directions must be accounted for (hence the integration over 4π sr). Its gradient in tissue is determined exclusively by the effective attenuation coefficient 3( ...

Context 2

... to explaining the details regarding treatment light quantification, it is important to define two quantities, irradiance and fluence rate, and their differences relevant to biophotonic applications in turbid media such as biological tissues. Although both quantities have the same units, their meanings are in fact vastly different. Irradiance, commonly denoted H, describes the power density [mW · cm -2 ] at a point P(x,y,z) through a surface of unit area in the direction of a surface normal r. Shown in the Figure 1 is a surface of unit area within an environment containing diffuse light. Irradiance is calculated by integrating all optical power through the surface that travel in the same hemisphere of r. In terms of clinical PDT, irradiance is the quantity of interest when an external collimated treatment light is delivered to a tissue surface such as the skin, the esophagus (van Veen et al. (2002)) or the surface of the bladder ( Star et al. (2008)). Fluence rate, commonly denoted as Φ, is the three-dimensional analogue of irradiance as it describes the power density [mW · cm -2 ] through a sphere of unit surface area, as shown in Figure 1b. Fluence rate can be derived from irradiance by integrating irradiance through a full solid angle of 4π sr. In PDT and other light-based therapies ( Robinson et al. (1998); Amabile et al. (2006)), fluence rate is used to quantify treatment light when it is delivered to a tissue volume using devices such as isotropic diffusing tip fibers. Since this delivered light travels omnidirectionally, the power delivered in all directions must be accounted for (hence the integration over 4π sr). Its gradient in tissue is determined exclusively by the effective attenuation coefficient 3( ...

Context 3

... polarographic Clark-type electrode (Clark et al. (1953)) is the current standard tool for measuring partial oxygen pressure (pO 2 ) [kPa] of tissue ( Cheema et al. (2008); Swartz (2007); Pogue et al. (2001)). Its mode of operation is based on the electrochemical reduction of ground state triplet oxygen ( 3 O 2 ) to generate a measurable electric current proportional to the concentration of 3 O 2 around the probe. Absolute pO 2 quantification can be made after calibrating the electrode at a known pO 2 concentration and in the absence of oxygen. One drawback of this technology is that oxygen is consumed to generate OH -ions during the measurement process: O 2 + 4e -1 + 2H 2 O→4OH -( Lee & Tsao (1979)). As a result, the sensitivity of Clark electrodes is directly related to the pO 2 of the environment it is measuring. To gain an appreciation of the impact that this may have within the context of PDT, it is worthwhile to note that the change in pO 2 from the atmosphere to tissue is a reduction of over 20 times ( Ward (2008)). Consequently, the operation of the electrode behaves as an additional "oxygen sink" that further contributes to the depletion of 3 O 2 in an environment that already contains low levels of oxygen, contributing further to the degradation of the measurable electrical signal. An alternative to using an electrode is to optically measure 3 O 2 . This technique relies on the ability of 3 O 2 to effectively quench the phosphorescence of molecules in the triplet excited (T1) state (Fitzgerald et al 2001). A phosphorescent molecule in the T1 state can return to the ground state via photon production (phosphorescence) or undergo a non-radiative energy exchange with 3 O 2 . In the event that an energy exchange takes place, the phosphorescence is said to be quenched and no photon is produced. This in effect reduces the exponential decay lifetime τ [s] of the compound, which is defined as the time required for the phosphorescence intensity to fall to 1/e or 37% of its initial peak value. Under constant temperature and atmospheric pressure, the variation between τ and pO 2 is linear and inversely related. An optical probe with embedded phosphorescent sensors, or an optode, can be fabricated to replace the electrode for oxygen quantification. This probe requires a short wavelength light source to promote the sensor material to the T1 state and hence induce phosphorescence which can be measured to derive the pO 2 . The advantage compared to the electrode is that measurement sensitivity is inversely proportional to pO 2 and 3 O 2 is consumed at a lower rate than the electrode. Commercially available oxygen measurement systems based on oxygen quenching have been made available from Oxford Optronics in the United Kingtom under the Oxylite brand, as well as from Ocean Optics sold under the NeoFox brand name. Both systems utilize a pulsed blue LED excitation source to generate the phosphor excitation and induce emissions from sensors embedded at the tip of fiber-based probes. Such systems, however, are capable of interrogating only one point at a time. Multiple fiber probes are thus required in order to perform spatially resolved pO 2 measurements, with the same limits to clinical acceptability as mentioned in previous ...

Context 4

... block diagram of the FD system is presented in the figure 4. A 50:50, 2x2 optical coupler is used to direct excitation light to the oxygen sensor, and to guide captured sensor emissions to the photo-multiplier tubes (PMT). The excitation source is a 405nm laser diode, intensity modulated by a laser driver whose output is controlled by a programmable signal generator. The function generator is programmed to sweep through a frequency range from 100 Hz to 1 kHz. During operation, the optical coupler directs the excitation light captured at Port 1 to ports 3 and 4. The PMT at port 3 is equipped with a 405 nm bandpass filter to monitor the excitation source to be used as the reference signal. At port 4, phosphorescence induced by the delivered excitation light is captured by the coupler and re-directed to port 2 for detection by a second PMT equipped with a 650 nm long-pass filter, which generates the emission signal. Phosphorescent palladium metalloporphyrin compound Pd-meso-Tetra(N-Methyl-4-Pyridyl) Porphine "TMPP" is used as the sensing material because of its long and measurable decay times in the μs range (Fitzgerald et al 2001). The compound is mixed into a compatible epoxy, spincoated onto a glass microscope slide, and allowed to cure. The decay lifetime of 760 μs at 21 kPa (atmospheric condition) and 903 μs at 0 kPa (anoxic) pO 2 is measured with the FD system. The value of τ should be constant for all modulation frequencies as long as the pO 2 does not change. Thus, the measured phase at different modulation frequencies follows the relationshiop described in Equation 13. Figure 5 shows a plot of the measured phase against modulation frequency at 21 kPa and 0 kPa. The solid and dotted lines represent the fitting used to determine τ based on the measured phase relationship for each oxygenation level, with a resulting R 2 greater than ...