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Principles of TPE
- Two-Photon Microscopy of Cells and Tissue


In conventional confocal laser scanning fluorescence microscopy, absorption of a single photon delivers sufficient energy for the fluorophore to reach the exited state from which it returns to the ground state by emitting a photon of fluorescence. As illustrated in Figure 1a, this technique causes excitation of fluorescent dyes above and below the plane of focus, resulting in blurring of the image. Confocal microscopes increase the spatial resolution of the image by using an adjustable pinhole in front of the detector to reject out-of-focus fluorescence.

The excited state can also be reached by the near simultaneous absorption of two longer wavelength photons, resulting in the squared dependence on laser light intensity rather than the linear dependence of conventional, single-photon fluorescence imaging. Neglecting excitation saturation, the average rate of TPE per molecule is given by the following equation:


where <I2> is the time average of the second power of local laser intensity in units of photons cm–2 s–1 and {delta} is the two-photon absorption cross section in units of cm4 s photon–1 (10–50 cm4 s photon–1 equals 1 GM, or Göppert-Mayer). The TPE cross section is a quantitative measure of the probability of a molecule to absorb two photons simultaneously. It is the product of the molecular absorption cross section and the fluorescence emission quantum efficiency. The intensity-squared dependence of TPE gives this technique its intrinsic three-dimensional resolution (see Figure 1b).1 Because the energy of a single long-wavelength photon is insufficient to excite commonly used fluorescent dyes, linear absorption by fluorophores above the focal plane does not occur. Excitation (and thus emission) is confined to a small ellipsoidal volume around the focal point, where photon flux is sufficiently high to give rise to two-photon absorption events. Because out-of-focus fluorescence is never generated, TPE microcopy provides optical sectioning without the need to introduce a pinhole in the detection path of the microscope, as in confocal microscopy. Thus, all of the signal generated by the sample can be collected by a large-area detector and contribute to the final image (nondescanned acquisition mode; see the online data supplement, available at

The size of the TPE volume (and thus the optical resolution of the TPE system) critically depends on the numerical aperture of the objective lens and the illumination wavelength. To illustrate the effect of numerical aperture size on the spatial scale of the <I2> distribution, isointensity contour plots in the x-y and x-z planes were simulated using an ellipsoidal Gaussian approximation to the diffraction-limited focus (Figure 2a).7,12 A 4-fold reduction in the numerical aperture of the objective lens will increase the spread of the excitation volume (measured at the 0.5 isointensity contours) @22-fold axially and »4-fold laterally, amounting to an increase in TPE volume by more than two orders of magnitude (Figure 2b), whereas increasing excitation wavelength from 700 to 1000 nm will increase TPE volume by only »3-fold. Thus, using TPE microscopy with a uniformly illuminated, high numerical aperture objective, fluorescence excitation is confined to less than femtoliter volumes around the focal point of the objective, with z direction. For comparison, the size of a mitochondrion in an eukaryotic cell is »1.5 to 2 µm in length, and 0.5 to 1 µm in diameter. Thus, TPE microscopy provides fluorescence imaging with subcellular resolution. Although calculated dimensions of TPE volumes may deviate from their actual values within the specimen, knowing them is helpful to estimate the thickness of an optical section or to predict the number of caged calcium ions that one expects to release during two-photon photolysis (see below). Besides using a high numerical aperture objective and shorter excitation wavelengths, the optical resolution of the TPE system can be increased by using descanned detection in conjunction with a confocal pinhole in the emission path (see also the online data supplement).13 However, a confocal pinhole will reject scattered emissions, even though they originated in the focal plane, thereby reducing fluorescence collection efficiency, and thus signal-to-background ratio.

TPE events are exceedingly rare at light intensities typically used for epifluorescence microscopy. To generate enough fluorescence practical for TPE laser scanning microscopy, sample illumination is typically provided by pulsed lasers such as the mode-locked Ti:Sapphire laser, which generates pulses of {approx}100 fs duration at a repetition rate of »80 MHz. When pulsed illumination is used, the instantaneous light intensity is extremely high, whereas the average energy received by the sample remains relatively low. Estimating the instantaneous focal intensities achieved during pulsed illumination is useful to minimize the occurrence of irreversible photodamage14,15 as well as to prevent fluorophore saturation, which will increase the size of the TPE volume and thereby reduce the optical resolution of TPE imaging.12 For a two-photon process, the excitation rate is proportional to the average squared intensity (<I2>) (see Equation 1) rather than the average intensity squared (<I2>). Because the average intensity <I2> equals the product of the pulse frequency, f, and the integrated intensity during a pulse of duration {tau} (full-width-at-half maximum), the dependence of <I2> on average intensity is given (for {tau}f)12 by the following equation:


where g is a dimensionless factor (0.5916; 0.57615). Compared with continuous illumination, pulsing will increase <I2>, and, consequently, TPE probability by a factor of (g/f{tau}), but, at the same time, reduce <I2> by the same factor. Thus, the yield of nonlinear excitation processes can be increased by shortening of the pulse width {tau} and/or by reducing the pulse repetition frequency f. For example, for 100-fs pulses and f=80 MHz, the TPE probability at the focal point is increased by approximately five orders of magnitude, whereas reduction of the pulsing frequency to 200 kHz without changing the pulse width will theoretically increase the probability of two-photon absorption events by a factor of 3x107. However, the peak laser intensity at the lower repetition frequency will be unusually high, resulting in degradation of the optical resolution caused by excitation saturation12 and in an increase in the relative contribution of higher-order (more than second-order) excitation processes to the fluorescence output, which in turn increases the risk of photobleaching17 and photodamage.14,15 The lowest usable repetition frequency is dictated by the pixel rate of the scanning module because at least one pulse must be delivered per image pixel. Fluorescence emission would be further increased if the pulse repetition rate were maximally increased to the inverse fluorescence lifetime of typically 1 to 2x10–9 s–1.18 Shortening of the pulse duration below the standard value of »100 fs is possible,19 but is limited by the appearance of group velocity dispersion.12

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