Figure 10.48 Energy level diagram for a molecule showing pathways for the deactivation of an excited state: vr is vibrational relaxation; ic is internal conversion; ec is external conversion; and isc is an intersystem crossing. A decrease in the solvents viscosity decreases f for similar reasons. Chopper Light is directed onto a sample, where it is absorbed and imparts excess energy into the material in a process called photo-excitation. Basic Principle- When light strikes a sample,it gets absorbed by impartingits excess energy to the material by thephenomenonknown as photo-excitation. Therefore, the fluorescent signal can be detected which indicate the existence of a particular DNA. Electrons can have a spin of (+1/2) or (-1/2). There are normally two slits, entrance and exit in a fluorometers. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Fluorescence also increases for aromatic ring systems and for aromatic molecules with rigid planar structures. Tryptophan (trp), tyrosine (tyr), and phenylalanine (phe) are three natural amino acid with strong fluorescence (Figure \(\PageIndex{12}\)). Molecular Luminescence Spectroscopy. Legal. PhotoluminescenceExcited state generated by absorption of a photon. 10 Principle of Photoluminescence Spectroscopy A spectrofluorometer is an analytical instrument used to measure and record the fluorescence of a sample. WHAT IS PHOTOLUMINESCENCE? Monocharomators help us to achieve this aim. As noted earlier, organic compounds containing aromatic rings generally are fluorescent and aromatic heterocycles are often phosphorescent. 0-0 When a system is in the triplet state, there exist two unpaired electrons with a total spin state of 1. An analyte that is fluorescent can be monitored directly. Legal. Fluorescence is the emission of electromagnetic radiation light by a substance that has absorbed radiation of a different wavelength. The phosphoroscope was experimentally devised by Alexandre-Edmond Becquerel, a pioneer in the field of luminescence, in 1857, Figure \(\PageIndex{25}\). 2.3 Photoluminescence spectroscopy PL is a nondestructive and contactless optical method of probing the electronic structure of materials. As the light is directed onto a sample, the electrons within the material move into excited states. As mentioned earlier, when combined with analysis models, FCS data can be used to find diffusion coefficients, hydrodynamic radii, average concentrations, kinetic chemical reaction rates, and single-triplet dynamics. PRINCIPLES OF PHOTOLUMINESCENCE output of intensity vs. wavelength For a Gaussian PSF, the autocorrelation function is given by \ref{2}, where \ref{3} is the stochastic displacement in space of a fluorophore after time T. \[ G(\tau )\ =\frac{1}{\langle N \rangle } \langle exp (- \frac{\Delta (\tau)^{2} \ +\ \Delta Y(\tau )^{2}}{w^{2}_{xy}}\ -\ \frac{\Delta Z(\tau )^{2}}{w^{2}_{z}}) \rangle \label{2} \], \[ \Delta \vec{R} (\tau )\ =\ (\Delta X(\tau ), \Delta (\tau ), \Delta (\tau )) \label{3} \]. The selectivity of fluorescence and phosphorescence is superior to that of absorption spectrophotometry for two reasons: first, not every compound that absorbs radiation is fluorescent or phosphorescent; and, second, selectivity between an analyte and an interferent is possible if there is a difference in either their excitation or their emission spectra. Photoluminescence is a common technique used to characterize the optoelectronic properties of semiconductors and other materials. Explain how you can modify the procedure to take this into account? wavelength of excitation It is used in spectroscopic measurements where the frequency of the excitation light is varied, and the luminescence is monitored at the typical emission . Emission between a triplet excited state and a singlet ground stateor between any two energy levels that differ in their respective spin statesis called phosphorescence. With a monochromator the excitation source is usually high-pressure Xe arc lamp, which has a continuous emission spectrum. Its principle is simple: electrons are excited from the valence to the conductance band of the material by a laser with an energy larger than the bandgap. Almost any desired transmission curve can be obtained using a thin film filter. As shown in Table 10.13, several important biochemical, pharmaceutical, and environmental compounds may be analyzed quantitatively by fluorimetry or phosphorimetry. https://www2.warwick.ac.uk/fac/sci/physics/current/postgraduate/regs/mpags/ex5/techniques/optical/pl/, spectra of Al0.24Ga0.756As Detection limits for phosphorescence are somewhat higher, with typical values in the nanomolar range for low-temperature phosphorimetry, and in the micromolar range for room-temperature phosphorimetry using a solid substrate. When one paired electron is excited to a higher-energy state, it can either occupy an excited singlet state or an excited triplet state. When the light is emitted with a time delay more than 10-8 sec. An excitation wavelength is selected by one monochromator, and luminescence is observed through a second monochromator, usually positioned at 90 to the incident light to minimize the intensity of scattered light reaching the dector. The detector produces an electronic signal that can be stored as intensity over time or can be immediately auto correlated. Measure the fluorescent emission at 450 nm using an excitation wavelength of 350 nm. If the basic excitation and emission properties of a particular system under study, then selectivity by using optical filters is better than by the use of monochromators. 1975, 52, 610612. The PowerPoint PPT presentation: "Photoluminescence (PL)" is the property of its rightful owner. A final form of radiationless deactivation is an intersystem crossing in which a molecule in the ground vibrational energy level of an excited electronic state passes into a higher vibrational energy level of a lower energy electronic state with a different spin state. The widely used conventional methods such as XRD, IR and Raman spectroscopy, are very often not sensitive enough for supported oxide catalysts with low metal oxide concentrations. Olko,Pawel, Advantages and Disadvantages of Luminescence Dosimetry, Radiation Measurements 45 (2010) 506511, H. Photoluminescence in Analysis of Surfaces and Interfaces. A few inorganic nonmetals are determined by their ability to decrease, or quench, the fluorescence of another species. Although the wavelength of output is still dominated by those Hg lines, these lines are broadened and fit to various fluorophores better. Source: modified from Splarka (commons.wikipedia.org). At present a wide range of fluorophores have been developed as fluorescence probes in bio-system. A laser beam with duration less than 10 ns is shot at the sample, and the light emitted by the sample will decay with time. Photoluminescence excitation (abbreviated PLE) is a specific type of photoluminescence and concerns the interaction between electromagnetic radiation and matter. http://archive.cnx.org/contents/81bb0311-98ee-4cfc-b3c8- A large amount of information can be extracted. Because the average lifetime for phosphorescence ranges from 104104 s, phosphorescence may continue for some time after removing the excitation source. i.e. Fluorescence is a type of luminescence caused by photons exciting a molecule, raising it to an electronic excited state. The probability of fluorescence is very high and the average lifetime of an electron in the excited state is only 105108 s. Fluorescence, therefore, decays rapidly once the source of excitation is removed. Lets assume that the molecule initially occupies the lowest vibrational energy level of its electronic ground state, which is a singlet state labeled S0 in Figure 10.48. Compared with xenon lamps, Hg lamps have higher intensities. However, there have recently been examples reported in which luminogen aggregation played a constructive, instead of destructive role in the light-emitting process. It is common to use two detectors and cross- correlate their outputs leading to a cross-correlation function that is similar to the auto correlation function but is free from after-pulsing (when a photon emits two electronic pulses). Gfroerer T., H. Photoluminescence in Analysis of Surfaces and Interfaces. Overall, the graph shows how different ETL materials in different concentrations emit light, and it is often used as a parameter for measuring how effective the material is as the electron transport layer. In the first of these extractions, quinine is separated from urine by extracting it into a mixture of chloroform and isopropanol, leaving the chloride behind in the original sample. From equation 10.28 and equation 10.29 we know that the sensitivity of a fluorescent or phosphorescent method is influenced by a number of parameters. and Sons Ltd.: Chichester,pp 9209-9231, (2000) The analysis of a sample containing n components, therefore, can be accomplished by measuring the total emission intensity at n wavelengths. Figure 10.52 Schematic diagram showing the orientation of the source and the detector when measuring fluorescence and phosphorescence. The absorbance spectrum is created by exciting electrons at varying wavelengths while monitoring the emission at a fixed wavelength. Emission of light (20%) (Photoluminescence) From equation 10.28 we know that If is a function of the following terms: k, f, P0, , b, and C. We know that f, b, and C are the same for both excitation wavelengths and that is larger for a wavelength of 250 nm; we can, therefore, ignore these terms. Photoluminescence Spectroscopy for studying Electron-Hole pair recombination Electron diffraction and Neutron diffraction, Spectroscopy techniques, it's principle, types and applications, CVB222 UV-vis Absorption and Fluorescence Lecture, FOURIER TRANSFORM - INFRARED SPECTROSCOPY, Basic understanding of Infrared Spectroscopy, Government Pharmacy College Sajong, Government of Sikkim, Prabhakar singh ii sem-paper v-detection & measurement of radioactivity, Department of Biochemistry, Veer Bahadur Singh Purvanchal Univarsity, Jaunpur. Photoluminescence spectra are recorded by measuring the intensity of emitted radiation as a function of either the excitation wavelength or the emission wavelength. Brief description about interpretation of a photo-luminescence spectrum. S2 JWST/NIRCam detections of dusty subsolar-mass young stellar objects in the Sm Photoluminescence (PL)? In this paper, experimental photoluminescence (PL) and piezoelectric photothermal (PPT) spectra of selected II-VI binary crystals are presented and analyzed. However, what is needed for experiments are various chromatic light with a wavelength range of 10 nm. For example, the enzyme creatine phosphokinase can be determined by using it to catalyze the formation of creatine from phosphocreatine. A direct quantitative analysis is possible when the analytes fluorescent or phosphorescent quantum yield is favorable. The net effect in Figure \(\PageIndex{1}\) is that the 0 emission energy is less than the 0 excitation energy. Ruthenium (II), iridium (III), rhenium (I), and osmium (II) are the most popular transition metals that can combine with one to three diimine ligands to form fluorescent metal complexes. Afterglow in The absorption and emission spectra will have an approximate mirror image relation if the spacings between vibrational levels are roughly equal and if the transition probabilities are similar. Encyclopaedia of Analytical Chemistry; Meyers, R. A., Ed. If an organic analyte is not naturally fluorescent or phosphorescent, it may be possible to incorporate it into a chemical reaction that produces a fluorescent or phosphorescent product. The best way to appreciate the theoretical and practical details discussed in this section is to carefully examine a typical analytical method. Fluorescence, therefore, occurs over a range of wavelengths. Many metal ions may be determined indirectly by reacting with an organic ligand to form a fluorescent, or less commonly, a phosphorescent metalligand complex. Table 10.12 provides additional examples of chelating reagents that form fluorescent metalligand complexes with metal ions. After applying the chosen autocorrelation function, it becomes much easier to analyze the data and extract the desired information (Figure \(\PageIndex{22}\)). The intensity of fluorescence, If, is proportional to the amount of radiation absorbed by the sample, P0 PT, and the fluorescent quantum yield, \[I_\ce{f} = k_\ce{f}(P_0 P_\ce{T})\tag{10.25}\], where k is a constant accounting for the efficiency of collecting and detecting the fluorescent emission. electrical signal Phosphorescence occurs when electrons from the excited triplet state return to the ground singlet state, \ref{4} - \ref{6}, where E represents an electron in the singlet ground state, E* represent the electron in the singlet excited state, and T* represents the electron in the triplet excited state. Figure 10.54 Schematic diagram showing how choppers are used to prevent fluorescent emission from interfering with the measurement of phosphorescent emission. It allows a selective excitation of defects, on which the site-selective luminescence is based. The 0 transitions in Figure \(\PageIndex{2}\), do not exactly overlap. The electronic ground state is shown in black and the three electronic excited states are shown in green. It may require more calculations to approximate PSF, depending on the particular shape. Thousands of fluorophores have been synthesized, but herein four categories of fluorophores will be discussed with regard their spectral properties and application. It can provides a steady light output from 250 - 700 nm (Figure \(\PageIndex{11}\)), with only some sharp lines near 450 and 800 nm. https://www2.warwick.ac.uk/fac/sci/physics/current/postgraduate/regs/m When these electrons return to their equilibrium states, the excess energy is released and may include the emission of light (a radiative process) or may not (a nonradiative process). Phosphorescent materials find use in radar screens, glow-in-the-dark toys, and in pigments, some of which are used to make highway signs visible to drivers. sec ). The fluorescent emission for quinine at 450 nm can be induced using an excitation frequency of either 250 nm or 350 nm. Phosphorescence is a specific type of photoluminescence related to fluorescence. Remote sensing with fiber optic probes also can be adapted for use with either a fluorimeter or spectrofluorimeter. Uploaded on Mar 14, 2013. After absorption, the vibrationally excited S1 molecule relaxes back to the lowest vibrational level of S1 prior to emitting any radiation. Naturally it follows that the emission spectrum is created by exciting electrons at a fixed wavelength but observing emissions at different wavelengths. From equation 10.28 and equation 10.29 we know that the intensity of fluorescent or phosphorescent emission is a linear function of the analytes concentration provided that the samples absorbance of source radiation (A = bC) is less than approximately 0.01. Manufacturers Chemo-sensor due to PL varying with molarity/concentration Calibration curves often are linear over four to six orders of magnitude for fluorescence and over two to four orders of magnitude for phosphorescence. This complex has excellent quantum yield and relatively long lifetime. One major advantage of the rotating can phosphoroscope over the rotating disk phosphoroscope is that, at high speeds, it can minimize other types of interferences such as fluorescence and Raman and Rayleigh scattering, the inelastic and elastic scattering of photons, respectively. Also, a high efficiency is required to increase the ability to detect low light levels. It is a non-destructive technique of examining the materials electronic structure. Excited state lifetime is a measure of the decay times of the fluorescence. Based on fluorescence spectroscopy, signal fluorescence can be detected which help us to locate the target DNA sequence. e%20.pdf Stokes shift is the difference between positions of the band maxima of the absorption and emission spectra of the same electronic transition. Quinines absorption spectrum shows that 250 is greater than 350. Unpaired electrons: At the excitation wavelength of 329 nm, as the molarity increases, the emission intensity decreases. S= (-1/2)+(+1/2)=0 Another approach is to measure a decrease in fluorescence or phosphorescence when the analyte is added to a solution containing a fluorescent or phosphorescent probe molecule. Transient Photoluminescence, also called Time-resolved Photoluminescence, is used to detect the radioactive decay of the samples in which excited electrons have a radio active decay channel. Using such value as the excitation wavelength can thus provide a more intense emission at a red-shifted wavelength, which is usually within twice of the excitation wavelength. One example is the analysis for F based on its ability to quench the fluorescence of the Al3+alizarin garnet R complex. This Gaussian is assumed with the auto-correlation with changes being applied to the equation when necessary (like the case of a triplet state, chemical relaxation, etc.). Photoluminescence Laser treated andifitis of natural measurements for cold(i.e., in liquid ofthe color origin of coral concentrations (ppb collection . In some cases an electron in a singlet excited state is transformed to a triplet excited state (Figure 10.47c) in which its spin is no longer paired with the ground state. Phosphorescence occurs when excited electrons of a different multiplicity from those in their ground state return to their ground state via emission of a photon, Figure \(\PageIndex{24}\). The precision for phosphorescence is often limited by reproducibility in preparing samples for analysis, with relative standard deviations of 510% being common. Time-Resolved Photoluminescence Spectroscopy of InGaAs/InP Heterostructures* Colleen Gillespie and Tim Gfroerer, Davidson College, Davidson, NC Mark Wanlass, National Renewable Energy Laboratory, Golden, CO Abstract Semiconductor-based thermophotovoltaic cells, which convert thermal radiation into electricity, show potential for an efficient . 3.2 molecular fluorescence and phosphorescence spectroscopy GaneshBhagure2 388 views 56 slides Flourescence a kh 24.2k views 24 slides Fluorescence spectrometry Hari Sharan Makaju 41.5k views 39 slides X ray spectroscopy. Nonlinearity may be observed for small concentrations of analyte due to the presence of fluorescent or phosphorescent contaminants. Photoluminescence (PL) spectroscopy, as applied in gemology, is a nondestructive analytical technique in which a material is illuminated with light, usually from a laser, and the resulting luminescence is recorded as a plot of emitted light intensity versus wavelength. In both techniques, light is focused on a sample and fluorescence intensity fluctuations are measured and analyzed using temporal autocorrelation. UV laser source Secondary Ion Mass Spectroscopy (SIMS) PPT. Suppose the slits dimensions are 0.1 mm 3 mm. Fluorescence is now defined as occurring when decaying electrons have the same multiplicity as those of their ground state. They are widely used for clinical diagnosis, bio-tracking and labeling. Difficult to study complex systems Most unsubstituted, nonheterocyclic aromatic compounds have favorable fluorescence quantum yields, although substitutions on the aromatic ring can significantly effect f. phosphorescence Herein, the application of fluorescence in DNA and RNA detecition is discussed. tyrosine (F) The energy of the emitted light (photoluminescence) relates to the difference in energy levels between the two electron states involved in the transition between the excited state and the equilibrium state. The latter can be many times stronger than the former and can prevent successful Raman analysis. The first scientists to be credited with the application of fluorescence to signal-correlation techniques were Douglas Magde, Elliot L. Elson, and Walt W.Webb, therefore they are commonly referred to as the inventors of FCS. Photoluminescence ; John Wiley A. Mamum, T. T. Ava, K. Zhang, H. Baumgart, G. Namkoong, New PCBM/carbon based electron transport layer for perovskite solar cells, Phys. Modern applications and state-of-the-art techniques are covered and make this . Besides quantum yield, the sensitivity of an analysis can be improved by using an excitation source that has a greater emission intensity, P0, at the desired wavelength, and by selecting an excitation wavelength that has a greater absorbance. Cryogenic conditions are usually used because, at low temperatures, there is little background interference from processes other than phosphorescence that contribute to loss of absorbed energy. Add 2.00 mL of 0.05 M H2SO4 to the organic phase and shake the contents for one minute. An excitation spectrum looks very much like an absorption spectrum. In Figure \(\PageIndex{8}\), however, it shows different patterns of emission under different excitation wavelengths. However, there are also a few long-lifetime organic fluorophore, such as pyrene and coronene with lifetime near 400 ns and 200 ns respectively (Figure \(\PageIndex{17}\)). The quantitative analysis of the photothermal spectra was performed using a modified and extended Jackson-Amer model. Specific light sources are chosen depending on the application. Figure 10.49 Tonic water, which contains quinine, is fluorescent when placed under a UV lamp. Figure 10.50 shows an example of phosphorescence. GFP is composed of 238 amino acids (Figure \(\PageIndex{13}\)), and it exhibits a characteristic bright green fluorescence when excited. A laser beam with duration less than 10 ns is shot at the sample, and the light emitted by the sample will decay with time. Common solvents include ethanol for polar samples and EPA (a mixture of diethyl ether, isopentane, and ethanol in a 5:5:2 ratio) for non-polar samples. In the UV-vis spectrum, an absorbance versus wavelength graph results and it measures transitions from the ground state to excited state, while photoluminescence deals with transitions from the excited state to the ground state. As shown in Figure \(\PageIndex{11}\) the intensity of Hg lamps is concentrated in a series of lines, so it is a potentially better excitation light source if matched to certain fluorophorescence. With regard to luminescent semiconductors, when energy of incident photon is equal or beyond the The photoluminescence energy associated with these levels can be used to identify specific defects, and the amount of photoluminescence can be used to determine their concentration. It is a longer-lasting and less common type of luminescence, as it is a spin forbidden process, but it finds applications across numerous different fields. The return to equilibrium, known as recombination, can involve both radiative and nonradiative processes. In addition, emission intensity depends on the molar absorptivity of the photoluminescent species, which is sensitive to the sample matrix. wavelengths while the excitation Changing the speed of the disks rotation allows a decay curve to be created, which tells the user how long phosphorescence lasts. The second type of phosphoroscope, the rotating can phosphoroscope, employs a rotating cylinder with a window to allow passage of light, Figure \(\PageIndex{27}\). The accuracy of a fluorescence method is generally between 15% when spectral and chemical interferences are insignificant. With its help, the autofluorescence in biological system can be removed adequately, and hence improve the detectability over background. Fourier transform photoluminescence microspectroscopy, which is of high sensitivity, provides the potential to identify extremely low concentrations of intentional and unintentional impurities that can strongly affect material quality and device performance. Discriminating samples of living (human) and non-living systems (glasses, metals) multiplicity does not change during an electronic Intensity increases In order to return to the ground state, they must undergo a spin conversion, which is not very probable, especially considering that there are many other means of releasing excess energy. After internal conversion and relaxing to T1, these molecules can emit phosphorescence and return to ground states. When an analyte absorbs an ultraviolet or visible photon, one of its valence electrons moves from the ground state to an excited state with a conservation of the electrons spin (Figure 10.47b). Interpretation of photoluminescence spectrums is relatively simple. Therefore, we need to apply some mathematic and physical approaches for correction. An improvement in p is realized by decreasing the efficiency of external conversion. \[ PSF(r,z) \ =\ I_{0} e^{-2r^{2}}/\omega^{2}_{xy}e^{-2z^{2}/\omega^{2}_{z}} \label{1} \]. This approach is particularly useful for the analysis of thin layer chromatography plates. When combined with analysis models, FCS can be used to find diffusion coefficients, hydrodynamic radii, average concentrations, kinetic chemical reaction rates, and single-triplet state dynamics. Light is directed onto a sample, where it is absorbed and imparts excess energy into the material in a process called photo-excitation. Photoluminescence spectroscopy is a widely used technique for characterisation of the optical and electronic properties of semiconductors and molecules. State formation refers to the transition between a singlet and a triplet state while photo-bleaching is when a fluorophore is photo-chemically altered such that it permanently looses its ability to fluoresce. For higher concentrations of analyte the calibration curve becomes nonlinear because the assumptions leading to equation 10.28 and equation 10.29 no longer apply. From the photoluminescence spectra of hexaphenylsilole (HPS, Figure \(\PageIndex{4}\)) show in Figure \(\PageIndex{5}\), it can be seen that as the water (bad solvent) fraction increases, the emission intensity of HPS increases. Figure 10.49 shows the fluorescence of quinine under a UV lamp. Because phosphorescence is unlikely and produces relatively weak emissions, samples using molecular phosphorescence spectroscopy must be very carefully prepared in order to maximize the observed phosphorescence. A classic Jablonski diagram is shown in Figure \(\PageIndex{10}\), where Sn represents the nth electronic states. The quantity of PL emitted from a material is directly related to the relative amount of radiative and nonradiative recombination rates. When the light source is steady, a phosphoroscope, or an attachment to a fluorescence spectrometer, is used. See Figure 3.5 to review the meaning of macro and meso for describing samples, and the meaning of major, minor, and ultratrace for describing analytes. A schematic of an emiision experiment is give in Figure \(\PageIndex{3}\). Unlike fluorescence, a phosphorescent material does not immediately re-emit the radiation it absorbs. From Beers law we know that, \[\dfrac{P_\ce{T}}{P_0} = 10^{bC}\tag{10.26}\], where C is the concentration of the fluorescing species. Accessibility StatementFor more information contact us atinfo@libretexts.org. The expression is valid if the average number of particles, N, is low and if dark states can be ignored. When a monochromator is used to select the excitation and emission wavelengths, the instrument is called a spectrofluorimeter. Fluorimeters are relatively inexpensive, ranging from several hundred to several thousand dollars, and often are satisfactory for quantitative work. Forensic science https://www.alibaba.com/showroom/spectrophotometer-price.html, ADVANTAGES https://www.youtube.com/watch?v=Q6owIVKXvAA, $800-9220 Brownian motion is the random motion of particles suspended in a fluid that results from collisions with other molecules or atoms in the fluid. Photoluminescence is when light energy, or photons, stimulate the emission of a photon. Advantages FCS is also a common technique in photo-physics, as it can be used to study triplet state formation and photo-bleaching. Schematic for excitation and relaxation processes of photoluminescence, (taken from Wikipedia on Photoluminescence). Here, FCS is used to analyze a very small space containing a small number of molecules and the motion of the fluorescence particles is observed. Example of For example, DNA is an example of a biomolecule without fluorescence. light is almost of wavelength higher than that of the absorbed light. Luminescence: radiation produced by a chemical reaction or internal electronic process, possibly following absorption. Given that quinine has a stronger absorbance at 250 nm, explain why its fluorescent emission intensity is greater when using 350 nm as the excitation wavelength. Power Meter In An emission spectrum is the wavelength distribution of an emission measured at a single constant excitation wavelength. Transition This means that it is necessary to use and study fluorophores in dilute solutions or as isolated molecules. http://archive.cnx.org/contents/81bb0311-98ee-4cfc-b3c8-0eab6aeace37@2/photoluminescence-spectroscopy-and-its-applications, APPLICATION OF PL MATERIALS By dye labeling a particular molecule in a system, FCS can be used to determine the kinetics of binding and unbinding (particularly useful in the study of assays). These ions produced by collision between Xe and electrons. With respect to confocal microscopy, the PSF is approximated well by a Gaussian, \ref{1}, where I0 is the peak intensity, r and z are radial and axial position, and wxy and wzare the radial and axial radii (with wz > wxy).
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