Photon

2PLSM makes use of the ability of fluorophores to absorb two photons of infrared light in a single quantum event to generate a phenomenon known as "localization of excitation."

From: Axons and Brain Architecture, 2016

Related terms:

Attenuation

Computer Assisted Tomography

Proton

Fluorescence

X Ray

Positron Emission Tomography

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Electroencephalography and neuroimaging

Pádraig Wright, ... James V. Lucey, in Core Psychiatry (Third Edition), 2012

Single photon emission tomography (SPET)

SPET refers to a computerized emission tomographic system that depends on isotopes that emit single photons (as distinct from positrons in PET). Single photons are detected singly rather than in coincident pairs (as in PET). Collimation – the trapping of emitted photons and their direction towards the detector – is required because single photons are scattered randomly, and this means that most photons are absorbed by collimators and thus go undetected. Thus only a fraction of emitted photons are counted by SPET detector systems and SPET resolution is achieved at the expense of SPET sensitivity. The sensitivity of SPET is the degree to which the system responds to an incoming signal measured as counts per second (CPS) per slice (megaBequerel per litre or MBq/L). The most frequently used detector systems in clinical practice are rotating γ cameras.

Once acquired, SPET data are organized as slices, and reconstructed separately from projections spaced over a 360° arc of rotation about the subject. The SPET detector system behind the collimator is made of sodium iodide crystals with photomultiplier tubes (PMTs) and SPET detector systems may have one large detector covered with many PMTs, or multiple detectors capable of higher count-rate detection and suitable for dynamic studies. Brain-dedicated SPET detector systems view the head from several angles simultaneously with separate scintillation detectors, while converging collimators increase the crystal surface area utilized for a given slice and thus maximize sensitivity. Reconstruction in transverse, coronal and sagittal planes is possible (Fig. 35.5). SPET images are collected over a much longer period of time and depend on many fewer photons than standard CT. Thus SPET images have more noise and less resolution than CT images. As with PET, ROI data analysis is still commonly used in SPET. However, SPM (see above) has recently been adapted for SPET. Ideal anatomical localization with SPET would require MRI co-registration as with PET, but in contrast to PET, this is difficult to achieve with SPET.

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Basics of Radiation Therapy

Elaine M. Zeman, ... Joel E. Tepper, in Abeloff's Clinical Oncology (Fifth Edition), 2014

Compton Scattering

When photon energy is significantly higher than the binding energy of an electron, the photon can scatter from the electron without being absorbed, as illustrated in Figure 27-1. The result of this interaction is a photon with reduced energy and new direction and a recoil electron with some fraction of the initial photon energy. The energy of the scattered electron varies with the scattering direction. An electron scattered in the direction of the incident photon claims most of the initial photon energy, whereas electrons scattered at greater angles have successively less energy. Compton scattering is only weakly dependent on Z and is the dominant photon interaction in tissue between 30 keV and 30 MeV.

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Brain Imaging in Traumatic Brain Injury

Timothy I. Alves, in Handbook of Neuroemergency Clinical Trials (Second Edition), 2018

Single-Photon Emission Computed Tomography

SPECT is a nuclear medicine study that uses a radioactive tracer to measure CBF to brain tissue. Theoretically, CT and MR perfusion findings in TBI should have analogous findings on SPECT. SPECT may provide additional prognostic information when compared to CT and conventional MRI.6,32 Worse prognosis is seen with multiple abnormalities, larger defects, and defects that involve the basal ganglia, temporal lobes, parietal lobes, and brain stem.7 Though promising in its ability to provide independent prognostic information, SPECT is still not in widespread clinical use in the evaluation of TBI.

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Applications of Stereotactic Radiosurgery in Neuro-Oncology

Kunal S. Patel, ... Clark C. Chen, in Handbook of Neuro-Oncology Neuroimaging (Second Edition), 2016

Photon and Proton Radiosurgery

Both photons and protons can be used to transfer energy in radiosurgery. Photons are discrete aliquots of energy produced in gamma- or X-irradiation. Whereas both gamma- and X-rays consist of photons, their photons are produced in different ways. Gamma-rays, used in Gamma Knife radiosurgery, use photons created by radioactive decay, whereas X-rays, used in linear accelerator (LINAC) radiosurgery, use photons created by LINACs. Because both Gamma Knife and LINAC radiosurgery use photon-based IR, their clinical outcomes are similar.30

Protons are created by removing an electron from an atom and accelerating the remaining proton in the magnetic field of a cyclotron or a synchrocyclotron.31 Relative to photon radiosurgery, proton radiosurgery is new. Access to proton radiosurgery remains limited, although the number of centers is rapidly growing. As of this writing, there are 49 operating proton radiotherapy centers worldwide with 30 more planned. As for the older, photon-based radiosurgery platforms, there are hundreds of Gamma Knife and LINAC radiosurgery centers.32

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Emerging Applications of Molecular Imaging to Oncology

Sudeep Das, ... Jan Grimm, in Advances in Cancer Research, 2014

2.6 CL in tissue

Photons generated by CL in vivo travel through tissue before being detected and may be absorbed or scattered on their way. Absorption of photons in tissue is dependent on the wavelength. Hemoglobin absorbs photons strongly in the blue–green region while photons in the near infrared are least absorbed (Weissleder & Ntziachristos, 2003). Scattering occurs when photons travel through areas with different refractive indices. For in vivo imaging using an optical source at a given depth under the tissue surface, a diffusion model of photons is required to quantify the number of photons with high spatial resolution for the point source. As shown by Rice et al. for photons traveling through a medium the photon fluence decreases exponentially with an increase in distance from the point source. Longer wavelengths were less attenuated than shorter ones. The attenuation per unit source depth was highest for shorter wavelengths (Rice, Cable, & Nelson, 2001), which unfortunately includes most of the CL photons. Image resolution was found to dissipate faster for longer wavelengths than shorter ones with increasing source depth. Hence, there is a tradeoff between sensitivity and resolution when varying the wavelength or the source depth (Rice et al., 2001). While the CL is mostly in the blue part of the spectrum, light exiting the tissue is mostly in the penetrating and less absorbed but also less intense part of the Cerenkov spectrum (Spinelli & Boschi, 2012; Spinelli et al., 2010). Using various filter sets or ratiometric imaging is currently explored to utilize the spectral characteristics of CL.

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Attenuation Correction and Scatter Correction of Myocardial Perfusion SPECT Images

James A. Case, in Clinical Nuclear Cardiology (Fourth Edition), 2010

SCIENTIFIC FOUNDATION OF ATTENUATION: COMPTON SCATTERING AND THE PHOTOELECTRIC EFFECT (See Chapter 6)

Photon attenuation is a natural process of electromagnetic radiation with matter. For optical light, this process is easily recognized as the natural opacity of solid objects. Some materials—colored glass, polarizing sunglasses, and so forth—are translucent, allowing some of the photon beam to pass through the object. Logically, the thicker the translucent object, the fewer photons can survive the trip through the material.

This process is played out in a similar way in the high-energy regimen, albeit with different physical processes in play. Nuclear cardiology (and x-ray imaging as well) exists because of a very peculiar fact of nature: At these energies, the seemingly solid object of the human body is not nearly as solid as it appears. To understand this, we have to introduce an interesting concept, the wave-particle duality of photons.1 At higher and higher energies, photons act as if they have smaller and smaller sizes. In the gamma ray and x-ray ranges, photons could pass through a solid object with little effort. To a high-energy gamma ray, the body looks less like a solid object and more like a cloud of electrons.1

To be precise, attenuation is a misnomer. Most of what is referred to as "attenuation" in nuclear cardiology is in reality photon scatter. The dominant process for "attenuating" photon signal in the energy range used in nuclear cardiology is known as Compton scattering. This process, discovered by Arthur H. Compton in 1923 (resulting in Compton and his graduate student being awarded the Nobel Prize in physics26), is the quantum scatter of light off of matter and the transfer of significant amounts of energy from the photon to the electron.

The photon in a Compton scattering event can be thought of as a billiard ball striking the electron. The electron then absorbs some of the energy from the photon, lowering the energy of the photon (Fig. 7-4). The key parameters of a Compton scattering event are the incident energy of the photon (E0) and the scattering angle of the photon relative to its incident and (θ). The higher the incident energy, the more relative energy can be delivered to the electron. (Imagine a compact car–against-truck head-on collision versus a truck-against-truck collision: The second truck will fare worse in the latter scenario.) Furthermore, the larger the scattering angle, the more energy that can be delivered to the electron. Compton demonstrated that the exact energy of the scattered photon can be calculated from the following formula:

E=E01+E0mec2(1−cosθ)

This is very important: Compton scattering does not destroy the incident photon. Each "attenuation" event is truly a scattering event. In other words, as we remove "good photons" from our signal, we add "bad photons" to the signal.

In the energy regimen of 99mTc (140 keV), Compton scattering dominates all scattering processes in human tissue. For lower-energy photons (201Tl, ~72 keV), the photoelectric effect also plays a role. In photoelectric-effect absorption, the photon interacts with the atomic structure of the material. In these interactions, a significant fraction of the energy of the incident photons is used in ionizing the atom. For atoms such as oxygen and hydrogen, the k-shell binding energies are very low relative to the energies of the photons used in nuclear cardiology. Because of the energy difference between the binding energy and the incident photon, the likelihood of photoelectric effect ionization is low.

Example problem 1:

A 140-keV photon is completely backscattered by an electron. What is the resulting energy of the scattered photon?

Answer:

Using the Compton formula:

E=E01+E0mec2(1−cosθ)

where E0 is the energy of the incident photon, mec2 is the resting energy of an electron (511 keV), and θ is the angle of the scattered photon relative to the incident photon. For a backscattered photon: θ = 180 degrees. Solving the Compton equation:

E=140keV1+140keV511keV(1−(−1))=140keV1+2*140keV511keV≈90keV

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Optical Molecular Imaging

M.R. Longmire, ... H. Kobayashi, in Comprehensive Biomedical Physics, 2014

4.05.3.3 Photochemical Aspects of Probe Activation: Photon-Induced Electron Transfer

PeT is a widely accepted mechanism for 'activating' fluorescence quenching, whereby electron transfer from the PeT donor to the excited fluorophore quenches the fluorescence signal (Figure 2(c)). When the PeT donor is cleaved from the fluorophore or inactivated by changing HOMO or LUMO energy status, full activation of fluorescent signal is achieved (Matsumoto et al., 2007). This switching can operate within a single small fluorophore by utilizing environmental queues including pH (proton density) oxidation by specific reactive oxygen species, specific metals, or enzymative cleavage to cleave the PeT donor (Gabe et al., 2006; Hanaoka et al., 2010; Mineno et al., 2006; Ogawa et al., 2010; Sunahara et al., 2007; Ueno et al., 2004). Therefore, activatable fluorophores based on the PeT mechanism can be conjugated with almost any target-specific macromolecular probe including monoclonal antibodies and receptor ligands.

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Mesoporous Silica-based Nanomaterials and Biomedical Applications, Part A

Jonas G. Croissant, Jean-Olivier Durand, in The Enzymes, 2018

1.2 Benefits of Two-Photon Absorption

Two-photon absorption is a rare phenomenon of nonlinear optics in which a molecule absorbs two photons simultaneously. In a two-photon absorption (TPA) process, two photons of identical or different frequencies are absorbed to excite a molecule from one state (typically the ground state) to a higher energy electronic state, and the energetic transition equals the sum of the energy of the two photons. Fig. 2 depicts the Jablonski diagrams of the one-photon and two-photon absorption processes in the case of TPA with two photons of equal energies in the case of TPA [50]. TPA differs from linear absorptions since its effectiveness varies with the square of the light intensity, whereas one-photon absorption varies linearly with the light intensity.

Fig. 2. Jablonski diagram of one (A) and two-photon excitations (B). Fluorescent absorption and emission transitions between the ground and excited states are depicted by vertical arrows.

The TPA phenomenon was first predicted by Maria Goeppert-Mayer in 1931 in her doctoral dissertation [1]. It took the invention of the laser, 30 years later, for the experimental verification of the TPA using a europium-doped crystal [51,52]. Since the probability of the simultaneous absorption of two photons is extremely low (thus the absence of commercially available and effective absorbers), enhancing the TPA is paramount. TPE enhancement is obtained using high-power continuous wave lasers or short-pulse of femtosecond lasers [53–56]. In addition, confocal two-photon microscopy densifies photons in space and in time which further increases the likelihood of a TPA event.

The benefits of two-photon-actuated medical applications of nanotechnology are many. Considering the case of cancer therapy [1], for instance, TPA enables a three-dimensional resolution of the therapeutic effect (down to a micron cube) along with the time resolution associated with the duration of the irradiation. The tumor could, therefore, be screened by the laser beam with the precision toward a single cell which is especially important for many cancers such as brain and eye cancers. The non-fulfillment of these criteria seriously diminished the effectiveness of the therapy and produces unpredictable and unacceptable side effects on patients. Fig. 3 illustrates the low scattering and 3-D resolution of two-photon versus on-photon absorptions. In summary, two-photon-excited nanomedicine in the NIR is particularly relevant for cancer therapy and imaging [23,57–65]. Pathologies involving short laser penetrations such as skin and retinoblastoma cancers could greatly benefit from efficient medical nanodevices using TPA in the NIR. Increasing the laser depth penetration threshold, surgery, and the well-developed endoscopy technologies could be harnessed.

Fig. 3. Comparison of the one-photon and two-photon absorptions of fluorene 3 dyes upon pulsed laser excitations (200 fs) at 380 nm (left) and 760 nm (right).

Adapted photograph, courtesy of the group of Prof. K. D. Belfield.

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Fluorescence-Based Biosensors

François Sipieter, ... Laurent Héliot, in Progress in Molecular Biology and Translational Science, 2013

4.1.4 Time domain: TCSPC

Most TCSPC systems are implemented on a confocal microscope equipped with

•

a pulsed laser source. The source must produce short laser pulses (from several hundred femtoseconds to picoseconds' width) with a frequency usually ranging from 10 to 80 MHz. It is interesting to note that the Ti:Sa laser matches these specifications, which can be of great help in deep and noninvasive biosensor imaging;

•

detectors with a fast instrumental response. Optimal instrumental response function can be obtained using a multichannel plate or the latest generation of avalanche photodiodes (< 50 ps full-width at half-maximum), but they are extremely fragile and require careful handling. TCSPC manufacturers therefore provide more robust detectors, that is, optimized photomultiplier tubes, with an IRF of around 250 ps adapted for TCSPC experiments, which, however, necessitates particular attention during photon decay curves analysis;

•

a photon counting card. All the systems rely on the same principle, which is based on a time amplitude converter. It consists in a linear voltage ramp started by the arrival of a photon and stopped by the next laser pulse. The output voltage will thus be proportional to the photon arrival time. However, the ramp is triggered only by a photon arrival followed by a laser pulse, which means that if two photons are acquired between two laser pulses, only the first photon will be measured. This is the "pulse pile-up" effect (Fig. 5.14A). To avoid this statistic selection of fastest photons, one has to limit the acquisition frequency to one-hundredth of the excitation frequency (giving rise to an error every 10,000 photons), which explains the longer acquisition time of this technique.

Figure 5.14. (A) Principle of the time amplitude conversion. On the left, a fast photon is measured and starts the linear tension ramp resulting on a large ΔU corresponding to the difference in time between a photon emission and the following laser pulse. While the excitation is at constant frequency, the measured ΔU allows the retrieval of the photon emission time. The same explanation is also valid for a slow photon (middle scheme). However, if two photons are emitted between two laser pulses, only the first one is measured. This effect, called "pulse pile-up," induces an artifactual decrease in the measured fluorescence lifetime. (B) Scheme of a typical TCSPC acquisition setup with a laser source allowing two-photon excitation. Pictures on the left show the injection of the infrared laser in a confocal scan head (upper panel) and the detection module adapted on the descanned position of the confocal microscope.

An example of such a setup23 is presented in Fig. 5.14B.

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Photometry

Herbert Blitzer, ... Jeffrey Huang, in Understanding Forensic Digital Imaging, 2008

THE SHOWER ANALOGY

Image that you have a shower head that sticks out from the ceiling and spurts out water in a wide pattern, as shown in the diagram in Figure 4.1. We will assume that there are a very large number of holes in the shower head to allow for very many streams of water to emerge. We will also assume that almost immediately after emerging, the water in the streams breaks up into droplets. The shower head stands for the light source in our analogy. The droplets of water represent photons. The rate at which droplets are emitted is analogous to candela in a light source.

FIGURE 4.1. The Shower Head Analogy. The shower head spews out diverging water streams that change into drops. The drops are meant to be analogous to photons. The can at the bottom is meant to be analogous to the camera or its sensor.

The streams of droplets diverge from one another as they extend away from the shower head. Once they emerge, they continue on their paths. In the case of photons, they continue to travel in straight lines until something like a lens or a mirror causes them to bend. Unfortunately the droplets from the shower are under the influence of gravity and their paths do not stay in straight lines. However they do continue to diverge. The envelope of streams of droplets is analogous to the conveyance of light from the source to the sensor. The number of droplets passing through a unit of area on the way down from the source is analogous to lumens.

On the floor of the shower there are a number of cans with different diameters placed near each other in the center of the water pattern. Each can has a lid that we can place over its open top to block droplets from falling into the can. The can is analogous to our sensor.

Considering the shower head, it can be characterized by the number of drops coming out per second and by the number of droplets coming out per second per unit area on its surface. The same concepts apply to a light source. It can be characterized by the total number of photons emerging per second, and the number emerging per second per unit area. In the following tabulation are photometric units of measure that that describe a light source. The first, the candela (abbreviated cd) measures luminous intensity and indicates the total number of photons per second emerging from the source. The second measures luminance and is given in cd per square meter on the surface of the source.

In the shower head analogy, we can increase the intensity by turning up the faucet. This will produce more droplets per second and more per unit area. If some of the holes in the shower head happen to be partially blocked, those areas will have fewer droplets per second per unit area, analogous to reduced luminous intensity.

TermDescriptionMeasurementPhoton BasisLuminous IntensityAn indication of the brightness of a light sourcecandela (cd)Total number of photons per unit time from a light sourceLuminanceThe brightness of a surface at a pointcandela meter−2 (cdm−2)Photons per unit time per unit of area on the surface of a source

Moving on from the source there is a basic measure of the light moving away from the source through space. This unit of measure is the lumen, which is a measure of luminous flux. There are two basic elements to this measure. The first is the amount of light and the second is the measure of space through which the light is flowing. The unit of light is the candela, defined earlier as the total number of photons per second emerging from a source. The unit of space is the sterradian. It is easier to start in two dimensions. Consider a circle with a point in the center. Draw a line segment from the center to the circle's circumference. That line is, by definition, r units long, where r is the radius of the circle. Now draw another line segment such that it touches the circumference at a distance along the circumference that is r units from the first line. The angle formed by the two line segments is a radian. Radians can be converted to degrees by noting that the circumference is equal to 2 * ϕ * r, and since the amount of circumference covered by a single radian is r, there are 2 * ϕ radians in the total 360 degrees of a circle.

A radian is a plane angle. Its three-dimensional counterpart is a sterradian. To get this, take a sphere with a point at the center and draw a line all the way around—like the equator goes around the earth. Now pick a point on this line and draw another circle that crosses the first at a right angle—just as the Greenwich Mean Time meridian crosses the equator. There is now a sphere with two great circles drawn on its surface. For each of the circles, draw another radius line one radian away from one of the points where the two circles cross. Repeat the process again and a fourth point will be located on the surface of the sphere. Connect all the lines on the surface and a closed figure will appear. It is something like a square in that all its sides are the same length and it has four corners that are all right angles. The difference is that the sides are not straight lines, but are arcs on circles. The four radial lines that go from the center to the four corners comprise a solid angle, and this particular solid angle is one sterradian.

If we consider our light source to be a point source (very, very small compared to the distance from it), and if we consider the source to radiate uniformly in all directions (that is, the luminance is constant in all locations), then the light will uniformly fill each sterradian of light with a certain number of photons per second. The measure that results is called the lumen and it is a measure of luminous flux. If the source does not radiate equally in all directions, the luminous flux will be different in different directions. In the shower analogy, it describes the number of drops per second per unit area where the unit of area increases as the distance below the shower head increases. Projectors are often rated in lumens, the number of photons per second per screen size, where the screen size increases as the distance from the projector is increased. Note that the number of photons per unit area on the screen will decrease, since the same number of photons must cover a larger area.

TermDescriptionMeasurementPhoton BasisLuminous fluxThe amount of light emitted into spaceLumen (Im) (cd sterradian−1)Photons per unit time emitted into a solid angle of space from a source

So far the measures of the source as well as the space between the source and the surface have been described. What remains is to measure the light falling on a surface. To do this we will refer to the illuminance, which is measured in lux. In this case what is being measured is essentially the number of photons per second per unit of area on the indicated surface, or in the analogy, the number of droplets falling on the tops of the cans per unit area per second. It indicates how bright the surface will appear.

TermDescriptionMeasurementPhoton BasisIlluminanceAmount of light falling Per unit areaLux (lx)Photons per unit time per square meter on a receiving surface

One key topic remains: exposure. In earlier chapters, sensitometric curves were constructed where the input was log exposure. Exposure is lux times seconds, or lux-seconds.

TermDescriptionMeasurementPhoton BasisExposureThe amount of light reaching a sensorLux seconds (lx seconds)Photons per unit area on a receiving surface

Getting back to the shower, the exposure is the total amount of water that accumulates in the can. If the can is placed on the floor of the shower, then the droplets will have separated from each other quite a bit. Thus the number falling into our can (which has a fixed opening and therefore a fixed open area) per unit of time will be considerably lower than if we held up the same can waist high, or close to the shower head. If we covered the can and turned on the shower no water would collect. Then if we remove the cover for a certain number of seconds, we will collect a certain number of liters of water. If the lid were kept off longer, more liters would be collected. If the can is moved closer to the shower head, and the short time of lid removal was repeated, we would get more liters of water than if the can were on the floor.

The point is that the exposure is analogous to the total amount of liters collected, which is the sum of the droplets captured. If a can with a bigger diameter is used, it will collect more liters per second and thus is more sensitive to droplets per second per unit area since this value is actual area of the can multiplied by the time the can is open. In silver halide photography the way to make a more sensitive film is to make the silver halide crystals larger. In digital cameras the way to increase the sensitivity is to make the individual pixels larger. The increase in sensitivity is directly proportional to the increase in area, which is the square of the linear dimension.

The system of units is complex and generally only people who work with them regularly can keep it all straight. So there are a few simple concepts to keep in mind. First of all, if the source gets brighter, everything else gets brighter as well, and does so in direct proportion. Second, all the units are linear with respect to this basic brightness, but vision and cameras are responsive to equal proportions of increase, which is a logarithmic scale, and not a linear one. Third, you might want to remember where to look up the definitions of the units since various meters and product descriptions frequently refer to them.

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Terms and conditions

Photon

Photons are generated by an atmospheric pressure helium discharge that can be doped with other inert gases to provide a range of photon energies.

From: Encyclopedia of Analytical Science (Second Edition), 2005

Related terms:

Attenuation

Computer Assisted Tomography

Proton

Fluorescence

Infrared Radiation

X Ray

Positron Emission Tomography

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Electroencephalography and neuroimaging

Pádraig Wright, ... James V. Lucey, in Core Psychiatry (Third Edition), 2012

Single photon emission tomography (SPET)

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Basics of Radiation Therapy

Elaine M. Zeman, ... Joel E. Tepper, in Abeloff's Clinical Oncology (Fifth Edition), 2014

Compton Scattering

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Brain Imaging in Traumatic Brain Injury

Timothy I. Alves, in Handbook of Neuroemergency Clinical Trials (Second Edition), 2018

Single-Photon Emission Computed Tomography

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Applications of Stereotactic Radiosurgery in Neuro-Oncology

Kunal S. Patel, ... Clark C. Chen, in Handbook of Neuro-Oncology Neuroimaging (Second Edition), 2016

Photon and Proton Radiosurgery

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Emerging Applications of Molecular Imaging to Oncology

Sudeep Das, ... Jan Grimm, in Advances in Cancer Research, 2014

2.6 CL in tissue

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Attenuation Correction and Scatter Correction of Myocardial Perfusion SPECT Images

James A. Case, in Clinical Nuclear Cardiology (Fourth Edition), 2010

SCIENTIFIC FOUNDATION OF ATTENUATION: COMPTON SCATTERING AND THE PHOTOELECTRIC EFFECT (See Chapter 6)

E=E01+E0mec2(1−cosθ)

Example problem 1:

A 140-keV photon is completely backscattered by an electron. What is the resulting energy of the scattered photon?

Answer:

Using the Compton formula:

E=E01+E0mec2(1−cosθ)

E=140keV1+140keV511keV(1−(−1))=140keV1+2*140keV511keV≈90keV

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Optical Molecular Imaging

M.R. Longmire, ... H. Kobayashi, in Comprehensive Biomedical Physics, 2014

4.05.3.3 Photochemical Aspects of Probe Activation: Photon-Induced Electron Transfer

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Mesoporous Silica-based Nanomaterials and Biomedical Applications, Part A

Jonas G. Croissant, Jean-Olivier Durand, in The Enzymes, 2018

1.2 Benefits of Two-Photon Absorption

Fig. 2. Jablonski diagram of one (A) and two-photon excitations (B). Fluorescent absorption and emission transitions between the ground and excited states are depicted by vertical arrows.

Fig. 3. Comparison of the one-photon and two-photon absorptions of fluorene 3 dyes upon pulsed laser excitations (200 fs) at 380 nm (left) and 760 nm (right).

Adapted photograph, courtesy of the group of Prof. K. D. Belfield.

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Fluorescence-Based Biosensors

François Sipieter, ... Laurent Héliot, in Progress in Molecular Biology and Translational Science, 2013

4.1.4 Time domain: TCSPC

Most TCSPC systems are implemented on a confocal microscope equipped with

•

An example of such a setup23 is presented in Fig. 5.14B.

View chapterPurchase book

Photometry

Herbert Blitzer, ... Jeffrey Huang, in Understanding Forensic Digital Imaging, 2008

THE SHOWER ANALOGY

TermDescriptionMeasurementPhoton BasisLuminous fluxThe amount of light emitted into spaceLumen (Im) (cd sterradian−1)Photons per unit time emitted into a solid angle of space from a source

TermDescriptionMeasurementPhoton BasisIlluminanceAmount of light falling Per unit areaLux (lx)Photons per unit time per square meter on a receiving surface

One key topic remains: exposure. In earlier chapters, sensitometric curves were constructed where the input was log exposure. Exposure is lux times seconds, or lux-seconds.

TermDescriptionMeasurementPhoton BasisExposureThe amount of light reaching a sensorLux seconds (lx seconds)Photons per unit area on a receiving surface

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Terms and conditions

Photons

Photons absorbed in a semiconductor release their energies to electrons in the valence band, causing them to rise to the conduction band.

From: Solar Energy Conversion, 1979

Related terms:

Energy Engineering

Semiconductor

Solar Energy

Solar Cells

Conduction Band

Wavelength

Photon Energy

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From Nuclear Fusion to Sunlight

Alexander P. Kirk, in Solar Photovoltaic Cells, 2015

2.15 Photon flux

Photon flux will become important later in Chapter 3 when calculating photogenerated current density in solar photovoltaic cells. Under a clear sky AM1.5G terrestrial spectrum, there are some 1017 photons irradiating a 1 cm2 Sun-facing surface area every second. Spectral photon flux φ(λ) is calculated from the spectral irradiance Iλ (W m–2 nm–1) through the following relationship:

(2.13)φ(λ)=Iλ/E,

where E = hc/λ and h is Planck's constant. The AM1.5G spectral photon flux is shown in Figure 2.7, and the integrated photon flux is shown in Figure 2.8.

Fig. 2.7. ASTM G173 AM1.5G spectral photon flux (plotted out to the full 4000 nm cutoff).

Fig. 2.8. ASTM G173 AM1.5G integrated photon flux (plotted out to the full 4000 nm cutoff).

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Quantum Computing and Communication

Paul E. Black, ... Carl J. Williams, in Advances in Computers, 2002

6.2.5 Photon

Photons are clearly the best way to transmit information, since they move at the speed of light and do not strongly interact with their environment. This near-perfect characteristic for quantum communication makes photons problematic for quantum computation. In fact, early approaches to using photons for quantum computation suffered from a requirement of exponential numbers of optical elements and resources as one scaled the system. A second problem was that creating conditional logic for two-qubit gates appeared very difficult since two photons do not interact strongly even in highly nonlinear materials. In fact, most nonlinear phenomena involving light fields result only at high intensity.

Recently, new approaches for doing quantum computation with photons that depend on using measurement in a "dual-rail" approach to create entanglement have appeared. This approach removes many of the constraints of early approaches, but provides an alternative approach to creating quantum logic. Experimental efforts using this approach are just beginning. The approach will still have to solve the technically challenging problems caused by high-speed motion of their qubits, a benefit in communication and a possible benefit in computational speed, and by the lack of highly efficient, single-photon detectors essential to the success of this approach.

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Simulation of biomedical signals and images using Monte Carlo methods for training of deep learning networks

Navid Mavaddat, ... Kamal Alameh, in Deep Learning Techniques for Biomedical and Health Informatics, 2020

Free path

The free path (sometimes referred to as the photon mean free path) is the average distance a photon travels in a particular direction before it collides with another particle causing it to change direction. In a vacuum, this distance may be extremely long, but within a turbid material using near infrared (NIR) light, this distance is often less than 100 μm [44].

Modeling individual photons is infeasible, due to the huge number of photons emitted by a typical OCT light source. To address this issue the process can be simplified by considering large groups of photons as "photon packets" with an associated total energy or "weight." For some interactions, there is a probability that individual photons might be absorbed. This interaction that results in photon absorption can be modeled as a proportional loss of packet weight, and simulation can then be continued with the remaining photons. The free path covered by a photon packet between the points of interaction within a medium is determined by the following equation [41]:

(9.3)s=−lnξμa+μs

where

s is the free distance covered by a photon package.

μs is the scattering coefficient.

μa is the absorption coefficient.

ξ is discrete character energy absorption—a random number uniformly distributed between 0 and 1.

As the free path is traversed, photons are absorbed by the material it passes through, and to model this, the change in weight of the photon packet can be calculated by the following equation [43]:

(9.4)ΔW=Wμaμa+μs

where

ΔW is the incremental change in the statistical weight of the photon packet at each point.

W is the statistical weight of the photon packet.

μs is the scattering coefficient.

μa is the absorption coefficient.

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Dosimetry

J.W. PostonSr., in Encyclopedia of Physical Science and Technology (Third Edition), 2003

III.C X and Gamma Radiation

Photons interact with matter through three primary mechanisms: the photoelectric effect, Compton scattering, and pair production. The probability of each of these interactions occurring depends on the energy of the radiation and the material through which it is passing.

The photoelectric effect occurs primarily at low photon energies and in high–atomic-number (Z) materials. This interaction should be considered to occur with the entire atom even though the energy transfer is between the photon and an orbital electron. In this interaction a photon strikes a tightly bound electron and transfers its entire energy to the electron. If this energy is greater than the binding-energy of the electron to the atom, then the electron will be knocked out of the atom. The electron (a photoelectron) may possess kinetic energy as a result of this interaction. This energy is the difference between the initial energy of the photon and the binding energy of the electron.

Photoelectric interactions are most probable with the most tightly bound electrons (K shell), and the loss of an electron from the inner shell(s) leaves a vacancy that must be filled. An electron from a higher orbit will drop into the vacancy, but it in turn leaves another vacancy. There is in effect a cascading of electrons as they drop into lower energy states to fill the existing vacancies. As each electron fills a vacancy, a photon is emitted whose energy is equal to the difference between the initial and final energy levels. These photons are called characteristic X-rays because the energy differences between the electron orbits are unique for an atom and the photons are characteristic of the element from which they originate.

As stated previously, photoelectric interactions are most probable at low photon energies. The interaction is relatively unimportant for photons with energies >1 MeV, except in very heavy elements.

Compton scattering is an interaction that occurs between a photon and an essentially "free" electron. That is, the electron is in one of the outer orbits and its binding energy is significantly less than the energy of the photon. In Compton scattering, the requirements for the conservation of momentum and energy make it impossible for complete transfer of the photon energy to the electron. Basically, the photon has a collision with the electron and transfers only a portion of its energy to the electron. The photon is deflected from its original path (scattered) and has less energy (longer wavelength) than the incident photon. The Compton electron has kinetic energy equivalent to the difference between the initial photon and the Compton-scattered photon.

The probability of Compton scattering decreases with increasing photon energy and with increasing Z of the absorber. This interaction is, therefore, more probable in the middle photon energy range (i.e., 0.1–1 MeV) and with light materials.

The third interaction, pair production, may be considered the opposite of the production of annihilation radiation. In this case, a high-energy photon comes into the near vicinity of the nucleus of an atom and has a coulombic interaction in which the photon disappears and two charged particles are produced in its place. These charged particles, a positron and an electron, share (as kinetic energy) any available energy of the photon over and above the threshold energy for the reaction. The rest-mass energy of each of these charged particles is equivalent to 0.511 MeV and, therefore, pair production is not possible below a "threshold" of 1.022 MeV. Even though the threshold for this reaction is just >1 MeV, pair production does not become important until a photon energy of ∼4 MeV is reached.

When the positron has expended its kinetic energy in the medium, it will annihilate with a free electron, as described previously.

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Rare-Earth Doped Upconversion Nanophosphors☆

F. Wang, X. Liu, in Comprehensive Nanoscience and Nanotechnology (Second Edition), 2011

1.18.2.1.1 Absorption processes

Photon absorption processes in UC that populate emitting states are mainly divided into three broad classes: excited-state absorption (ESA), energy-transfer upconversion (ETU), and photon avalanche (PA). All these processes involve sequential absorption of multiple photons (Fig. 1). Thus, UC processes are different from concerted multiphoton processes where the photon absorptions occur simultaneously.

Fig. 1. Principal upconversion (UC) processes: (a) excited-state absorption, (b) energy-transfer UC, and (c) photon avalanche. The dashed-dotted, dashed, and full arrows represent photon excitation, energy transfer, and emission processes, respectively.

In the case of ESA, excitation takes the form of a successive absorption of pump photons by a single ion. The general energy diagram of the ESA process is shown in Fig. 1(a) for a simple three-level system. If the excitation energy is resonant with the transition from the ground level G to an excited metastable level E1, photon absorption occurs and populates E1 from G in a process known as ground-state absorption (GSA). A second pump photon that promotes the ion from E1 to higher-lying state E2 results in UC emission, corresponding to the E2–G optical transition.

ETU is similar to ESA in that both processes utilize sequential absorption of two photons to populate the metastable level. The main difference between ETU and ESA is that the excitation in ETU is realized through energy transfer between two neighboring ions. In the ETU process, each of two neighboring ions can absorb a pump photon of the same energy, thereby populating the metastable level E1 (Fig. 1(b)). A nonradiative energy-transfer process promotes one of the ions to an upper emitting state E2 while the other ion relaxes back to its ground state G. The dopant concentration that determines the average distance between the neighboring dopant ions has a strong influence on the UC efficiency of an ETU process.

PA-induced UC features an unusual pump mechanism that requires a pump intensity above a certain threshold value. The PA process starts with population of level E1 by nonresonant weak GSA, followed by resonant ESA to populate an upper visible-emitting level E2 (Fig. 1(c)). After the metastable-level population is established, cross-relaxation energy transfer (or ion pair relaxation) occurs between the excited ion and a neighboring ground-state ion, resulting in both ions occupying the intermediate level E1. The two ions readily populate level E2 to further initiate cross-relaxation and exponentially increase level E2 population by ESA, thereby producing strong UC emission as an avalanche process.

The UC efficiency in these three processes varies considerably. ESA is the least efficient UC process [1]. Efficient UC is possible in PA with metastable, intermediate levels that can act as a storage reservoir for pump energy. However, the PA process suffers from a number of drawbacks, including pump-power dependence and slow response to excitation (up to several seconds) due to numerous looping cycles of ESA and cross-relaxation processes. In contrast, ETU is instant and pump-power-independent, and thus has been widely used to offer highly efficient UC (~2 orders of magnitude higher than ESA) [1] over the past decade.

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Optical and Electro-Optic Processes

Kwan Chi Kao, in Dielectric Phenomena in Solids, 2004

The Outstanding Differences between Photons and Electrons or Protons

There are several significant differences between photons and electrons or protons.1

•

Photons may be created and annihilated, whereas electrons or protons are conserved.

•

Photons do not interact with each other, and they obey Bose–Einstein statistics; electrons or protons do interact with each other and obey Fermi–Dirac statistics.

•

Photons do not have electrostatic charges, spin moments, or rest mass; these are possessed by electrons or protons.

•

All photons have a common constant velocity c in free space (constant velocity v = c/n in materials), whereas the velocities of electrons or protons are variable, depending on the accelerating voltage.

•

Photons have diffraction wavelength λd equal to their radiation (conversion) wavelength λE, whereas electrons or protons have λd ∞ V−1/2 but λE ∞ V−1, where V is the accelerating voltage.

•

Photons have momentum p and kinetic energy Ek, depending on their frequency, whereas electrons or protons have momentum and kinetic energy, depending on their velocity.

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Radiation Physics

John H. Hubbell, in Encyclopedia of Physical Science and Technology (Third Edition), 2003

II.B Photons

Photons that have energies in the keV and MeV (megavolt) range (x rays and γ rays) have the ability to penetrate matter deeply and, when absorbed, to produce strong effects. X rays are generated when an electron beam strikes matter; an x-ray generator consists of a powerful electron gun and a metal target in which the photons are generated. For x-ray crystallography applications, the photons will be in the energy range from 5 to 30 keV, including line-energies characteristic of the atomic number of the metal in the target, superimposed on a bremsstrahlung continuum spectrum. For imaging and irradiation applications, the energies commonly range up to 3 MeV, mostly in the form of bremsstrahlung. For research applications, electron accelerators such as synchrotrons and linacs (linear accelerators) produce photons up to the GeV (109 electron volts) region, but for imaging and irradiation purposes the energy is usually kept below 5 MeV to avoid producing radioactivities in the sample due to the photonuclear effect which has a resonance peak in the region 5 to 40 MeV.

γ Rays are high-energy monoenergetic photons. The term is used specifically for photons created during the disintegration of atomic nuclei. A well-known example is the pair of photons created in the spontaneous disintegration of the cobalt-60 atomic nucleus. These photons have energies of 1.1732 and 1.3325 MeV, and cobalt-60 (60Co) is frequently used in plaque and other geometrical configurations in irradiation facilities. γ Rays are created by nuclear chain reactions such as those that occur in a nuclear reactor core or a nuclear explosion. The isotopes contained in nuclear fuel represent concentrated sources of γ rays. These can be used for experimental irradiation in spent-fuel ponds. Table I presents data on 60Co and some of the other radioisotopes useful in medical therapy and industrial irradiation applications, also on 90Sr which can be important as an environmental hazard.

TABLE I. Radioisotopes Important in Medical Therapy and Industrial Irradiation Applications, also as Environmental Hazards (90Sr)a

NuclideHalf-life (year)Type of decayPhotonsParticlesEnergy (MeV)Percentage emitted (%)Energy (MeV)Transition probability (%)60Co5.271.17399.860.31899.9β−1.33399.981.4910.1(av 1.25)192Ir0.5260.29629.6(192 d)0.30830.70.31682.70.53042.6β−0.46847.00.67047.20.6048.20.6125.3137Cs0.66285.190Sr + daughter28β−0.54100——90Y0.176β−2.27100——85Kr10.6β−0.150.70.510.7β−0.6799.3——252Cf2.65Spontaneous fission——Neutrons, 2 MeVγs, 5.9–6.1 MeVFission fragments, 80 and 104 MeV

aMain emission energies.

In recent decades, synchrotron radiation has become a major high-flux source of photons for research and analytical applications. This radiation is produced in high-energy accelerators from the bending of electron orbital trajectories in the confining magnetic field, sometimes by magnetic "wigglers and undulators" interposed in the electron path. The photon energies thus produced range from tens of eV from accelerators in the hundreds of MeV range, to above 100 keV for electron accelerators in the multi-GeV range. Another recently developed source of photons in the γ-ray energy range is by inverse Compton scattering. In such devices, intense laser beams in the visible or ultraviolet (eV range) are collided with GeV-range electrons in an accelerator, boosting the eV laser photons up to MeV energies.

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Electromagnetic Radiation

David L. Andrews, in Encyclopedia of Spectroscopy and Spectrometry, 1999

Photon properties

Mass

Photons are elementary particles with zero rest mass – necessarily so, since, from special relativity theory, no particle with a finite mass can move at the speed of light.

Velocity

The speed of light is normally quoted as speed in vacuo, c0, with refractive corrections applied as appropriate; the free propagation of any photon also has a well-defined direction, usually denoted by the unit vector kˆ.

Energy

Photon energy is linked to optical frequency ν through the relation E = hν (where h = 6.6261 × 10−34 J s). Each photon essentially conveys an energy E from one piece of matter to another, for example from a television screen to a human retina.

Frequency

The optical frequency ν expresses the number of wave cycles per unit time. Also commonly used in quantum mechanics is the circular frequency ω = 2πν (radians per unit time), in terms of which the photon energy is E = ℏω where ℏ = h/2π. The lower the optical frequency, the more photons we have for a given amount of energy; and the larger the number of photons, the more their behaviour approaches that of a classical wave (this is one instance of the 'large numbers' hypothesis of quantum mechanics). It is for this reason that electromagnetic radiation becomes increasingly wave-like at low frequencies, and why we tend to think of radiofrequency and microwave radiation primarily in terms of waves rather than particles.

Wavelength

The wavelength λ of the electric and magnetic waves is given by λ = c/ν. In spectroscopy, common reference is made to its inverse, the wavenumber v¯ = 1/λ, usually expressed in cm−1.

Momentum

Each photon carries a linear momentum p, a vector quantity of magnitude h/λ = ℏk pointing in the direction of propagation. It is then convenient to define a wave vector or propagation vector k = kkˆ such that p = ħk. Since the photon momentum is proportional to frequency, photons of high frequency have high momenta and so exhibit the most particle-like behaviour. X-rays and gamma rays, for example, have many clearly ballistic properties not evident in electromagnetic radiation of lower frequencies.

Electromagnetic fields

The electric and magnetic fields, E and B respectively, associated with a photon are vector quantities oriented such that the unit vectors (Ê, Bˆ, kˆ) form a right-handed orthogonal set.

Polarization

For plane-polarized (also called linearly polarized) photons, the plane within which the electric field vector oscillates can sit at any angle to a reference plane containing the wave vector, as shown in Figures 2A and 2B. Other polarization states are also possible: in the right- and left-handed circular polarizations depicted in Figures 2C and 2D, the electric field vector sweeps out a helix about the direction of propagation. Elliptical polarization states are of an intermediate nature, between linear and circular. Together, the wave vector and polarization of a photon determine its mode.

Figure 2. Polarization states: (A) and (B) plane; (C) and (D) circular.

Spin

Many of the key properties of photons as elementary particles relate to the fact that they have an intrinsic spin S = 1, and so are classified as bosons (particles with integer spin as opposed to half-integer spin particles of matter such as electrons). As such, photons collectively display a behaviour properly described by a Bose–Einstein distribution. At simplest, this means that it is possible for their oscillating electromagnetic fields to keep in step as they propagate. Through this, coherent beams of highly monochromatic and unidirectional light can be produced; this is of course the basis for laser action.

Angular momentum

The intrinsic spin of each photon is associated with an angular momentum, a feature that plays an important role in the selection rules for many spectroscopic processes. Circularly polarized photons have the special property of quantum angular momentum: the two circular polarization states, left- and right-handed, respectively carry +1 or −1 unit of angular momentum, ℏ.

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Radiation Effects in Electronic Materials and Devices

Andrew Holmes-Siedle, Victor A.J. van Lint, in Encyclopedia of Physical Science and Technology (Third Edition), 2003

II.B Photons

Photons that have energies in the keV and MeV range (X rays and gamma-rays) have the ability to penetrate matter deeply and, when absorbed, to produce strong effects. X-rays are generated when an electron beam strikes matter; an X-ray generator consists of a powerful electron gun and a metal target in which the photons are generated. Energies from 30 keV to 3 MeV are common. Small fluxes of X-rays are also generated naturally in radioisotope samples by the collision of beta rays within the sample itself or with the capsule in which the sample is contained. In electron-beam devices (cathode-ray tubes and electron accelerators), a hazard to humans may be created by the unintentional generation of X-rays when the beam collides with the wall of the chamber.

Gamma-rays are high-energy, often monoenergetic photons. The term is used specifically for photons created during the disintegration of atomic nuclei. A well-known example is the pair of photons created in the spontaneous disintegration of the cobalt-60 atom. These photons have energies of 1.17 and 1.33 MeV. Gamma rays are commonly created during nuclear chain reactions, such as those that occur in a nuclear reactor core or a nuclear explosion. The isotopes contained in nuclear fuels represent concentrated sources of gamma-rays. These can be used for experimental irradiation in spent-fuel ponds. When certain equipment used in reprocessing nuclear fuel is directly exposed to the isotope sample, there is danger that exposed optical and electronic parts may degrade in performance. Thus, the equipment has to be radiation hardened (see later).

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PHOTON PICTURE OF LIGHT

S.J. Bentley, in Encyclopedia of Modern Optics, 2005

Introduction

The photon nature of light is the central topic in the field of quantum optics, which has developed into a leading area of research. The possible technological impacts of this field to many areas, such as imaging, computing, and lithography, have greatly expanded interest into the nature of the photon. A photon description of light goes well beyond the particle nature of light, to include any optical phenomena that cannot be adequately described by classical physical optics. This article will introduce the nature of the photon through a discussion of many such phenomena, covering topics from the beginning of quantum mechanics, including black-body radiation and Compton scattering, to areas of modern interest, such as squeezed light and entangled photons.

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