Evaluation of blurring and noise of a medical image using a digital phantom

Blurring and noise are an essential characteristic of a medical image on the imaging system. This study shows the characteristics of blurring and noise of a medical image using a digital phantom. A square-shaped digital phantom was produced with pixels that consist of black and white. The line profile was selected on a binary digital image. An image with noise added was generated and a corresponding line profile was also drawn. The degree of noise was increased using the gaussian noise value. The blurring images obtained by applying gaussian blur to a digital phantom was produced similarities to real images. Also, the degree of blurring was increased using the gaussian blur value. As noise increased, the standard deviation of pixels inside and background the object also increased. However, the boundary of the object was retained. As image blurring increased, the boundary of the object was not clearly distinguished. However, the standard deviation of pixels inside and background the object was retained. When extreme noise and blurring are increased, the resulting images are different. For adding noise, the shape is visually maintained. However, the blurred image does not maintain a square shape. Therefore, it is shown that blurring due to movement of object cannot maintain original form. In the image processing method, the reduction of noise is achieved through blur processing. The noise was reduced through blur processing in the image with noise. The degree of noise decreased, but the ambiguity of the boundary increased.

Accreting protoplanets: Spectral signatures and magnitude of gas and dust extinction at H α

Context. Accreting planetary-mass objects have been detected at H α, but targeted searches have mainly resulted in non-detections. Accretion tracers in the planetary-mass regime could originate from the shock itself, making them particularly susceptible to extinction by the accreting material. High-resolution (R > 50 000) spectrographs operating at H α should soon enable one to study how the incoming material shapes the line profile. Aims. We calculate how much the gas and dust accreting onto a planet reduce the H α flux from the shock at the planetary surface and how they affect the line shape. We also study the absorption-modified relationship between the H α luminosity and accretion rate. Methods. We computed the high-resolution radiative transfer of the H α line using a one-dimensional velocity–density–temperature structure for the inflowing matter in three representative accretion geometries: spherical symmetry, polar inflow, and magnetospheric accretion. For each, we explored the wide relevant ranges of the accretion rate and planet mass. We used detailed gas opacities and carefully estimated possible dust opacities. Results. At accretion rates of Ṁ ≲ 3 × 10−6 MJ yr−1, gas extinction is negligible for spherical or polar inflow and at most AH α ≲ 0.5 mag for magnetospheric accretion. Up to Ṁ ≈ 3 × 10−4 MJ yr−1, the gas contributes AH α ≲ 4 mag. This contribution decreases with mass. We estimate realistic dust opacities at H α to be κ ~ 0.01–10 cm2 g−1, which is 10–104 times lower than in the interstellar medium. Extinction flattens the LH α –Ṁ relationship, which becomes non-monotonic with a maximum luminosity LH α ~ 10−4 L⊙ towards Ṁ ≈ 10−4 MJ yr−1 for a planet mass ~10 MJ. In magnetospheric accretion, the gas can introduce features in the line profile, while the velocity gradient smears them out in other geometries. Conclusions. For a wide part of parameter space, extinction by the accreting matter should be negligible, simplifying the interpretation of observations, especially for planets in gaps. At high Ṁ, strong absorption reduces the H α flux, and some measurements can be interpreted as two Ṁ values. Highly resolved line profiles (R ~ 105) can provide (complex) constraints on the thermal and dynamical structure of the accretion flow.

Spontaneous emission of radiation

“Spontaneous emission of radiation” calculates the rate of spontaneous electric-dipole emission of a photon by an excited atom or molecule. The calculation proceeds by using basic quantum mechanics (i.e. not using the short cuts of Chapter 19); it uses quantum electrodynamics but is not, on that account, particularly difficult. A 2p–1s transition in hydrogen is used as exemplar; the radiation is elliptically polarized. The spectral line profile (lineshape function) is approximately Lorentzian, but has a high-frequency cut-off, needed to prevent the power radiated from diverging. A radiation-induced frequency shift is negligible. The width of the line profile agrees with the Einstein A-coefficient. A high-frequency cut-off is shown to apply similarly in the derivation of Golden Rule Number Two.

The Einstein A and B coefficients

The Einstein A and B coefficients for atom–photon reactions are defined: they describe absorption, stimulated emission, and spontaneous emission. We calculate B and consequently find A by the Einstein trick. The procedure is validated by application of detailed balance. Separating out frequencies permits introduction of the spectral lineshape function (normalized line profile). A reformulation describes transitions involving single atomic states and single field modes. This points to a link with quantum electrodynamics.

Methods for Line Shapes in Plasmas in the Presence of External Electric Fields

Line broadening is usually dominated by interactions of an atomic system with a stochastic, random medium. When, in addition to the random medium, a non-random field (such as a laser) is applied, the line profile may be modified in significant ways. The present work discusses these modifications and the methods to deal with them.