Planck's Radiation Law Research Articles

About Cosmic Microwave Background Radiation (CMBR)

Because the CMBR follows the PLANCK's radiation law more or less exactly, it should, because of the indistinguishability of individual photons, apply to a whatever black emitter. Therefrom arises the guess, that the existence of an upper cut- off frequency of the vacuum could be the cause for the decrease in the upper frequency range. Since the lower-frequent share of the curve correlates with the frequency response of an oscillating circuit with the Qfactor ½, it is examined, whether it succeeds to approximate the Planck curve by multi-plication of the initial curve with the dynamic, time- dependent frequency response of the above-mentioned model. Reason of the time-dependence is the expansion of the universe. This work is based on a model published in [1]. It is shown, that the PLANCK graph can be approximated by application of the cumulative frequency response given by the model, upon the spectrum of an oscillatory circuit with the Q-factor ½. Furthermore, the progression of frequency, energy and entropy is analysed. The results point out, that origin and progression of the CMBR have elapsed in a totally different manner than generally assumed. Because photons behaved like neutrinos immediately after BB they did not interact with other matter then. Thus, we can exactly calculate back to 8.08·10–106s instead of 379,000 years after BB. Section 6 has been reworked.

Neural Networks Based on Synthesized Training Data for the Automated Detection of Chemical Plumes in Passive Infrared Multispectral Images.

Automated detection of volatile organic compounds in the atmosphere can be achieved by applying pattern recognition analysis to passive infrared (IR) multispectral remote sensing data. However, obtaining analyte-active training data through field experiments is time-consuming and expensive. To address this issue, methodology has been developed for simulating radiance profiles acquired using a multispectral IR line-scanner mounted in a downward-looking position on a fixed-wing aircraft. The simulation strategy used Planck's radiation law and a radiometric model along with the laboratory spectrum of the target compound to compute the upwelling IR background radiance with the presence of the analyte within the instrumental field-of-view. By combining the simulated analyte-active radiances and field-collected analyte-inactive radiances, a synthetic training dataset was constructed. A backpropagation neural network was employed to build classifiers with the synthetic training dataset. Employing methanol as the target compound, the performance of the classifiers was evaluated with field-collected data from airborne surveys at two test fields.

Minimally-intrusive, dual-band, fiber-optic sensing system for high-enthalpy exhaust plumes

<abstract> <p>The propulsion research lab at Utah State University has developed a minimally-intrusive optical sensing system for high-temperature/high-velocity gas-generator exhaust plumes. For this application glass fiber-optic cables, acting as radiation conduits, are inserted through the combustion chamber or nozzle wall and look directly into the flow core. The cable transmits data from the flame zone to externally-mounted spectrometers. In order to capture the full-optical spectrum, a blended dual-spectrum system was employed, with one spectrometer system tuned for best-response across the visible-light and near-infrared spectrum, and one spectrometer tuned for best-response in the near- and mid-infrared spectrum. The dual-band sensors are radiometrically-calibrated and the sensed-spectra are spliced together using an optimal Wiener filtering algorithm to perform the deconvolution. The merged spectrum is subsequently curve-fit to Planck's black-body radiation law, and flame temperature is calculated from associated curve maxima (Wien's law). The presented fiber-optic sensing systems performs a function that is analogous to Raman spectroscopy. The system non-contact, high-temperature measurement, and does not interfere with the heat transfer processes. In this report data collected from a lab-scale (200 N) hybrid rocket system are analyzed using the described method. Optically-sensed flame-temperatures are correlated to analytical predictions, and shown to generally agree within a few degrees. Additionally, local maxima in the optical spectra are shown to correspond to emission frequencies of atomic and molecular oxygen, water vapor, and molecular nitrogen; all species known to exist in the hybrid combustion plume. Presented data demonstrate that selected fiber-optics can survive temperature greater than 3000 ℃, for durations of up to 25 seconds.</p> </abstract>

Illuminating a bacterial adaptation mechanism: Infrared-driven cell division in deep-sea hydrothermal vent environments

<p>Based on Planck's black-body radiation law, deep-sea hydrothermal vent chimneys emit light, predominantly infrared light, which potentially supports bacterial photosynthesis in this ecosystem independently of the solar energy. To investigate the impact of this geothermal light on bacterial growth, we collected samples from the Southwest Indian Ridge and demonstrated that infrared light alone promotes bacterial growth and alters population composition. The mechanism of infrared stimulated growth was analyzed by monitoring cell wall synthesis using the <i>Tepidibacter hydrothermalis</i> strain SWIR-1, which was isolated from cultures enriched through infrared irradiation. The results showed that the elevated hydrostatic pressure inhibited septal peptidoglycan synthesis and cell division, but had less effect on cell elongation, chromosome replication and segregation. The dominant cell shape was filaments with some swelling and inertness in cell wall synthesis depending on the level of pressure applied. Interestingly, irradiation with 880 nm infrared light effectively initiated septal synthesis and alleviated the obstruction. This revelation uncovers a novel adaptation mechanism involving infrared light for bacteria dwelling in deep-sea environments, and sheds light on the potential of infrared-mediated photobiomodulation.</p>

Some Interesting Facts About Planck’s Law of Blackbody Radiation

Introductory textbooks of Modern and Thermal Physics discuss the Planck radiation law as a backbone of the blackbody radiation spectrum. This law is used to explain the intensity of blackbody radiation as a function of either frequency or wavelength at a given temperature. In the introductory coursework, the Planck’s formula is also used to study other blackbody radiation laws such as Stefans–Boltzmann law, Wien’s Displacement law, Rayleigh–Jeans Law and Wien’s Distribution law. In this work, we highlight some interesting facts related to the total energy density, photon number density and average energy of photon of blackbody radiation. The main objective of this work is to focus on the lesser known features associated with physics of blackbody radiation. We believe that these simple analytic calculations may give very useful and interesting information about the Planck radiation law to the undergraduate students.

Data processing for simultaneous inversion of emissivity and temperature using improved CABCSMA and target-to-best DE algorithms in multispectral radiation thermometry (MRT).

In this paper, what we believe to be, a new combined algorithm of artificial bee colony and slime mould algorithm (CABCSMA) and a differential evolution (DE) algorithm using target-to-best variation strategy are proposed to process the data based on Planck's radiation law and the mathematical model of reference temperature. The material model with 6 different emissivity trends is simulated. Simulation results show that the average relative error of CABCSMA algorithm is less than 0.68%, and the average calculation time is 0.44s. The average relative error of DE algorithm is less than 0.43%, and the average calculation time is only 0.06s. The two algorithms were applied to the temperature test of silicon carbide sample, tungsten material and rocket engine nozzle. The experimental results show that the relative error of silicon carbide experimental temperature is less than 0.41% and 0.28%, and the relative error of tungsten material experimental temperature is less than 0.31% and 0.3%. The relative errors of rocket engine nozzle temperature experiments are within 0.68% and 0.52%, respectively. The results show that these two algorithms are expected to be applied in practical measurement scenarios.

Arthur E. Haas, from the Atom to the Cosmos—Struggles for a Scientific Career in the Early 20th Century

Arthur E. Haas, from the Atom to the Cosmos—Struggles for a Scientific Career in the Early 20th Century

Noncommutative Derivation of the Planck's Radiation Law

Noncommutative Derivation of the Planck's Radiation Law

Experimental Determination of Absolute Spectral Radiance and Emissivity of a Photonic Crystal Filament

A recent discovery of super-Planckian radiation in the far-field has attracted a great deal of interest in thermal radiation control using photonic crystals (PC) architecture. The finding is based on a careful comparison of radiation intensity emitted from a PC nano-filament and a blackbody at the same temperature and same wavelength at λ∼1.7 μm. Extending that finding, we determined the absolute spectral radiance of such a PC filament at λ∼1.7 μm at elevated temperature, T = 445–723 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> °</sup> K, and compared its value to that predicted by Planck's blackbody radiation law. Our data confirmed that the PC spectral radiance surpassed that of a blackbody by an order-of-magnitude. We also determined the spectral emissivity of our PC filament and showed that its value far exceeded unity at resonance and fell below unity away from resonance. The observation of non-equality between absorptivity and emissivity suggests that a strong optical non-reciprocity takes place in our PC nano-filament.

Einstein on measurement theory: A heuristic point of view

Einstein did not contribute significantly to the quantum mechanics we are familiar with, but he did contribute to its theoretical foundations. In a seminal theory on black body radiation, he used two physically distinct sets of coordinates, a classical set to describe the continuity of heat energy with Maxwell Boltzmann statistics and an atomic set to describe discrete energy states required by the Planck radiation law. His methods are extended here to reveal that matrix mechanics is an incomplete description of atomic structure. In addition to the discrete energy states of the diagonal matrix elements, classically derived components of kinetic energy are necessary. We conclude that the diagonalized matrix elements and eigenvalues of the Schrödinger equation both describe characteristics of the steady states, but the physical variables they describe are different, because they are measured with respect to different coordinate systems. Einstein’s assumptions lead to a resolution of the measurement problem by introducing statistical laws at the microscopic level.

An optimal derivative-free King's family for multiple zeros and its dynamics

PurposeThe purpose of this article is to develop and analyze a new derivative-free class of higher-order iterative methods for locating multiple roots numerically.Design/methodology/approachThe scheme is generated by using King-type iterative methods. By employing the Traub-Steffensen technique, the proposed class is designed into the derivative-free family.FindingsThe proposed class requires three functional evaluations at each stage of computation to attain fourth-order convergency. Moreover, it can be observed that the theoretical convergency results of family are symmetrical for particular cases of multiplicity of zeros. This further motivates the authors to present the result in general, which confirms the convergency order of the methods. It is also worth mentioning that the authors can obtain already existing methods as particular cases of the family for some suitable choice of free disposable parameters. Finally, the authors include a wide variety of benchmark problems like van der Waals's equation, Planck's radiation law and clustered root problem. The numerical comparisons are included with several existing algorithms to confirm the applicability and effectiveness of the proposed methods.Originality/valueThe numerical results demonstrate that the proposed scheme performs better than the existing methods in terms of CPU timing and absolute residual errors.

High-order nonlinear response correction method for infrared radiation detector

The infrared detector can generate nonlinear response error when the Fourier transform infrared spectrometer is used for implementing the radiometric calibration or observing the high temperature targets. Based on the relationship between the incident radiation intensity and the electron concentration in the optical conduction band, the mechanism of the nonlinear response error caused by the high incident photon flow is analyzed. According to Planck radiation law and interference principle, the effect of nonlinear error on spectrum is studied by simulating blackbody radiation data with nonlinear error. It is found that the nonlinear response with a different order has a different influence region, and the higher-order nonlinear response has a wider influence range and generates a larger nonlinear response error. By the general nonlinear response correction method the nonlinear response coefficient is obtained through constructing the nonlinear response model of the interference data and then the spectral distortion produced by the detector is corrected. According to the convolution iteration method, the polar orbit meteorological satellite CrIS constructs the convolution equation to correct the second-order nonlinear response by taking the low-wave number band of 50－500 cm&lt;sup&gt;–1&lt;/sup&gt; as the characteristic region. The European Meteorological Agency’s Airborne Infrared Interferometer Evaluation System (ARIES) selected two feature areas, 50－500 cm&lt;sup&gt;–1&lt;/sup&gt; and 2000－2500 cm&lt;sup&gt;–1&lt;/sup&gt;, and iteratively corrected the second-order and third-order nonlinear response. The gradient descent method is often used to solve the optimization problems of unconstrained multivariate functions. Based on the gradient descent algorithm, an iterative method suitable for correcting the high-order nonlinear response errors is proposed in this paper. In this method, the information about the iteration point is obtained by constructing the nonlinear response function of the high-order detector and setting the appropriate iteration initialization. According to the initial value of the iteration and the information about the known iteration point, the gradient of the iteration variable is calculated to determine the iteration value of the next unknown variable, thus quickly searching for the global minimum point and determining the nonlinear response coefficient. We use Fourier transform infrared spectrometer to carry out radiometric calibration experiment and compare the effects of three correction methods: convolution, cross iteration and gradient descent method. The results show that the three correction methods can effectively reduce the nonlinear error, and improve the fitting extent by 0.15%, 0.29% and 0.39% respectively. The spectral data corrected by gradient descent method are more accurate.

Photoelectron distribution on sunlit surface of the Moon: A formalism

An analytical formulation describing the characteristic energy distribution of photoelectrons over the sunlit regolith of the Moon has been presented. In deriving the distribution function, Fowler's approach based on fermionic lattice electrons for photoemission has been coupled with observed solar spectra, photoelectric quantum yield, and latitude dependent surface temperature. It is noticed that the dominant contribution in the photoelectron distribution function comes from extreme ultraviolet photons (3 eV–300 eV) of the solar spectra. The analysis also illustrates that the photoelectron distribution for the observed solar spectra is significantly different from the spectrum based on Planck's radiation law. In results, the photoelectron distribution is found to be a significant function of the lunar surface potential—the photoelectron distribution in the steady state considerably differs from that of the uncharged surface. In calculations, the variation in the photoelectron distribution function with the lunar latitude, quantum yield, and work function of the surface material has been parametrically analyzed, and it is found to be sensitive to the constituent parameters.

PLANK'S RADIATION LAW AS A CONSEQUENCE OF NONEQUILIBRIUM THERMODYNAMICS

The conclusion of the Planck radiation law is proposed, which does not require the involvement of non-thermodynamic considerations. The conclusion is based on the concept of the wave nature of the radiation process and the existence of harmonics in oscillators. It is shown that the true radiation quantum is a wave that is discrete both in time and in space, and the Planck constant plays the role of the proportionality coefficient between the fluxes of radiant energy and traveling waves. The de Broglie relation is obtained as a consequence of the identity of the oscillation frequency of the oscillators to the flow of emitted waves. The proposed approach removes a number of contradictions of quantum theory with classical physics.

Planck's generalised radiation law and its implications for cathodoluminescence spectra

Cathodoluminescence (CL) is an important analytical technique for probing the optical properties of materials at high spatial resolution. Interpretation of CL spectra is however complicated by the fact that the spectrum depends on the carrier injection density of the incident electron beam. Here a generalised version of Planck's radiation law is used to uncover the evolution of CL spectra with injection under steady-state conditions. The importance of the quasi-Fermi level is highlighted and it is shown that steady-state luminescence is suppressed when the carrier distributions undergo a population inversion. The theory is consistent with some well-known luminescence phenomena, such as the blue shifting of donor-acceptor pair transitions with increased injection, and its predictions are experimentally verified on CdTe and GaN, which are exemplar thin-film solar cell and light emitting diode materials respectively. Furthermore, the discussion is broadened to include pulsed illumination in time resolved CL, where the carrier distribution is dynamically evolving with time.

The κ-deformed boson algebra and parafermion algebra

In this paper we consider κ-deformed boson algebra [a,a†]=1+2κN. We discuss the κ-deformed quantum harmonic oscillator problem. We also apply this algebra to the photon and phonon to formulate the κ-deformed Planck radiation law and κ-deformed Debye model and compare our results with undeformed ones. Finally, we discuss the case of κ=−1/p which gives the parafermion model.

Biparametric complexities and generalized Planck radiation law

Complexity theory embodies some of the hardest, most fundamental and most challenging open problems in modern science. The very term complexity is very elusive, so the main goal of this theory is to find meaningful quantifiers for it. In fact, we need various measures to take into account the multiple facets of this term. Here, some biparametric Crámer–Rao and Heisenberg–Rényi measures of complexity of continuous probability distributions are defined and discussed. Then, they are applied to blackbody radiation at temperature T in a d-dimensional universe. It is found that these dimensionless quantities do not depend on T nor on any physical constants. So, they have a universal character in the sense that they only depend on spatial dimensionality. To determine these complexity quantifiers, we have calculated their dispersion (typical deviations) and entropy (Rényi entropies and the generalized Fisher information) constituents. They are found to have a temperature-dependent behavior similar to the celebrated Wien’s displacement law of the dominant frequency at which the spectrum reaches its maximum. Moreover, they allow us to gain insights into new aspects of the d-dimensional blackbody spectrum and the quantification of quantum effects associated with space dimensionality.

Evaluation of blackbody radiation emitted by arbitrarily shaped bodies using the source model technique.

Planck's famous blackbody radiation law was derived under the assumption that the dimensions of the radiating body are significantly larger than the radiated wavelengths. What is unique about Planck's formula is the fact that it is independent of the exact loss mechanism and the geometry. Therefore, for a long period of time, it was regarded as a fundamental property of all materials. Deviations from its predictions were attributed to imperfections and referred to as the emissivity of the specific body, a quantity which was always assumed to be smaller than unity. Recent studies showed that the emission spectrum is affected by the geometry of the body and in fact, in a limited frequency range, the emitted spectrum may exceed Planck's prediction provided the typical size of the body is of the same order of magnitude as the emitted wavelength. For the investigation of the blackbody radiation from an arbitrarily shaped body, we developed a code which incorporates the fluctuation-dissipation theorem (FDT) and the source model technique (SMT). The former determines the correlation between the quasi-microscopic current densities in the body and the latter is used to solve the electromagnetic problem numerically. In this study we present the essence of combining the two concepts. We verify the validity of our code by comparing its results obtained for the case of a sphere against analytic results and discuss how the accuracy of the solution is assessed in the general case. Finally, we illustrate several configurations in which the emitted spectrum exceeds Planck's prediction as well as cases in which the geometrical resonances of the body are revealed.

Thermodynamic properties of the blackbody radiation: A Kaniadakis approach

The thermodynamic properties of the blackbody radiation are revisited, for the first time, within the theoretical framework of the κ-statistics introduced by Kaniadakis. Using the κ-counterpart of the Bose–Einstein distribution, generalized expressions for the free energy, the entropy, the specific heat, and the pressure are obtained. All quantities are shown to recover their standard expressions in the limit κ→0. The reexamination of the thermodynamic properties of the blackbody radiation shows that it emits more energy with an increase of the value of |κ| in comparison with the standard Planck radiation law. Moreover, the effects of the deformed Kaniadakis statistics are shown to be more appreciable for high temperatures. Our results could be used as a theoretical support for experimental studies implying blackbody radiation such as the study of microwave background radiation.

Room temperature direct-bandgap electroluminescence from a horizontal Ge ridge waveguide on Si**Project supported by the National Basic Research Program of China (Grant No. 2013CB632103), the National Natural Science Foundation of China (Grant Nos. 61176013 and 61036003), and the Science Fund from Beijing Science and Technology Commission, China (Grant No. Z151100003315019).

We report a lateral Ge-on-Si ridge waveguide light emitting diode (LED) grown by ultrahigh vacuum chemical vapor deposition (UHV-CVD). Direct-bandgap electroluminescence (EL) of Ge waveguide under continuous current is observed at room temperature. The heat-enhancing luminescence and thermal radiation-induced superlinear increase of edge output optical power are found. The spontaneous emission and thermal radiation based on the generalized Planck radiation law are calculated and fit very well to the experimental results. The Ge waveguides with different lengths are studied and the shorter one shows stronger EL intensity.