Key Concepts

Truth Values: The evaluation of statements about remote sensing data and models, estimating their reliability or likelihood.

Sensors: Devices that transform energy from one domain to another for data collection. Remote sensing sensors are often transducers.

Photons and Electrons: Fundamental particles relevant to physical interactions in remote sensing.

Imaging Sensors: Sensors, often based on arrays of cells, that convert photons into electronic signals.

Quantum Efficiency: The probability of a photon transforming into an electron in a sensor cell.

Thermal Infrared Sensors: Sensors that detect thermal radiation but face challenges distinguishing between photons and electrons generated within the sensor. Cooling is often required.

Bolometers: Cheaper sensors based on heating due to radiation, measuring temperature change.

Microwave Sensors: Sensors that measure the electrical field of microwaves, often employing electromagnetic resonators to increase the amplitude of the signal.

Resonator: A system that amplifies a signal at its natural frequency, analogous to a swing.

Electromagnetic (E.M.) Radiation: The form of energy detected by many remote sensing sensors. Understanding static or potential energy and dynamic or movement energy is important for evaluating statements about E.M. radiation.

Potential Energy: Energy stored by position or state, proportional to height in a mechanical system or to the electrical field E in electromagnetism.

Kinetic Energy: Energy of motion, proportional to the square of velocity in a mechanical system or to the square of current I in electromagnetism.

Conservation of Energy: In a closed system without energy loss, the sum of potential and kinetic energy remains constant.

The E.M. Swing: An analogy to a mechanical swing, representing the harmonic flow of energy between maximum voltage (potential energy) and maximum current (kinetic energy) in an electrical circuit with capacitance and inductance.

Man-made Resonators: Devices designed to resonate at specific frequencies, including acoustic (guitar strings, tuning forks) and microwave (dipole antennas, resonance cavities). MASERS and LASERS are examples of optical/quantum resonators based on molecular resonances.

Properties of Photons (and Microwave) Waves: The effects of the electrical field (E) are often stronger than the magnetic field (M). The M field can be derived from the changing E field. The E field has a polarisation angle. The E field vector has components.

Frequency and Wavelength: Frequency is the inverse of the time period required for the E(x,t) pattern to reproduce itself. Wavelength depends on the medium. The speed of propagation in a vacuum is constant.

Spectroscopic Data: Horizontal scales of spectroscopic data often use "units" related to 2π times the frequency or 2π divided by the wavelength.

Output of Electro-Optical Devices: An estimation of the number of photons "captured" per sensor cell during an exposure time.

Photon Stream or Photon Flux: The number of photons falling on/into a sensor element.Potential Energy of Electrons in a capacitor : Vc = Q/C, where Q is the total charge and C is the capacitance. Voltage Vc is an analog value. The number of electrons is derived from Q = Vc x C as charge Q is the number of electrons x charge of 1 electron.

Analog to Digital Conversion (ADC): Converting analog voltage values into digital data. RGB cameras usually have 8 bit adc’s per channel. Spectrometers may have 16 bit adc’s .

Numerical Output (N_e): Represents steps of change in Vc, relating to the quantum efficiency and the number of photons.

Truth Interpretation: Establishing an explicit model linking the numerical output of the ADC to the number of photons allows evaluation of the truth value of interpretations or sensor models. The likelihood of true measurement is reduced by systematic and random errors and the use of false sensor models.

Photon Sorting/Filtering: Achieved using selective resonance absorption filters (e.g., RGB, IR cameras) or interference filters based on making resonance paths (layers) that pass a small range of wavelengths or frequencies.

Measurement: The interaction between two objects in space-time that produces data about that interaction.

Information: A relationship between possible questions and answers. Useful information specifies the data and the interaction models used to obtain the data. Information is a statistical relationship ( likelihood).

Truth-of-Answer: Prob(question, data|model), meaning the probability of the question given the data and model. The probability model for photon counts must be asymmetric with arrival time (e.g., Poisson distribution). Otherwise, the information extraction method is FALSE.

Knowledge: Based on hypotheses and measured evidence.

Know(hypothesis(i), evidence(j)) = prob(hypothesis(i) given evidence(j)).

Knowledge from Photon Sensors: Derived from controlled experiments, hypotheses about object characteristics (radiometric properties, 2D/3D patterns) are evaluated based on coincidence statistics of the evidence given hypothesis( label,class, parameters) . Hypotheses should preferably be formulated as prediction models.

Truth Value of Classification: The probability of TRUE/false is reported by the frequencies of correct and misidentified data samples for discrete classes. This assumes the experimenter has determined the frequency of evidence for each class.

Relationship Probabilities: Prob(E_i | C_j) is estimated from controlled, supervised measurements. This knowledge should be independent of sample size. Prob(C_j | E_i) can be calculated using frequencies (histograms, counts over intervals).

Likelihood Vector or Likelihood Array: for each evidence datum the likelihood for all current hypotheses is calculated.

Maximum Likelihood: Mapping to maximum likelihood by selecting the maximum of each likelihood array per datum, produces a binary approximation of probabilistic truth to pseudo-truth.

Coincidence (confusion) Matrix: A table showing the counts or frequencies of co-occurrences between likely or predicted classes and actual or true classes over all data in a region of interest . This matrix is relevant for decision making.

Basic Physics and Mathematics

• Everyday physics is based on interactions of atoms and molecules via electrons and photons.
• In medical applications, protons, electrons, and photons are relevant.
• Basic requirements for remote sensing are evaluating truth and reliability of statements about sensors, data, classification, predictions, and models.

Sensor Mechanisms

• Imaging Sensors: Convert photons to electrons. Quantum efficiency is crucial.
• Thermal Infrared Sensors: It is challenging to distinguish photon-generated electrons from those generated in the sensor. Cooling helps. Bolometers are an alternative.

Microwave Sensors: Use the electrical field of wavelets (photons) to generate voltages in antenna type detectors, often with resonators to increase the signal.

Energy Concepts

• Potential and kinetic energy are important for evaluating statements about E.M. radiation.
• Conservation of energy is a fundamental principle.
• The E.M. swing analogy illustrates energy flow in electrical circuits.

Relevant energy units are Joule per integration time. Electron volt (Ev) is used for the energy per photon.

Wave Properties

• Frequency, wavelength, polarisation, and electric field components are key properties of E.M. waves.
• Spectroscopic data analysis relies on understanding these properties.

Data Acquisition and Conversion

• The output of electro-optical devices estimates photon counts.
• Photon flux determines the charge accumulated in a sensor element.
• Analog voltage from accumulated charge is converted to digital data via an ADC.
• Understanding the relationship between digital output and photon count is crucial for evaluating truth.

Information and Knowledge

• Information is a statistical relationship derived from measurements and models.
• The probability model for photon counts affects the validity of information extraction.
• Knowledge is built upon hypotheses and evidence, evaluated through probability.
• Truth values for classification are assessed using statistical analysis of classification accuracy, often represented in a confusion matrix.