Introduction to linear and nonlinear programming

Ecological data are often lognormally distributed. Nutrient concentrations, population densities and biomasses, rates of production and other flows are always positive, and generally have standard deviations that increase as the mean increases. Lognormally distributed variables have these characteristics, whereas normally distributed variables can be negative and have a standard deviation that does not change as the mean changes. Lognormal errors arise when sources of variation accumulate multiplicatively, whereas normal errors arise when sources of variation are additive. Given a normally distributed random variable Y, one can calculate a lognormally distributed random variable Z = exp(Y) where exp stands for the exponential function (exp(x) = e x). The mean Z and the standard deviation s Z of the lognormal variable are related to the mean Y and standard deviation s Y of the normal variable by) 2 / exp() exp(2 Y s Y Z = [1] 5. 0 2 ] 1) [exp(− = Y Z s Z s [2] Equation 1 can be used to correct for transformation bias in logarithmic regression. Suppose that lognormally-distributed observations Z have been log transformed as Y = log(Z) to fit a regression model such as ε + =) , (ˆ b X f Y [3] where Y is the log-transformed response variable which is predicted to be Y ˆ computed from the function f, X is a matrix of predictors, b is a vector of parameters, and the errors ε are normally distributed with mean zero and standard deviation s ε. Predictions Z ˆ in the original units are calculated using equation 1 as ] 2) ˆ exp[(ˆ 2 ε s Y Z + = [4] Note that estimates the median prediction of Z, which will be smaller than the mean for a lognormally distributed variate. Thus it makes sense to adjust the median upward, as in equation 4.) ˆ exp(Y Equation 1 is also used in drawing random numbers from a lognormal distribution. Generators for normally-distributed random variables Y are common. Suppose we draw many values of Y with mean zero and standard deviation s Y. Then from equation 1, the mean of exp(Y) will not be 1 = e 0 ; instead the mean of exp(Y) will be. Generally, however, one would prefer to have the mean of a set of lognormally distributed random numbers be 1. This can be accomplished by shifting the random numbers to Y) 2 / exp(2 Y …

対数正規分布(Lognormal Distribution)のあてはめについて

Confocal microscopes unlike their conventional counterparts have the ability to optically ‘section’ thick specimens. However the resolution and optical sectioning can be severely degraded by system or specimen-induced aberrations. The use of high aperture lenses further exacerbates the difficulties. We will describe an adaptive optics solution to this fundamental problem.

Adaptive optics in microscopy

Monolayer transition metal dichalcogenides are considered to be promising candidates for flexible and transparent optoelectronics applications due to their direct bandgap and strong light-matter interactions. Although several monolayer-based photodetectors have been demonstrated, single-layered optical memory devices suitable for high-quality image sensing have received little attention. Here we report a concept for monolayer MoS2 optoelectronic memory devices using artificially-structured charge trap layers through the functionalization of the monolayer/dielectric interfaces, leading to localized electronic states that serve as a basis for electrically-induced charge trapping and optically-mediated charge release. Our devices exhibit excellent photo-responsive memory characteristics with a large linear dynamic range of ∼4,700 (73.4 dB) coupled with a low OFF-state current (<4 pA), and a long storage lifetime of over 104 s. In addition, the multi-level detection of up to 8 optical states is successfully demonstrated. These results represent a significant step toward the development of future monolayer optoelectronic memory devices. Memory devices are key building blocks of image sensing circuitry. Here, the authors demonstrate a MoS2monolayer optoelectronic memory device based on charge trapping and subsequent optically-induced charge release, capable of 12-bit operation.

/pdf/monolayer-optical-memory-cells-based-on-artificial-trap-1g3yqbuhzf.pdf

Monolayer optical memory cells based on artificial trap-mediated charge storage and release.

Lacking rich and realistic data, learned single image denoising algorithms generalize poorly in real raw images that not resemble the data used for training. Although the problem can be alleviated by the heteroscedastic Gaussian noise model, the noise sources caused by digital camera electronics are still largely overlooked, despite their significant effect on raw measurement, especially under extremely low-light condition. To address this issue, we present a highly accurate noise formation model based on the characteristics of CMOS photosensors, thereby enabling us to synthesize realistic samples that better match the physics of image formation process. Given the proposed noise model, we additionally propose a method to calibrate the noise parameters for available modern digital cameras, which is simple and reproducible for any new device. We systematically study the generalizability of a neural network trained with existing schemes, by introducing a new low-light denoising dataset that covers many modern digital cameras from diverse brands. Extensive empirical results collectively show that by utilizing our proposed noise formation model, a network can reach the capability as if it had been trained with rich real data, which demonstrates the effectiveness of our noise formation model.

/pdf/a-physics-based-noise-formation-model-for-extreme-low-light-3grd8oop5f.pdf

A Physics-Based Noise Formation Model for Extreme Low-Light Raw Denoising

In many applications, such as development and testing of image processing algorithms, it is often necessary to simulate images containing realistic noise from solid-state photosensors. A high-level model of CCD and CMOS photosensors based on a literature review is formulated in this paper. The model includes photo-response non-uniformity, photon shot noise, dark current Fixed Pattern Noise, dark current shot noise, offset Fixed Pattern Noise, source follower noise, sense node reset noise, and quantisation noise. The model also includes voltage-to-voltage, voltage-to-electrons, and analogue-to-digital converter non-linearities. The formulated model can be used to create synthetic images for testing and validation of image processing algorithms in the presence of realistic images noise. An example of the simulated CMOS photosensor and a comparison with a custom-made CMOS hardware sensor is presented. Procedures for characterisation from both light and dark noises are described. Experimental results that confirm the validity of the numerical model are provided. The paper addresses the issue of the lack of comprehensive high-level photosensor models that enable engineers to simulate realistic effects of noise on the images obtained from solid-state photosensors.

High-level numerical simulations of noise in CCD and CMOS photosensors: review and tutorial.

Diffraction image correlator based on commercial digital SLR photo camera was reported earlier. The correlator was
proposed for recognition of external scenes illuminated by quasimonochromatic spatially incoherent light. The
correlator hardware consists of digital camera with plugged in optical correlation filter unit and control computer. The
kinoform used as correlation filter is placed in a free space of the SLR camera body between the interchangeable camera
lens and the swing mirror. On the other hand, this correlator can be considered as a hybrid optical-digital imaging
system with wavefront coding. It allows not only to recognize objects in input scene but to restore, if needed, the whole
image of input scene from correlation signals distribution registered by SLR camera sensor. Linear methods for image
reconstruction in the correlator are discussed. The experimental setup of the correlator and experimental results on
images recognition and input scenes restoration are presented.

Input scene restoration in pattern recognition correlator based on digital photo camera

Performance capabilities of commercial digital cameras are demonstrated by the example of a Canon EOS 400D camera in measuring and detecting spatial distributions of laser radiation intensity. It is shown that software extraction of linear data expands the linear dynamic range of the camera by a factor greater than 10, up to 58 dB. Basic measurement characteristics of the camera are obtained in the regime of linear data extraction: the radiometric function, deviation from linearity, dynamic range, temporal and spatial noises (both dark and those depending on the signal value). The parameters obtained correspond to those of technical measuring cameras.

http://iopscience.iop.org/article/10.1070/QE2010v040n04ABEH014202/pdf

Extension of the possibilities of a commercial digital camera in detecting spatial intensity distribution of laser radiation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Publications and Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Acronyms and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Online constrained receding horizon control for astronomical adaptive optics

Wavefront sensors, which use solid-state CCD or CMOS photosensors, are sources of errors in adaptive optic
systems. Inaccuracy in the detection of wavefront distortions introduces considerable errors into wavefront reconstruction
and leads to overall performance degradation of the adaptive optics system. The accuracy of wavefront
sensors is significantly affected by photosensor noise. Thus, it is crucial to formulate high-level photosensor models
that enable adaptive optic engineers to simulate realistic effects of noise from wavefront sensors. However,
the complexity of solid-state photosensors and multiple noise sources makes it difficult to formulate an adequate
model of the photosensor. Moreover, the characterisation of the simulated sensor and comparison with real
hardware is often incomplete due to lack of comprehensive standards and guidelines. Owe to these difficulties,
engineers work with oversimplified models of the wavefront sensors and consequently have imprecise numerical
simulation results.
The paper presents an approach for the modelling of noise sources for CCD and CMOS sensors that are used for
wavefront sensing in adaptive optics. Both dark and light noise such as fixed pattern noise, photon shot noise,
and read noises, as well as, charge-to-voltage noises are described. Procedures for characterisation of both light
and dark noises of the simulated photosensors are provided. Numerical simulation results of a photosensor for a
high-frame rate Shack-Hartmann wavefront sensor are presented.

/pdf/on-numerical-simulation-of-high-speed-ccd-cmos-based-2hcv13uzua.pdf

Mikhail V. Konnik

Papers

High-level numerical simulations of noise in CCD and CMOS photosensors: review and tutorial.

Input scene restoration in pattern recognition correlator based on digital photo camera

Extension of the possibilities of a commercial digital camera in detecting spatial intensity distribution of laser radiation

Online constrained receding horizon control for astronomical adaptive optics

On numerical simulation of high-speed CCD/CMOS-based wavefront sensors in adaptive optics